Can we solve Sudoku using MATLAB?

Yes we can.

Here is the code for the same.

Solving Sudoku Using Recursive Backtracking

1. function X = sudoku(X)  
2. % SUDOKU Solve Sudoku using recursive backtracking.  
3. % sudoku(X), expects a 9-by-9 array X.  
4. % Fill in all “singletons”.  
5. % C is a cell array of candidate vectors for each cell.  
6. % s is the first cell, if any, with one candidate.  
7. % e is the first cell, if any, with no candidates.  
8. [C,s,e] = candidates(X);  
9. while ~isempty(s) && isempty(e)  
10. X(s) = C{s};  
11. [C,s,e] = candidates(X);  
12. end  
13. % Return for impossible puzzles.  
14. if ~isempty(e)  
15. return  
16. end  
17. % Recursive backtracking.  
18. if any(X(:) == 0)  
19. Y = X;  
20. z = find(X(:) == 0,1); % The first unfilled cell.  
21. for r = [C{z}] % Iterate over candidates.  
22. X = Y;  
23. X(z) = r; % Insert a tentative value.  
24. X = sudoku(X); % Recursive call.  
25. if all(X(:) > 0) % Found a solution.  
26. return  
27. end  
28. end  
29. end  
30. % ------------------------------  
31. function [C,s,e] = candidates(X)  
32. C = cell(9,9);  
33. tri = @(k) 3*ceil(k/3-1) + (1:3);  
34. for j = 1:9  
35. for i = 1:9  
36. if X(i,j)==0  
37. z = 1:9;  
38. z(nonzeros(X(i,:))) = 0;  
39. z(nonzeros(X(:,j))) = 0;  
40. z(nonzeros(X(tri(i),tri(j)))) = 0;  
41. C{i,j} = nonzeros(z)’;  
42. end  
43. end  
44. end  
45. L = cellfun(@length,C); % Number of candidates.  
46. s = find(X==0 & L==1,1);  
47. e = find(X==0 & L==0,1);  
48. end % candidates  
49. end % sudoku 

Source :- Solving Sudoku with MATLAB