diff --git a/amc-templates/amc_template/exam.amc b/amc-templates/amc_template/exam.amc
index c088273..4501875 100644
--- a/amc-templates/amc_template/exam.amc
+++ b/amc-templates/amc_template/exam.amc
@@ -1,106 +1,126 @@
 AUTOQCM[TOTAL=1]
 
 AUTOQCM[NUM=1=q:mc-03]
 
 AUTOQCM[FQ]
 
 AUTOQCM[NUM=2=q:mc-02]
 
 AUTOQCM[FQ]
 
 AUTOQCM[NUM=3=q:mc-01]
 
 AUTOQCM[FQ]
 
 AUTOQCM[NUM=4=q:tf-02]
 
 AUTOQCM[FQ]
 
 AUTOQCM[NUM=5=q:tf-01]
 
 AUTOQCM[FQ]
 
 AUTOQCM[NUM=6=q-open-A]
 
 AUTOQCM[FQ]
 
-AUTOQCM[NUM=7=q-open-B]
+AUTOQCM[NUM=7=q-open-A1]
 
 AUTOQCM[FQ]
 
-AUTOQCM[NUM=8=q-open-C]
+AUTOQCM[NUM=8=q-open-A2]
 
 AUTOQCM[FQ]
 
-AUTOQCM[NUM=9=q-open-D]
+AUTOQCM[NUM=9=q-open-B]
+
+AUTOQCM[FQ]
+
+AUTOQCM[NUM=10=q-open-C]
+
+AUTOQCM[FQ]
+
+AUTOQCM[NUM=11=q-open-D]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[TOTAL=1]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
+AUTOQCM[FQ]
+
+AUTOQCM[FQ]
+
 AUTOQCM[TOTAL=1]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
+AUTOQCM[FQ]
+
+AUTOQCM[FQ]
+
 AUTOQCM[TOTAL=1]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
 AUTOQCM[FQ]
 
