valid([]).
valid([Head|Tail]) :- fd_all_different(Head), valid(Tail).

sudoku(Puzzle, Solution) :-
  Solution = Puzzle,
  Puzzle = [S11, S12, S13, S14,
            S21, S22, S23, S24,
            S31, S32, S33, S34,
            S41, S42, S43, S44],

  fd_domain(Solution, 1, 4),

  Row1 = [S11, S12, S13, S14],
  Row2 = [S21, S22, S23, S24],
  Row3 = [S31, S32, S33, S34],
  Row4 = [S41, S42, S43, S44],

  Col1 = [S11, S21, S31, S41],
  Col2 = [S12, S22, S32, S42],
  Col3 = [S13, S23, S33, S43],
  Col4 = [S14, S24, S34, S44],

  Square1 = [S11, S12, S21, S22],
  Square2 = [S13, S14, S23, S24],
  Square3 = [S31, S32, S41, S42],
  Square4 = [S33, S34, S43, S44],

  valid([Row1, Row2, Row3, Row4,
         Col1, Col2, Col3, Col4,
         Square1, Square2, Square3, Square4]).

print_sudoku(List) :-
    length(List, 16),
    print_rows(List, 0).
print_rows([], _).
print_rows([Head|Tail], Count) :-
    write('    '),
    write(Head),
    (Count mod 4 =:= 3 -> nl ; tab(3)),
    NewCount is Count + 1,
    print_rows(Tail, NewCount).

solve_and_print(Sudoku) :-
  sudoku(Sudoku, Solution),
  print_sudoku(Solution).