			% puzzle game
			function Y = puzzle(X)

			[Ni, Nj] = size(X);
			assert(Ni == Nj, "X must be diagonal");
			N = Ni;

			T = diag(ones(N-1,1), -1) + diag(ones(N,1), 0) + diag(ones(N-1,1), 1);
			I = eye(N);
			A = kron(T, I) + kron(I, T) - kron(I, I);

			% transform b into the vector format
			b = zeros(N^2, 1);
			for i=1:N
			for j=1:N
			b(grid(i,j,N)) = X(i,j);
			end
			end

			result = A \ b; % solve with matlab built-in

			% transform result into the matrix format
			Y = zeros(N);
			for i=1:N
			for j =1:N
			Y(i,j) = result(grid(i,j,N));
			end
			end
			end

			function k = grid(i, j, N)
			k = (i-1) * N + j;
			end

compphys/exo3/puzzle.m
33bba04159d6master

puzzle.m
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