+AUTOQCM[FQ]
+
+AUTOQCM[FQ]
+
diff --git a/amc-templates/amc_template/exam.log b/amc-templates/amc_template/exam.log
index ffc1b0e..14a87b3 100644
--- a/amc-templates/amc_template/exam.log
+++ b/amc-templates/amc_template/exam.log
@@ -1,1920 +1,2001 @@
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+This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2020.7.3)  21 DEC 2020 17:21
 entering extended mode
  restricted \write18 enabled.
  %&-line parsing enabled.
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 )
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 )
 Now handling font encoding OMS ...
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 File: omsenc.dfu 2017/01/28 v1.1t UTF-8 support for inputenc
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 )
 Now handling font encoding OMX ...
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 ))
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+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.7 \renewcommand{\AMCbeginQuestion}
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+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: No counter 'AMCquestionaff' defined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.12 \addtocounter{AMCquestionaff}{1}
+                                     
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
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+
+! LaTeX Error: Missing \begin{document}.
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+See the LaTeX manual or LaTeX Companion for explanation.
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+ ...                                              
+                                                  
+l.15 \subsection*
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+See the LaTeX manual or LaTeX Companion for explanation.
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+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no g in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no L in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no : in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (8.88889pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se^^Se
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^e
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (5.00002pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Ra
+ []
+
+
+Overfull \hbox (8.88889pt too wide) in paragraph at lines 17--20
+\/cmr/m/n/10 ^^Se^^Se
+ []
+
+
+! LaTeX Error: Environment description undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.30 \begin{description}
+                        
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: No counter 'AMCquestionaff' defined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.31 \addtocounter{AMCquestionaff}{1}
+                                     
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Lonely \item--perhaps a missing list environment.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.32 \item[Question~\theAMCquestionaff :]
+                                          \textit{Cette question est not\'ee...
+
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: \begin{document} ended by \end{description}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.33 \end{description}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+! Undefined control sequence.
+l.34 \correctorPointsPerGroup
+                             {5/3}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 5 in font nullfont!
+Missing character: There is no / in font nullfont!
+Missing character: There is no 3 in font nullfont!
+! Undefined control sequence.
+l.35 \correctorOneFive
+                      {q-open-A}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no A in font nullfont!
+! Undefined control sequence.
+l.36 \correctorTwoFive
+                      {q-open-A1}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no A in font nullfont!
+Missing character: There is no 1 in font nullfont!
+! Undefined control sequence.
+l.37 \correctorThreeFive
+                        {q-open-A2}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no A in font nullfont!
+Missing character: There is no 2 in font nullfont!
+! Undefined control sequence.
+l.38 \correctorStop
+                   
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (22.9998pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 Cette
+ []
+
+
+Overfull \hbox (22.23317pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 ques-
+ []
+
+
+Overfull \hbox (17.12212pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 tion
+ []
+
+
+Overfull \hbox (12.01102pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 est
+ []
+
+
+Overfull \hbox (23.25539pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 not^^See
+ []
+
+
+Overfull \hbox (13.67213pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 sur
+ []
+
+
+Overfull \hbox (5.11108pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 5
+ []
+
+
+Overfull \hbox (28.8776pt too wide) in paragraph at lines 32--39
+\OT1/cmr/m/it/10 points.
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.40 S
+      oit $\Psi : \R_3[x]\to \R_3[x]$ l'application d\'efinie par
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <7> on input line 40.
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <5> on input line 40.
+! Undefined control sequence.
+l.40 Soit $\Psi : \R
+                    _3[x]\to \R_3[x]$ l'application d\'efinie par
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+l.40 Soit $\Psi : \R_3[x]\to \R
+                               _3[x]$ l'application d\'efinie par
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no l in font nullfont!
+Missing character: There is no ' in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+
+Overfull \hbox (17.81943pt too wide) in paragraph at lines 40--41
+\/cmr/m/n/10 	 :[]
+ []
+
+
+Overfull \hbox (28.5347pt too wide) in paragraph at lines 40--41
+\/cmr/m/n/10 [\OML/cmm/m/it/10 x\/cmr/m/n/10 ] \OMS/cmsy/m/n/10 ![]
+ []
+
+
+Overfull \hbox (11.27084pt too wide) in paragraph at lines 40--41
+\/cmr/m/n/10 [\OML/cmm/m/it/10 x\/cmr/m/n/10 ]$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 40--41
+\/cmr/m/n/10 ^^Se
+ []
+
+! Undefined control sequence.
+l.41 $$\Psi(p)(x) = (x-1)p'(x)\text
+                                   {.}$$
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (97.7917pt too wide) detected at line 41
+\/cmr/m/n/10 	(\OML/cmm/m/it/10 p\/cmr/m/n/10 )(\OML/cmm/m/it/10 x\/cmr/m/n/10 
+) = (\OML/cmm/m/it/10 x \OMS/cmsy/m/n/10 ^^@ \/cmr/m/n/10 1)\OML/cmm/m/it/10 p[
+]\/cmr/m/n/10 (\OML/cmm/m/it/10 x\/cmr/m/n/10 )\OML/cmm/m/it/10 :
+ []
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.43 \begin{itemize}
+                    
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no M in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ) in font nullfont!
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 44--45
+\/cmr/m/n/10 	$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 44--45
+\/cmr/m/n/10 ^^Se 
+ []
+
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no ) in font nullfont!
+
+Overfull \hbox (28.71951pt too wide) in paragraph at lines 45--46
+\/cmr/m/n/10 [	][]$
+ []
+
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 45--46
+\/cmr/m/n/10 	$
+ []
+
+
+Overfull \hbox (5.00002pt too wide) in paragraph at lines 45--46
+\/cmr/m/n/10 ^^Ra
+ []
+
+
+Overfull \hbox (18.51382pt too wide) in paragraph at lines 45--46
+\OML/cmm/m/it/10 E \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (52.22913pt too wide) in paragraph at lines 45--46
+\/cmr/m/n/10 (1\OML/cmm/m/it/10 ; x; x[]; x[]\/cmr/m/n/10 )$ 
+ []
+
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no g in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no ( in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no ) in font nullfont!
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 46--47
+\/cmr/m/n/10 	$
+ []
+
+! Undefined control sequence.
+l.49 \OpenGrid
+              {16cm}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 6 in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no m in font nullfont!
+! Undefined control sequence.
+l.50 \FullPageOpenGrid
+                      
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+! LaTeX Error: Environment description undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.57 \begin{description}
+                        
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Lonely \item--perhaps a missing list environment.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.58 \item[Question~\theAMCquestionaff :]
+                                          \textit{Cette question est not\'ee...
+
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: \begin{document} ended by \end{description}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.59 \end{description}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+! Undefined control sequence.
+l.60 \correctorPointsPerGroup
+                             {6/2}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 6 in font nullfont!
+Missing character: There is no / in font nullfont!
+Missing character: There is no 2 in font nullfont!
+! Undefined control sequence.
+l.61 \correctorTwoFive
+                      {q-open-B}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no B in font nullfont!
+! Undefined control sequence.
+l.62 \correctorStop
+                   
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (22.9998pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 Cette
+ []
+
+
+Overfull \hbox (22.23317pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 ques-
+ []
+
+
+Overfull \hbox (17.12212pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 tion
+ []
+
+
+Overfull \hbox (12.01102pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 est
+ []
+
+
+Overfull \hbox (23.25539pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 not^^See
+ []
+
+
+Overfull \hbox (13.67213pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 sur
+ []
+
+
+Overfull \hbox (5.11108pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 6
+ []
+
+
+Overfull \hbox (28.8776pt too wide) in paragraph at lines 58--63
+\OT1/cmr/m/it/10 points.
+ []
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no e in font nullfont!
+! Undefined control sequence.
+<recently read> \operatorname 
+                              
+l.65 tels que $\operatorname
+                            {dim}(X) \geq \operatorname{dim}(Y)$. Montrer qu...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+l.65 ... $\operatorname{dim}(X) \geq \operatorname
+                                                  {dim}(Y)$. Montrer qu'il e...
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no . in font nullfont!
+Missing character: There is no M in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no ' in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no q in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (8.05556pt too wide) in paragraph at lines 64--66
+ $\OML/cmm/m/it/10 V$
+ []
+
+
+Overfull \hbox (9.20833pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 K$
+ []
+
+
+Overfull \hbox (20.98607pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 X; Y$
+ []
+
+
+Overfull \hbox (8.05556pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 V$
+ []
+
+
+Overfull \hbox (44.83287pt too wide) in paragraph at lines 64--66
+[]\/cmr/m/n/10 (\OML/cmm/m/it/10 X\/cmr/m/n/10 ) \OMS/cmsy/m/n/10 ^^U
+ []
+
+
+Overfull \hbox (33.23572pt too wide) in paragraph at lines 64--66
+[]\/cmr/m/n/10 (\OML/cmm/m/it/10 Y\/cmr/m/n/10 )$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 64--66
+\/cmr/m/n/10 ^^Se
+ []
+
+
+Overfull \hbox (12.78815pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 T \/cmr/m/n/10 :
+ []
+
+
+Overfull \hbox (20.83328pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 V \OMS/cmsy/m/n/10 !
+ []
+
+
+Overfull \hbox (8.05556pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 V$
+ []
+
+
+Overfull \hbox (34.63539pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 T\/cmr/m/n/10 (\OML/cmm/m/it/10 X\/cmr/m/n/10 ) =
+ []
+
+
+Overfull \hbox (8.02779pt too wide) in paragraph at lines 64--66
+\OML/cmm/m/it/10 Y$ 
+ []
+
+! Undefined control sequence.
+l.68 \OpenBox
+             {22cm}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no m in font nullfont!
+
+! LaTeX Error: Environment description undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.73 \begin{description}
+                        
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Lonely \item--perhaps a missing list environment.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.74 \item[Question~\theAMCquestionaff :]
+                                          \textit{Cette question est not\'ee...
+
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: \begin{document} ended by \end{description}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.75 \end{description}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+! Undefined control sequence.
+l.76 \correctorSix
+                  {q-open-C}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no C in font nullfont!
+! Undefined control sequence.
+l.77 \correctorStop
+                   
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (22.9998pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 Cette
+ []
+
+
+Overfull \hbox (22.23317pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 ques-
+ []
+
+
+Overfull \hbox (17.12212pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 tion
+ []
+
+
+Overfull \hbox (12.01102pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 est
+ []
+
+
+Overfull \hbox (23.25539pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 not^^See
+ []
+
+
+Overfull \hbox (13.67213pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 sur
+ []
+
+
+Overfull \hbox (5.11108pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 6
+ []
+
+
+Overfull \hbox (28.8776pt too wide) in paragraph at lines 74--78
+\OT1/cmr/m/it/10 points.
+ []
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+! Undefined control sequence.
+l.79 Soit $\alpha\in \C
+                       $.
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (15.87843pt too wide) in paragraph at lines 79--80
+\OML/cmm/m/it/10  \OMS/cmsy/m/n/10 2$ 
+ []
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no T in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+! Misplaced alignment tab character &.
+l.82 ... la matrice $A_n = \begin{pmatrix}\alpha &
+                                                  1\\ 0 &\alpha\end{pmatrix}...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.82 ...rice $A_n = \begin{pmatrix}\alpha &1\\ 0 &
+                                                  \alpha\end{pmatrix}^{n}$, ...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no , in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no M in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.49886pt too wide) in paragraph at lines 82--84
+\OML/cmm/m/it/10 A[] \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (24.21173pt too wide) in paragraph at lines 82--84
+[] \/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (16.87738pt too wide) in paragraph at lines 82--84
+\/cmr/m/n/10 0\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (5.55557pt too wide) in paragraph at lines 82--84
+\/cmr/m/n/10 ^^Ru
+ []
+
+
+Overfull \hbox (16.55786pt too wide) in paragraph at lines 82--84
+\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^U
+ []
+
+
+Overfull \hbox (5.00002pt too wide) in paragraph at lines 82--84
+\/cmr/m/n/10 1$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 82--84
+\/cmr/m/n/10 ^^Se 
+ []
+
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no O in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (16.98955pt too wide) in paragraph at lines 84--85
+\OML/cmm/m/it/10  \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (12.77782pt too wide) in paragraph at lines 84--85
+\/cmr/m/n/10 1 +
+ []
+
+
+Overfull \hbox (2.77779pt too wide) in paragraph at lines 84--85
+[]$
+ []
+
+
+Overfull \hbox (14.9063pt too wide) in paragraph at lines 84--85
+\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (18.89243pt too wide) in paragraph at lines 84--85
+\OML/cmm/m/it/10 []$ 
+ []
+
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+! Misplaced alignment tab character &.
+l.85 ...] Calculer $\begin{pmatrix} 1+\textrm{i} &
+                                                  1\\ 0 &1+\textrm{i}\end{pm...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.85 ...ler $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &
+                                                  1+\textrm{i}\end{pmatrix}^...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.88887pt too wide) in paragraph at lines 85--86
+[] \/cmr/m/n/10 +
+ []
+
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 85--86
+[]\/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (17.77783pt too wide) in paragraph at lines 85--86
+\/cmr/m/n/10 01 +
+ []
+
+
+Overfull \hbox (15.23618pt too wide) in paragraph at lines 85--86
+[][]$ 
+ []
+
+! Undefined control sequence.
+l.89 \OpenGrid
+              {17cm}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 7 in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no m in font nullfont!
+
+! LaTeX Error: Environment description undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.93 \begin{description}
+                        
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Lonely \item--perhaps a missing list environment.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.94 \item[Question~\theAMCquestionaff :]
+                                          \textit{Cette question est not\'ee...
+
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: \begin{document} ended by \end{description}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.95 \end{description}
+                      
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+! Undefined control sequence.
+l.96 \correctorTenHalf
+                      {q-open-D}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no D in font nullfont!
+! Undefined control sequence.
+l.97 \correctorStop
+                   
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (22.9998pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 Cette
+ []
+
+
+Overfull \hbox (22.23317pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 ques-
+ []
+
+
+Overfull \hbox (17.12212pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 tion
+ []
+
+
+Overfull \hbox (12.01102pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 est
+ []
+
+
+Overfull \hbox (23.25539pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 not^^See
+ []
+
+
+Overfull \hbox (13.67213pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 sur
+ []
+
+
+Overfull \hbox (10.22217pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 10
+ []
+
+
+Overfull \hbox (28.8776pt too wide) in paragraph at lines 94--98
+\OT1/cmr/m/it/10 points.
+ []
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+! Undefined control sequence.
+l.99 Soit $\alpha\in \C
+                       $.
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (15.87843pt too wide) in paragraph at lines 99--100
+\OML/cmm/m/it/10  \OMS/cmsy/m/n/10 2$ 
+ []
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no T in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+! Misplaced alignment tab character &.
+l.102 ...la matrice $A_n = \begin{pmatrix}\alpha &
+                                                  1\\ 0 &\alpha\end{pmatrix}...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.102 ...ice $A_n = \begin{pmatrix}\alpha &1\\ 0 &
+                                                  \alpha\end{pmatrix}^{n}$, ...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no , in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no M in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.49886pt too wide) in paragraph at lines 102--104
+\OML/cmm/m/it/10 A[] \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (24.21173pt too wide) in paragraph at lines 102--104
+[] \/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (16.87738pt too wide) in paragraph at lines 102--104
+\/cmr/m/n/10 0\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (5.55557pt too wide) in paragraph at lines 102--104
+\/cmr/m/n/10 ^^Ru
+ []
+
+
+Overfull \hbox (16.55786pt too wide) in paragraph at lines 102--104
+\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^U
+ []
+
+
+Overfull \hbox (5.00002pt too wide) in paragraph at lines 102--104
+\/cmr/m/n/10 1$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 102--104
+\/cmr/m/n/10 ^^Se 
+ []
+
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no O in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (16.98955pt too wide) in paragraph at lines 104--105
+\OML/cmm/m/it/10  \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (12.77782pt too wide) in paragraph at lines 104--105
+\/cmr/m/n/10 1 +
+ []
+
+
+Overfull \hbox (2.77779pt too wide) in paragraph at lines 104--105
+[]$
+ []
+
+
+Overfull \hbox (14.9063pt too wide) in paragraph at lines 104--105
+\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (18.89243pt too wide) in paragraph at lines 104--105
+\OML/cmm/m/it/10 []$ 
+ []
+
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+! Misplaced alignment tab character &.
+l.105 ... Calculer $\begin{pmatrix} 1+\textrm{i} &
+                                                  1\\ 0 &1+\textrm{i}\end{pm...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.105 ...er $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &
+                                                  1+\textrm{i}\end{pmatrix}^...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.88887pt too wide) in paragraph at lines 105--106
+[] \/cmr/m/n/10 +
+ []
+
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 105--106
+[]\/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (17.77783pt too wide) in paragraph at lines 105--106
+\/cmr/m/n/10 01 +
+ []
+
+
+Overfull \hbox (15.23618pt too wide) in paragraph at lines 105--106
+[][]$ 
+ []
+
+! Undefined control sequence.
+l.109 \OpenGrid
+               {17cm}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 7 in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no m in font nullfont!
+! Undefined control sequence.
+l.110 \FullPageOpenGrid
+                       
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+! LaTeX Error: Environment description undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.114 \begin{description}
+                         
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+
+! LaTeX Error: Lonely \item--perhaps a missing list environment.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.115 \item[Question~\theAMCquestionaff :]
+                                           \textit{Cette question est not\'e...
+
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+
+! LaTeX Error: \begin{document} ended by \end{description}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.116 \end{description}
+                       
+Your command was ignored.
+Type  I <command> <return>  to replace it with another command,
+or  <return>  to continue without it.
+
+! Undefined control sequence.
+l.117 \correctorTwenty
+                      {q-open-C}{~}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no q in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no - in font nullfont!
+Missing character: There is no C in font nullfont!
+! Undefined control sequence.
+l.118 \correctorStop
+                    
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+Overfull \hbox (22.9998pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 Cette
+ []
+
+
+Overfull \hbox (22.23317pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 ques-
+ []
+
+
+Overfull \hbox (17.12212pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 tion
+ []
+
+
+Overfull \hbox (12.01102pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 est
+ []
+
+
+Overfull \hbox (23.25539pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 not^^See
+ []
+
+
+Overfull \hbox (13.67213pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 sur
+ []
+
+
+Overfull \hbox (10.22217pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 20
+ []
+
+
+Overfull \hbox (28.8776pt too wide) in paragraph at lines 115--119
+\OT1/cmr/m/it/10 points.
+ []
+
+Missing character: There is no S in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+! Undefined control sequence.
+l.120 Soit $\alpha\in \C
+                        $.
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (15.87843pt too wide) in paragraph at lines 120--121
+\OML/cmm/m/it/10  \OMS/cmsy/m/n/10 2$ 
+ []
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no T in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no v in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no à in font nullfont!
+Missing character: There is no © in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+! Misplaced alignment tab character &.
+l.123 ...la matrice $A_n = \begin{pmatrix}\alpha &
+                                                  1\\ 0 &\alpha\end{pmatrix}...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.123 ...ice $A_n = \begin{pmatrix}\alpha &1\\ 0 &
+                                                  \alpha\end{pmatrix}^{n}$, ...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no , in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no M in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.49886pt too wide) in paragraph at lines 123--125
+\OML/cmm/m/it/10 A[] \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (24.21173pt too wide) in paragraph at lines 123--125
+[] \/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (16.87738pt too wide) in paragraph at lines 123--125
+\/cmr/m/n/10 0\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (5.55557pt too wide) in paragraph at lines 123--125
+\/cmr/m/n/10 ^^Ru
+ []
+
+
+Overfull \hbox (16.55786pt too wide) in paragraph at lines 123--125
+\OML/cmm/m/it/10 n \OMS/cmsy/m/n/10 ^^U
+ []
+
+
+Overfull \hbox (5.00002pt too wide) in paragraph at lines 123--125
+\/cmr/m/n/10 1$
+ []
+
+
+Overfull \hbox (4.44444pt too wide) in paragraph at lines 123--125
+\/cmr/m/n/10 ^^Se 
+ []
+
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no O in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no p in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (16.98955pt too wide) in paragraph at lines 125--126
+\OML/cmm/m/it/10  \/cmr/m/n/10 =
+ []
+
+
+Overfull \hbox (12.77782pt too wide) in paragraph at lines 125--126
+\/cmr/m/n/10 1 +
+ []
+
+
+Overfull \hbox (2.77779pt too wide) in paragraph at lines 125--126
+[]$
+ []
+
+
+Overfull \hbox (14.9063pt too wide) in paragraph at lines 125--126
+\OML/cmm/m/it/10 []$
+ []
+
+
+Overfull \hbox (18.89243pt too wide) in paragraph at lines 125--126
+\OML/cmm/m/it/10 []$ 
+ []
+
+Missing character: There is no 3 in font nullfont!
+Missing character: There is no . in font nullfont!
+Missing character: There is no C in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+! Misplaced alignment tab character &.
+l.126 ... Calculer $\begin{pmatrix} 1+\textrm{i} &
+                                                  1\\ 0 &1+\textrm{i}\end{pm...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+! Misplaced alignment tab character &.
+l.126 ...er $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &
+                                                  1+\textrm{i}\end{pmatrix}^...
+I can't figure out why you would want to use a tab mark
+here. If you just want an ampersand, the remedy is
+simple: Just type `I\&' now. But if some right brace
+up above has ended a previous alignment prematurely,
+you're probably due for more error messages, and you
+might try typing `S' now just to see what is salvageable.
+
+Missing character: There is no . in font nullfont!
+
+Overfull \hbox (23.88887pt too wide) in paragraph at lines 126--127
+[] \/cmr/m/n/10 +
+ []
+
+
+Overfull \hbox (7.7778pt too wide) in paragraph at lines 126--127
+[]\/cmr/m/n/10 1[] 
+ []
+
+
+Overfull \hbox (17.77783pt too wide) in paragraph at lines 126--127
+\/cmr/m/n/10 01 +
+ []
+
+
+Overfull \hbox (15.23618pt too wide) in paragraph at lines 126--127
+[][]$ 
+ []
+
+! Undefined control sequence.
+l.130 \OpenGrid
+               {17cm}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 7 in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no m in font nullfont!
+! Undefined control sequence.
+l.131  \FullPageOpenGrid
+                        
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+! Undefined control sequence.
+l.132  \FullPageOpenGrid
+                        
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+)
+! Emergency stop.
+<*> extra_section.tex
+                     
+*** (job aborted, no legal \end found)
+
+ 
+Here is how much of TeX's memory you used:
+ 35 strings out of 492982
+ 467 string characters out of 6134897
+ 61952 words of memory out of 5000000
+ 3699 multiletter control sequences out of 15000+600000
+ 3986 words of font info for 15 fonts, out of 8000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 18i,11n,16p,251b,119s stack positions out of 5000i,500n,10000p,200000b,80000s
+!  ==> Fatal error occurred, no output PDF file produced!
diff --git a/amc-templates/amc_template/extra_section.tex b/amc-templates/amc_template/extra_section.tex
index 5b26068..77d156f 100644
--- a/amc-templates/amc_template/extra_section.tex
+++ b/amc-templates/amc_template/extra_section.tex
@@ -1,130 +1,132 @@
 \setlength{\parindent}{0pt}%
 \newpage
 
 
 %*******************************************************************%
 % Suppress begin-question texts
 \renewcommand{\AMCbeginQuestion}[2]{\QuestionText{#1}}
 \def\QuestionText{\TEXT}
 \def\TEXT#1{}
 \def\NOTEXT#1{}
 \setlength{\parindent}{0pt}%
 \addtocounter{AMCquestionaff}{1}
 %*******************************************************************%
 
 \subsection*{Trois\`eme partie, questions de type ouvert}
 
 \noindent
 R\'epondre dans l’espace d\'edi\'e. Votre r\'eponse doit \^etre soigneusement justifi\'ee, 
 toutes les \'etapes de votre raisonnement doivent figurer dans votre r\'eponse. Laisser libres les cases \`a cocher\,: elles sont r\'eserv\'ees au correcteur. 
 
 
 \bigskip
 
 
 %% Leave at least 2 empty lines after the \bigskip
 %*******************************************************************%
 % Question A - 5 points
 %*******************************************************************%
 
 \begin{description}
 \addtocounter{AMCquestionaff}{1}
 \item[Question~\theAMCquestionaff :] \textit{Cette question est not\'ee sur 5 points.}
 \end{description}
 \correctorPointsPerGroup{5/3}
-\correctorThreeFive{q-open-A}{~}
+\correctorOneFive{q-open-A}{~}
+\correctorTwoFive{q-open-A1}{~}
+\correctorThreeFive{q-open-A2}{~}
 \correctorStop
 
 Soit $\Psi : \R_3[x]\to \R_3[x]$ l'application d\'efinie par 
 $$\Psi(p)(x) = (x-1)p'(x)\text{.}$$
 
 \begin{itemize}
  \item [1.] Montrer que $\Psi$ est lin\'eaire. (1 pt)
  \item [2.] Calculer la matrice $[\Psi]_{E,E}$ de $\Psi$ par rapport \`a la base canonique $E = (1,x, x^2, x^3)$. (2 pts)
  \item [3.] Calculer le rang de $\Psi$. (2 pt)
 \end{itemize}
 
 \OpenGrid{16cm}
 \FullPageOpenGrid
 %*******************************************************************%
 
 %*******************************************************************%
 % Question B - 6 points
 %*******************************************************************%
 
 \begin{description}
 \item[Question~\theAMCquestionaff :] \textit{Cette question est not\'ee sur 6 points.}
 \end{description}
 \correctorPointsPerGroup{6/2}
 \correctorTwoFive{q-open-B}{~}
 \correctorStop
 
 \noindent Soient $V$ un $K$-espace vectoriel de dimension finie, et $X,Y$ deux sous-espaces vectoriels de $V$ 
 tels que $\operatorname{dim}(X) \geq \operatorname{dim}(Y)$. Montrer qu'il existe une application lin\'eaire $T : V\to V$ telle que $T(X) = Y$. 
 
 \vskip 5pt
 \OpenBox{22cm}
 
 %***************************
 % Question C - 6points 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{description}
 \item[Question~\theAMCquestionaff :] \textit{Cette question est not\'ee sur 6 points.}
 \end{description}
 \correctorSix{q-open-C}{~}
 \correctorStop
 
 Soit $\alpha\in \C$. 
 
 \begin{itemize}
 \item [1.] Trouver la formule explicite pour les éléments de la matrice $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurence.
 % \item [1.] Trouver la formule pour $\begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurance.  
  \item [2.] On pose $\alpha = 1+\textrm{i}$. Calculer $\alpha^{99}$ et $\alpha^{100}$. 
  \item [3.] Calculer $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. 
 \end{itemize}
 
 
 \OpenGrid{17cm}
 
 % Question D - 10points 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{description}
 \item[Question~\theAMCquestionaff :] \textit{Cette question est not\'ee sur 10 points.}
 \end{description}
 \correctorTenHalf{q-open-D}{~}
 \correctorStop
 
 Soit $\alpha\in \C$. 
 
 \begin{itemize}
 \item [1.] Trouver la formule explicite pour les éléments de la matrice $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurence.
 % \item [1.] Trouver la formule pour $\begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurance.  
  \item [2.] On pose $\alpha = 1+\textrm{i}$. Calculer $\alpha^{99}$ et $\alpha^{100}$. 
  \item [3.] Calculer $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. 
 \end{itemize}
 
 
 \OpenGrid{17cm}
 \FullPageOpenGrid
 
 % Question E - 15points 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{description}
 \item[Question~\theAMCquestionaff :] \textit{Cette question est not\'ee sur 20 points.}
 \end{description}
 \correctorTwenty{q-open-C}{~}
 \correctorStop
 
 Soit $\alpha\in \C$. 
 
 \begin{itemize}
 \item [1.] Trouver la formule explicite pour les éléments de la matrice $A_n = \begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurence.
 % \item [1.] Trouver la formule pour $\begin{pmatrix}\alpha &1\\ 0 &\alpha\end{pmatrix}^{n}$, o\`u $n \geq 1$ est un entier. Montrer la formule par r\'eccurance.  
  \item [2.] On pose $\alpha = 1+\textrm{i}$. Calculer $\alpha^{99}$ et $\alpha^{100}$. 
  \item [3.] Calculer $\begin{pmatrix} 1+\textrm{i} &1\\ 0 &1+\textrm{i}\end{pmatrix}^{100}$. 
 \end{itemize}
 
 
 \OpenGrid{17cm}
  \FullPageOpenGrid
  \FullPageOpenGrid
\ No newline at end of file
diff --git a/amc-templates/amc_template/style_extra.log b/amc-templates/amc_template/style_extra.log
new file mode 100644
index 0000000..aa7fc67
--- /dev/null
+++ b/amc-templates/amc_template/style_extra.log
@@ -0,0 +1,127 @@
+This is pdfTeX, Version 3.14159265-2.6-1.40.18 (TeX Live 2017/Debian) (preloaded format=pdflatex 2020.7.3)  21 DEC 2020 17:17
+entering extended mode
+ restricted \write18 enabled.
+ %&-line parsing enabled.
+**style_extra.tex
+(./style_extra.tex
+LaTeX2e <2017-04-15>
+Babel <3.18> and hyphenation patterns for 84 language(s) loaded.
+
+! LaTeX Error: \usepackage before \documentclass.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.2 \usepackage{
+                array}
+\usepackage may only appear in the document preamble, i.e.,
+between \documentclass and \begin{document}.
+
+! Undefined control sequence.
+l.5 \AMCopenOpts
+                {lines=10,lineheight=2ex,framerulecol=black,dots=false}
+The control sequence at the end of the top line
+of your error message was never \def'ed. If you have
+misspelled it (e.g., `\hobx'), type `I' and the correct
+spelling (e.g., `I\hbox'). Otherwise just continue,
+and I'll forget about whatever was undefined.
+
+
+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.5 \AMCopenOpts{l
+                  ines=10,lineheight=2ex,framerulecol=black,dots=false}
+You're in trouble here.  Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 1 in font nullfont!
+Missing character: There is no 0 in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no n in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no i in font nullfont!
+Missing character: There is no g in font nullfont!
+Missing character: There is no h in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no 2 in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no x in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no m in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no r in font nullfont!
+Missing character: There is no u in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no e in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no b in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no c in font nullfont!
+Missing character: There is no k in font nullfont!
+Missing character: There is no , in font nullfont!
+Missing character: There is no d in font nullfont!
+Missing character: There is no o in font nullfont!
+Missing character: There is no t in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no = in font nullfont!
+Missing character: There is no f in font nullfont!
+Missing character: There is no a in font nullfont!
+Missing character: There is no l in font nullfont!
+Missing character: There is no s in font nullfont!
+Missing character: There is no e in font nullfont!
+
+Overfull \hbox (20.0pt too wide) in paragraph at lines 5--6
+[] 
+ []
+
+
+! LaTeX Error: \labelenumi undefined.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
+ ...                                              
+                                                  
+l.11 \renewcommand{\labelenumi}
+                               {(\theenumi)}
+Try typing  <return>  to proceed.
+If that doesn't work, type  X <return>  to quit.
+
+)
+! Emergency stop.
+<*> style_extra.tex
+                   
+*** (job aborted, no legal \end found)
+
+ 
+Here is how much of TeX's memory you used:
+ 155 strings out of 492982
+ 2800 string characters out of 6134897
+ 69800 words of memory out of 5000000
+ 3821 multiletter control sequences out of 15000+600000
+ 3640 words of font info for 14 fonts, out of 8000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 8i,0n,6p,301b,16s stack positions out of 5000i,500n,10000p,200000b,80000s
+!  ==> Fatal error occurred, no output PDF file produced!
diff --git a/amc-templates/amc_template/style_extra.tex b/amc-templates/amc_template/style_extra.tex
index a95c03d..6d83151 100644
--- a/amc-templates/amc_template/style_extra.tex
+++ b/amc-templates/amc_template/style_extra.tex
@@ -1,1441 +1,1441 @@
 %%Package for tabular in openquestion
 \usepackage{array}
 
 %% Default values for open questions:
 \AMCopenOpts{lines=10,lineheight=2ex,framerulecol=black,dots=false}
 
 \newcommand{\letter}{A}
 
 \makeatletter
 \renewcommand{\theenumi}{\alph{enumi}}
 \renewcommand{\labelenumi}{(\theenumi)}
 \makeatother
 
 %% OpenBox commands ============================
 \newcommand{\OpenBox}[1]{
 \noindent
   \fbox{
     \centering
     \begin{minipage}{.97\textwidth}
 ~
     \vspace{#1}
 ~
     \end{minipage}
   }
 }
 
 \newcommand{\FullPageOpenBox}{
   \clearpage
   \OpenBox{24.5cm}
 %  \vspace{-5mm}
 }
 
 
 \newcommand{\FullPageOpenBoxForever}{
 	\loop \ifnum \thepage < \totalPages  \FullPageOpenBox \repeat
 }
 
 %% OpenGrid commands ============================
 \newcommand{\OpenGrid}[1]{
 \noindent
 \begin{tikzpicture}
 \draw[step=.5cm,lightgray]
 (0cm,0cm) grid (16.5cm,#1);
 \end{tikzpicture}
 }
 
 \newcommand{\FullPageOpenGrid}{
   \clearpage
   \OpenGrid{24.5cm}
   %\vspace{-5mm}
 }
 
 \newcommand{\FullPageOpenGridForever}{
 	\loop \ifnum \thepage < \totalPages  \FullPageOpenGrid \repeat
 }
 
 %% Extra sheets message
 \newcommand{\ExtraSheet}{\mbox{}\hfil\smash{\fbox{\scriptsize\quad Si vous avez besoin de place suppl\'ementaire, demandez une feuille quadrill\'ee \`a un des surveillants\quad}}}%
 
 %% 5 boxes correctors (0,1/4,1/2,3/4 and 1 * openquestionmax) ====================
 
 \newcommand{\openquestionmax}{1}
 
 \newcommand{\correctorPointsPerGroup}[1]{
 \renewcommand{\openquestionmax}{#1}
 }
 
 \newcommand{\correctorChoices}{\correctchoice[0]{}\scoring{b=0}\correctchoice[Y]{}\scoring{b=\openquestionmax/4}\correctchoice[X]{}\scoring{b=\openquestionmax/2}\correctchoice[W]{}\scoring{b=\openquestionmax*3/4}\correctchoice[V]{\qquad}\scoring{b=\openquestionmax}}
 
 
 \newcommand{\correctorOneFive}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax}
 #3~\\
-\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\makebox[301pt][c]{}}
+\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\makebox[358pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorTwoFive}[3][0]{
 \par
 \noindent\begin{questionmultx}{#2}\bareme{MAX=\openquestionmax*2}
 #3~\\
-\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\correctorChoices\makebox[192.2pt][c]{}}
+\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\correctorChoices\makebox[249pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorThreeFive}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax*3}
 #3~\\
-\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\correctorChoices\correctorChoices\makebox[1pt][c]{}}
+\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoices\correctorChoices\correctorChoices\makebox[140pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 %% 3 boxes correctors (0,1/2,and 1 * openquestionmax) ====================
 
 \newcommand{\correctorChoicesSimple}{\correctchoice[0]{}\scoring{b=0}\correctchoice[Y]{}\scoring{b=\openquestionmax/2}\correctchoice[X]{}{\qquad}\scoring{b=\openquestionmax}}
 
 \newcommand{\correctorOneThree}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoicesSimple\makebox[340pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorTwoThree}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax*2}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoicesSimple\correctorChoicesSimple\makebox[260pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorThreeThree}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax*3}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoicesSimple\correctorChoicesSimple\correctorChoicesSimple\makebox[180pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorFourThree}[3][0]{
 \par
 \noindent
 \begin{questionmultx}{#2}\bareme{MAX=\openquestionmax*4}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{\correctorChoicesSimple\correctorChoicesSimple\correctorChoicesSimple\correctorChoicesSimple\makebox[100pt][c]{}}
 \end{questionmultx}
 \vspace{-55pt}~
 \par
 }
 
 
 % Standard points correctors boxes ===================================
 \newcommand{\correctorChoicesOne}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \correctchoice[Y]{\tiny{1}\qquad}\scoring{1}}
 \newcommand{\correctorOne}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=1}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesOne}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesTwo}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \correctchoice[X]{\tiny{2}\qquad}\scoring{2}}
 \newcommand{\correctorTwo}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=2}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesTwo}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesThree}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \wrongchoice[X]{\tiny{2}}\scoring{2}
 \correctchoice[W]{\tiny{3}\qquad}\scoring{3}}
 \newcommand{\correctorThree}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=3}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesThree}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFour}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \wrongchoice[X]{\tiny{2}}\scoring{2}
 \wrongchoice[W]{\tiny{3}}\scoring{3}
 \correctchoice[V]{\tiny{4}\qquad}\scoring{4}}
 \newcommand{\correctorFour}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=4}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFour}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFive}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \wrongchoice[X]{\tiny{2}}\scoring{2}
 \wrongchoice[W]{\tiny{3}}\scoring{3}
 \wrongchoice[V]{\tiny{4}}\scoring{4}
 \correctchoice[U]{\tiny{5}\qquad}\scoring{5}}
 \newcommand{\correctorFive}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=5}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFive}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesSix}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \wrongchoice[X]{\tiny{2}}\scoring{2}
 \wrongchoice[W]{\tiny{3}}\scoring{3}
 \wrongchoice[V]{\tiny{4}}\scoring{4}
 \wrongchoice[U]{\tiny{5}}\scoring{5}
 \correctchoice[T]{\tiny{6}\qquad}\scoring{6}}
 \newcommand{\correctorSix}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=6}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesSix}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesSeven}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}
 \wrongchoice[X]{\tiny{2}}\scoring{2}
 \wrongchoice[W]{\tiny{3}}\scoring{3}
 \wrongchoice[V]{\tiny{4}}\scoring{4}
 \wrongchoice[U]{\tiny{5}}\scoring{5}
 \wrongchoice[T]{\tiny{6}}\scoring{6}
 \correctchoice[S]{\tiny{7}\qquad}\scoring{7}}
 \newcommand{\correctorSeven}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=7}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesSeven}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesEight}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}\hspace{-0.5ex}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}\hspace{-0.5ex}
 \wrongchoice[X]{\tiny{2}}\scoring{2}\hspace{-0.5ex}
 \wrongchoice[W]{\tiny{3}}\scoring{3}\hspace{-0.5ex}
 \wrongchoice[V]{\tiny{4}}\scoring{4}\hspace{-0.5ex}
 \wrongchoice[U]{\tiny{5}}\scoring{5}\hspace{-0.5ex}
 \wrongchoice[T]{\tiny{6}}\scoring{6}\hspace{-0.5ex}
 \wrongchoice[S]{\tiny{7}}\scoring{7}\hspace{-0.5ex}
 \correctchoice[R]{\tiny{8}\qquad}\scoring{8}}
 \newcommand{\correctorEight}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=8}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 %{\makebox[100ex][l]{\correctorChoicesEight}}
 {\makebox[0.9\linewidth][l]{\correctorChoicesEight}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesNine}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}\hspace{-0.5ex}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}\hspace{-0.5ex}
 \wrongchoice[X]{\tiny{2}}\scoring{2}\hspace{-0.5ex}
 \wrongchoice[W]{\tiny{3}}\scoring{3}\hspace{-0.5ex}
 \wrongchoice[V]{\tiny{4}}\scoring{4}\hspace{-0.5ex}
 \wrongchoice[U]{\tiny{5}}\scoring{5}\hspace{-0.5ex}
 \wrongchoice[T]{\tiny{6}}\scoring{6}\hspace{-0.5ex}
 \wrongchoice[S]{\tiny{7}}\scoring{7}\hspace{-0.5ex}
 \wrongchoice[R]{\tiny{8}}\scoring{8}\hspace{-0.5ex}
 \correctchoice[Q]{\tiny{9}\qquad}\scoring{9}}
 \newcommand{\correctorNine}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=9}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesNine}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesTen}{
 \wrongchoice[0]{\tiny{0}}\scoring{0}\hspace{-0.5ex}
 \wrongchoice[Y]{\tiny{1}}\scoring{1}\hspace{-0.5ex}
 \wrongchoice[X]{\tiny{2}}\scoring{2}\hspace{-0.5ex}
 \wrongchoice[W]{\tiny{3}}\scoring{3}\hspace{-0.5ex}
 \wrongchoice[V]{\tiny{4}}\scoring{4}\hspace{-0.5ex}
 \wrongchoice[U]{\tiny{5}}\scoring{5}\hspace{-0.5ex}
 \wrongchoice[T]{\tiny{6}}\scoring{6}\hspace{-0.5ex}
 \wrongchoice[S]{\tiny{7}}\scoring{7}\hspace{-0.5ex}
 \wrongchoice[R]{\tiny{8}}\scoring{8}\hspace{-0.5ex}
 \wrongchoice[Q]{\tiny{9}}\scoring{9}\hspace{-0.5ex}
 \correctchoice[P]{\tiny{10}\qquad}\scoring{10}}
 \newcommand{\correctorTen}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=10}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesTen}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesEleven}{
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{llllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5}
 \\
 \wrongchoice[T]{\tiny{6}}\scoring{6} &
 \wrongchoice[S]{\tiny{7}}\scoring{7} &
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \correctchoice[O]{\tiny{11}}\scoring{11}
 \\
 \end{tabular}}}
 \newcommand{\correctorEleven}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=11}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesEleven\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesTwelve}{
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{lllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} 
 \\
 &
 \wrongchoice[S]{\tiny{7}}\scoring{7} &
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} &
 \correctchoice[N]{\tiny{12}\qquad}\scoring{12}
 \\
 \end{tabular}}}
 \newcommand{\correctorTwelve}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=12}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesTwelve\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesThirteen}{
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{lllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} 
 \\
 \wrongchoice[S]{\tiny{7}}\scoring{7} &
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} &
 \wrongchoice[N]{\tiny{12}}\scoring{12} &
 \correctchoice[M]{\tiny{13}}\scoring{13}
 \\
 \end{tabular}}}
 \newcommand{\correctorThirteen}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=13}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesThirteen\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFourteen}{
 %\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{llllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} &
 \wrongchoice[S]{\tiny{7}}\scoring{7} 
 \\
 &
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} &
 \wrongchoice[N]{\tiny{12}}\scoring{12} &
 \wrongchoice[M]{\tiny{13}}\scoring{13} &
 \correctchoice[L]{\tiny{14}}\scoring{14}
 \\
 \end{tabular}}}
 \newcommand{\correctorFourteen}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=14}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesFourteen\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFifteen}{
 %\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{llllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} &
 \wrongchoice[S]{\tiny{7}}\scoring{7} 
 \\
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} &
 \wrongchoice[N]{\tiny{12}}\scoring{12} &
 \wrongchoice[M]{\tiny{13}}\scoring{13} &
 \wrongchoice[L]{\tiny{14}}\scoring{14} &
 \correctchoice[K]{\tiny{15}}\scoring{15}
 \\
 \end{tabular}}}
 \newcommand{\correctorFifteen}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=15}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesFifteen\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesSixteen}{
 %\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \setlength{\tabcolsep}{0.08em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{lllllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} &
 \wrongchoice[S]{\tiny{7}}\scoring{7} &
 \wrongchoice[R]{\tiny{8}}\scoring{8} 
 \\
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} &
 \wrongchoice[N]{\tiny{12}}\scoring{12} &
 \wrongchoice[M]{\tiny{13}}\scoring{13} &
 \wrongchoice[L]{\tiny{14}}\scoring{14} &
 \wrongchoice[K]{\tiny{15}}\scoring{15} &
 \correctchoice[J]{\tiny{16}}\scoring{16} 
 \end{tabular}}}
 \newcommand{\correctorSixteen}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=16}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 \parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesSixteen\makebox[0pt][c]{}}
 \hspace*{5ex}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesNineteen}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 		\hspace{.2cm}\begin{tabular}{lllllllllll}
 			\wrongchoice[0]{\tiny{0}}\scoring{0} &
 			\wrongchoice[Y]{\tiny{1}}\scoring{1} &
 			\wrongchoice[X]{\tiny{2}}\scoring{2} &
 			\wrongchoice[W]{\tiny{3}}\scoring{3} &
 			\wrongchoice[V]{\tiny{4}}\scoring{4} &
 			\wrongchoice[U]{\tiny{5}}\scoring{5} &
 			\wrongchoice[T]{\tiny{6}}\scoring{6} &
 			\wrongchoice[S]{\tiny{7}}\scoring{7} &
 			\wrongchoice[R]{\tiny{8}}\scoring{8} &
 			\wrongchoice[Q]{\tiny{9}}\scoring{9} 
 			\\
 			\wrongchoice[P]{\tiny{10}}\scoring{10}& 
 			\wrongchoice[O]{\tiny{11}}\scoring{11} &
 			\wrongchoice[N]{\tiny{12}}\scoring{12} &
 			\wrongchoice[M]{\tiny{13}}\scoring{13} &
 			\wrongchoice[L]{\tiny{14}}\scoring{14} &
 			\wrongchoice[K]{\tiny{15}}\scoring{15}&
 			\wrongchoice[I]{\tiny{16}}\scoring{16} &
 			\wrongchoice[H]{\tiny{17}}\scoring{17} &
 			\wrongchoice[G]{\tiny{18}}\scoring{18} &
 			\correctchoice[F]{\tiny{19}}\scoring{19} 
 			\\
 \end{tabular}}}
 \newcommand{\correctorNineteen}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=19}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesNineteen\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 \newcommand{\correctorChoicesTwenty}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 		\hspace{.2cm}\begin{tabular}{lllllllllll}
 			\wrongchoice[0]{\tiny{0}}\scoring{0} &
 			\wrongchoice[Y]{\tiny{1}}\scoring{1} &
 			\wrongchoice[X]{\tiny{2}}\scoring{2} &
 			\wrongchoice[W]{\tiny{3}}\scoring{3} &
 			\wrongchoice[V]{\tiny{4}}\scoring{4} &
 			\wrongchoice[U]{\tiny{5}}\scoring{5} &
 			\wrongchoice[T]{\tiny{6}}\scoring{6} &
 			\wrongchoice[S]{\tiny{7}}\scoring{7} &
 			\wrongchoice[R]{\tiny{8}}\scoring{8} &
 			\wrongchoice[Q]{\tiny{9}}\scoring{9} &
 			\wrongchoice[P]{\tiny{10}}\scoring{10} 
 			\\ 
 			\wrongchoice[O]{\tiny{11}}\scoring{11} &
 			\wrongchoice[N]{\tiny{12}}\scoring{12} &
 			\wrongchoice[M]{\tiny{13}}\scoring{13} &
 			\wrongchoice[L]{\tiny{14}}\scoring{14} &
 			\wrongchoice[K]{\tiny{15}}\scoring{15} &
 			\wrongchoice[J]{\tiny{16}}\scoring{16} &
 			\wrongchoice[I]{\tiny{17}}\scoring{17} &
 			\wrongchoice[H]{\tiny{18}}\scoring{18} &
 			\wrongchoice[G]{\tiny{19}}\scoring{19} &
 			\correctchoice[F]{\tiny{20}}\scoring{20} 
 			\\
 \end{tabular}}}
 \newcommand{\correctorTwenty}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=20}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesTwenty\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 \newcommand{\correctorChoicesTwentyOne}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 		\hspace{.2cm}\begin{tabular}{lllllllllll}
 			\wrongchoice[0]{\tiny{0}}\scoring{0} &
 			\wrongchoice[Y]{\tiny{1}}\scoring{1} &
 			\wrongchoice[X]{\tiny{2}}\scoring{2} &
 			\wrongchoice[W]{\tiny{3}}\scoring{3} &
 			\wrongchoice[V]{\tiny{4}}\scoring{4} &
 			\wrongchoice[U]{\tiny{5}}\scoring{5} &
 			\wrongchoice[T]{\tiny{6}}\scoring{6} &
 			\wrongchoice[S]{\tiny{7}}\scoring{7} &
 			\wrongchoice[R]{\tiny{8}}\scoring{8} &
 			\wrongchoice[Q]{\tiny{9}}\scoring{9} &
 			\wrongchoice[P]{\tiny{10}}\scoring{10} 
 			\\ 
 			\wrongchoice[O]{\tiny{11}}\scoring{11} &
 			\wrongchoice[N]{\tiny{12}}\scoring{12} &
 			\wrongchoice[M]{\tiny{13}}\scoring{13} &
 			\wrongchoice[L]{\tiny{14}}\scoring{14} &
 			\wrongchoice[K]{\tiny{15}}\scoring{15} &
 			\wrongchoice[J]{\tiny{16}}\scoring{16} &
 			\wrongchoice[I]{\tiny{17}}\scoring{17} &
 			\wrongchoice[H]{\tiny{18}}\scoring{18} &
 			\wrongchoice[G]{\tiny{19}}\scoring{19} &
 			\wrongchoice[F]{\tiny{20}}\scoring{20} &
 			\correctchoice[F]{\tiny{21}}\scoring{21} 
 			\\
 \end{tabular}}}
 \newcommand{\correctorTwentyOne}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=21}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesTwentyOne\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 
 \newcommand{\correctorChoicesTwentyTwo}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \hspace{.2cm}\begin{tabular}{llllllllllll}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{1}}\scoring{1} &
 \wrongchoice[X]{\tiny{2}}\scoring{2} &
 \wrongchoice[W]{\tiny{3}}\scoring{3} &
 \wrongchoice[V]{\tiny{4}}\scoring{4} &
 \wrongchoice[U]{\tiny{5}}\scoring{5} &
 \wrongchoice[T]{\tiny{6}}\scoring{6} &
 \wrongchoice[S]{\tiny{7}}\scoring{7} &
 \wrongchoice[R]{\tiny{8}}\scoring{8} &
 \wrongchoice[Q]{\tiny{9}}\scoring{9} &
 \wrongchoice[P]{\tiny{10}}\scoring{10} &
 \wrongchoice[O]{\tiny{11}}\scoring{11} 
 \\ &
 \wrongchoice[N]{\tiny{12}}\scoring{12} &
 \wrongchoice[M]{\tiny{13}}\scoring{13} &
 \wrongchoice[L]{\tiny{14}}\scoring{14} &
 \wrongchoice[K]{\tiny{15}}\scoring{15} &
 \wrongchoice[J]{\tiny{16}}\scoring{16} &
 \wrongchoice[I]{\tiny{17}}\scoring{17} &
 \wrongchoice[G]{\tiny{18}}\scoring{18} &
 \wrongchoice[F]{\tiny{19}}\scoring{19} &
 \wrongchoice[E]{\tiny{20}}\scoring{20} &
 \wrongchoice[D]{\tiny{21}}\scoring{21} &
 \correctchoice[C]{\tiny{22}}\scoring{22}                                        
 \\
 \end{tabular}}}
 \newcommand{\correctorTwentyTwo}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=22}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesTwentyTwo\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 \newcommand{\correctorChoicesTwentyFive}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 		\hspace{.2cm}\begin{tabular}{llllllllll}
 			\wrongchoice[0]{\tiny{0}}\scoring{0} &
 			\wrongchoice[Y]{\tiny{1}}\scoring{1} &
 			\wrongchoice[X]{\tiny{2}}\scoring{2} &
 			\wrongchoice[W]{\tiny{3}}\scoring{3} &
 			\wrongchoice[V]{\tiny{4}}\scoring{4} &
 			\wrongchoice[U]{\tiny{5}}\scoring{5} &
 			\wrongchoice[T]{\tiny{6}}\scoring{6} &
 			\wrongchoice[S]{\tiny{7}}\scoring{7} &
 			\wrongchoice[R]{\tiny{8}}\scoring{8} &
 			\wrongchoice[Q]{\tiny{9}}\scoring{9} 
 			\\ &
 			\wrongchoice[P]{\tiny{10}}\scoring{10} &
 			\wrongchoice[O]{\tiny{11}}\scoring{11} &
 			\wrongchoice[N]{\tiny{12}}\scoring{12} &
 			\wrongchoice[M]{\tiny{13}}\scoring{13} &
 			\wrongchoice[L]{\tiny{14}}\scoring{14} &
 			\wrongchoice[K]{\tiny{15}}\scoring{15} &
 			\wrongchoice[J]{\tiny{16}}\scoring{16} &
 			\wrongchoice[I]{\tiny{17}}\scoring{17} &
 			\wrongchoice[H]{\tiny{18}}\scoring{18} &
 			\wrongchoice[G]{\tiny{19}}\scoring{19} 
 			\\ &
 			\wrongchoice[F]{\tiny{20}}\scoring{20} &
 			\wrongchoice[E]{\tiny{21}}\scoring{21} &
 			\wrongchoice[D]{\tiny{22}}\scoring{22} &
 			\wrongchoice[C]{\tiny{23}}\scoring{23} &
 			\wrongchoice[B]{\tiny{24}}\scoring{24} &
 			\wrongchoice[A]{\tiny{25}}\scoring{25} 
 			\\
 \end{tabular}}}
 \newcommand{\correctorTwentyFive}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=25}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesTwentyFive\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 \newcommand{\correctorChoicesThirty}{
 	%\newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 	\setlength{\tabcolsep}{0.08em} % for the horizontal padding
 	{\renewcommand{\arraystretch}{1.2}% for the vertical padding
 		\hspace{.2cm}\begin{tabular}{lllllllllll}
 			\wrongchoice[0]{\tiny{0}}\scoring{0} &
 			\wrongchoice[Y]{\tiny{1}}\scoring{1} &
 			\wrongchoice[X]{\tiny{2}}\scoring{2} &
 			\wrongchoice[W]{\tiny{3}}\scoring{3} &
 			\wrongchoice[V]{\tiny{4}}\scoring{4} &
 			\wrongchoice[U]{\tiny{5}}\scoring{5} &
 			\wrongchoice[T]{\tiny{6}}\scoring{6} &
 			\wrongchoice[S]{\tiny{7}}\scoring{7} &
 			\wrongchoice[R]{\tiny{8}}\scoring{8} &
 			\wrongchoice[Q]{\tiny{9}}\scoring{9} &
 			\wrongchoice[P]{\tiny{10}}\scoring{10} 
 			\\ &
 			\wrongchoice[O]{\tiny{11}}\scoring{11} &
 			\wrongchoice[N]{\tiny{12}}\scoring{12} &
 			\wrongchoice[M]{\tiny{13}}\scoring{13} &
 			\wrongchoice[L]{\tiny{14}}\scoring{14} &
 			\wrongchoice[K]{\tiny{15}}\scoring{15} &
 			\wrongchoice[J]{\tiny{16}}\scoring{16} &
 			\wrongchoice[I]{\tiny{17}}\scoring{17} &
 			\wrongchoice[H]{\tiny{18}}\scoring{18} &
 			\wrongchoice[G]{\tiny{19}}\scoring{19} &
 			\wrongchoice[F]{\tiny{20}}\scoring{20} 
 			\\ &
 			\wrongchoice[E]{\tiny{21}}\scoring{21} &
 			\wrongchoice[D]{\tiny{22}}\scoring{22} &
 			\wrongchoice[C]{\tiny{23}}\scoring{23} &
 			\wrongchoice[B]{\tiny{24}}\scoring{24} &
 			\wrongchoice[A]{\tiny{25}}\scoring{25} &
 			\wrongchoice[AY]{\tiny{26}}\scoring{26} &
 			\wrongchoice[AX]{\tiny{27}}\scoring{27} &
 			\wrongchoice[AW]{\tiny{28}}\scoring{28} &
 			\wrongchoice[AV]{\tiny{29}}\scoring{29} &
 			\correctchoice[AU]{\tiny{30}}\scoring{30} 
 			\\
 \end{tabular}}}
 \newcommand{\correctorThirty}[3][0]{%
 	\par
 	\noindent
 	\begin{question}{#2}\bareme{MAX=30}
 		#3~\\
 		\noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}{
 			\parbox{0.85\linewidth}{\linespread{1.25}\selectfont \correctorChoicesThirty\makebox[0pt][c]{}}
 			\hspace*{5ex}}
 	\end{question}
 	\vspace{-55pt}~
 	\par
 }
 
 
 %% half points correctors boxes ===================================
 \newcommand{\correctorChoicesTwoHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \correctchoice[V]{\tiny{2}}\scoring{2} 
 \\
 \end{tabular}}}
 \newcommand{\correctorTwoHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=2}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesTwoHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesThreeHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \correctchoice[T]{\tiny{3}}\scoring{3}
 \\
 \end{tabular}}}
 \newcommand{\correctorThreeHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=3}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesThreeHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFourHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \correctchoice[R]{\tiny{4}}\scoring{4}
 \\
 \end{tabular}}}
 \newcommand{\correctorFourHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=4}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFourHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesFiveHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \correctchoice[P]{\tiny{5}}\scoring{5}
 \\
 \end{tabular}}}
 \newcommand{\correctorFiveHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=5}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFiveHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesSixHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \correctchoice[N]{\tiny{6}}\scoring{6}
 \\
 \end{tabular}}}
 \newcommand{\correctorSixHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=6}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesSixHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesSevenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5}
 \\
 &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \correctchoice[L]{\tiny{7}}\scoring{7}
 \\
 \end{tabular}}}
 \newcommand{\correctorSevenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=7}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesSevenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesEightHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4}
 \\
 &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \correctchoice[J]{\tiny{8}}\scoring{8} 
 \\
 \end{tabular}}}
 \newcommand{\correctorEightHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=8}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesEightHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorChoicesNineHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5}
 \\
 &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \correctchoice[H]{\tiny{9}}\scoring{9}
 \\
 \end{tabular}}}
 \newcommand{\correctorNineHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=9}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesNineHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesTenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} 
 \\
 &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \correctchoice[F]{\tiny{10}}\scoring{10}
 \\
 \end{tabular}}}
 \newcommand{\correctorTenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=10}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesTenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesElevenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5}
 \\
  &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \correctchoice[D]{\tiny{11}}\scoring{11}
 \\
 \end{tabular}}}
 \newcommand{\correctorElevenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=11}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesElevenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesTwelveHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6}
 \\
 &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \wrongchoice[D]{\tiny{11}}\scoring{11} &
 \wrongchoice[C]{\tiny{.5}}\scoring{11.5} &
 \correctchoice[B]{\tiny{12}}\scoring{12}
 \\
 \end{tabular}}}
 \newcommand{\correctorTwelveHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=12}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesTwelveHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesThirteenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5}
 \\ 
 &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \wrongchoice[D]{\tiny{11}}\scoring{11} &
 \wrongchoice[C]{\tiny{.5}}\scoring{11.5} &
 \wrongchoice[B]{\tiny{12}}\scoring{12} &
 \wrongchoice[A]{\tiny{.5}}\scoring{12.5} &
 \correctchoice[AY]{\tiny{13}}\scoring{13}
 \\
 \end{tabular}}}
 \newcommand{\correctorThirteenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=13}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesThirteenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesFourteenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7}
 \\
 &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \wrongchoice[D]{\tiny{11}}\scoring{11} &
 \wrongchoice[C]{\tiny{.5}}\scoring{11.5} &
 \wrongchoice[B]{\tiny{12}}\scoring{12} &
 \wrongchoice[A]{\tiny{.5}}\scoring{12.5} &
 \wrongchoice[AY]{\tiny{13}}\scoring{13} &
 \wrongchoice[AX]{\tiny{.5}}\scoring{13.5} &
 \correctchoice[AW]{\tiny{14}}\scoring{14}
 \\
 \end{tabular}}}
 \newcommand{\correctorFourteenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=14}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFourteenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 \newcommand{\correctorChoicesFifteenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} 
 \\
 &
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \wrongchoice[D]{\tiny{11}}\scoring{11} &
 \wrongchoice[C]{\tiny{.5}}\scoring{11.5} &
 \wrongchoice[B]{\tiny{12}}\scoring{12} &
 \wrongchoice[A]{\tiny{.5}}\scoring{12.5} &
 \wrongchoice[AY]{\tiny{13}}\scoring{13} &
 \wrongchoice[AX]{\tiny{.5}}\scoring{13.5} &
 \wrongchoice[AW]{\tiny{14}}\scoring{14} &
 \wrongchoice[AV]{\tiny{.5}}\scoring{14.5} &
 \correctchoice[AU]{\tiny{15}}\scoring{15}
 \\
 \end{tabular}}}
 \newcommand{\correctorFifteenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=15}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesFifteenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 
 
 
 \newcommand{\correctorChoicesSixteenHalf}{
 \setlength{\tabcolsep}{0em} % for the horizontal padding
 {\renewcommand{\arraystretch}{1.2}% for the vertical padding
 \newcolumntype{L}{>{\raggedright\let\newline\\\arraybackslash\hspace{0pt}}m{2em}}
 \hspace{-0.25cm}\begin{tabular}{LLLLLLLLLLLLLL}
 \wrongchoice[0]{\tiny{0}}\scoring{0} &
 \wrongchoice[Y]{\tiny{.5}}\scoring{0.5} &
 \wrongchoice[X]{\tiny{1}}\scoring{1} &
 \wrongchoice[W]{\tiny{.5}}\scoring{1.5} &
 \wrongchoice[V]{\tiny{2}}\scoring{2} &
 \wrongchoice[U]{\tiny{.5}}\scoring{2.5} &
 \wrongchoice[T]{\tiny{3}}\scoring{3} &
 \wrongchoice[S]{\tiny{.5}}\scoring{3.5} &
 \wrongchoice[R]{\tiny{4}}\scoring{4} &
 \wrongchoice[Q]{\tiny{.5}}\scoring{4.5} &
 \wrongchoice[P]{\tiny{5}}\scoring{5} &
 \wrongchoice[O]{\tiny{.5}}\scoring{5.5} &
 \wrongchoice[N]{\tiny{6}}\scoring{6} &
 \wrongchoice[M]{\tiny{.5}}\scoring{6.5} 
 \\
 &
 \wrongchoice[L]{\tiny{7}}\scoring{7} &
 \wrongchoice[K]{\tiny{.5}}\scoring{7.5} & 
 \wrongchoice[J]{\tiny{8}}\scoring{8} &
 \wrongchoice[I]{\tiny{.5}}\scoring{8.5} &
 \wrongchoice[H]{\tiny{9}}\scoring{9} &
 \wrongchoice[G]{\tiny{.5}}\scoring{9.5} &
 \wrongchoice[F]{\tiny{10}}\scoring{10} &
 \wrongchoice[E]{\tiny{.5}}\scoring{10.5} &
 \wrongchoice[D]{\tiny{11}}\scoring{11} &
 \wrongchoice[C]{\tiny{.5}}\scoring{11.5} &
 \wrongchoice[B]{\tiny{12}}\scoring{12} &
 \wrongchoice[A]{\tiny{.5}}\scoring{12.5} 
 \\
 &
 \wrongchoice[AY]{\tiny{13}}\scoring{13} &
 \wrongchoice[AX]{\tiny{.5}}\scoring{13.5} &
 \wrongchoice[AW]{\tiny{14}}\scoring{14} &
 \wrongchoice[AV]{\tiny{.5}}\scoring{14.5} &
 \wrongchoice[AU]{\tiny{15}}\scoring{15} &
 \wrongchoice[AV]{\tiny{.5}}\scoring{15.5} &
 \correctchoice[AU]{\tiny{16}}\scoring{16}
 \\
 \end{tabular}}}
 \newcommand{\correctorSixteenHalf}[3][0]{%
 \par
 \noindent
 \begin{question}{#2}\bareme{MAX=16}
 #3~\\
 \noindent\AMCOpen{lines=#1,boxframerulecol=lightgray,framerulecol=white}%
 {\makebox[0.9\linewidth][l]{\correctorChoicesSixteenHalf}}
 \end{question}
 \vspace{-55pt}~
 \par
 }
 
 \newcommand{\correctorStop}{
 \bigskip
 
 
 \noindent
 }