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

sudoku(Puzzle, Solution) :-
  Solution = Puzzle,
  Puzzle = [S11, S12, S13, S14, S15, S16, S17, S18, S19,
            S21, S22, S23, S24, S25, S26, S27, S28, S29,
            S31, S32, S33, S34, S35, S36, S37, S38, S39,
            S41, S42, S43, S44, S45, S46, S47, S48, S49,
            S51, S52, S53, S54, S55, S56, S57, S58, S59,
            S61, S62, S63, S64, S65, S66, S67, S68, S69,
            S71, S72, S73, S74, S75, S76, S77, S78, S79,
            S81, S82, S83, S84, S85, S86, S87, S88, S89,
            S91, S92, S93, S94, S95, S96, S97, S98, S99],

  fd_domain(Puzzle, 1, 9),

  Row1 = [S11, S12, S13, S14, S15, S16, S17, S18, S19],
  Row2 = [S21, S22, S23, S24, S25, S26, S27, S28, S29],
  Row3 = [S31, S32, S33, S34, S35, S36, S37, S38, S39],
  Row4 = [S41, S42, S43, S44, S45, S46, S47, S48, S49],
  Row5 = [S51, S52, S53, S54, S55, S56, S57, S58, S59],
  Row6 = [S61, S62, S63, S64, S65, S66, S67, S68, S69],
  Row7 = [S71, S72, S73, S74, S75, S76, S77, S78, S79],
  Row8 = [S81, S82, S83, S84, S85, S86, S87, S88, S89],
  Row9 = [S91, S92, S93, S94, S95, S96, S97, S98, S99],

  Col1 = [S11, S21, S31, S41, S51, S61, S71, S81, S91],
  Col2 = [S12, S22, S32, S42, S52, S62, S72, S82, S92],
  Col3 = [S13, S23, S33, S43, S53, S63, S73, S83, S93],
  Col4 = [S14, S24, S34, S44, S54, S64, S74, S84, S94],
  Col5 = [S15, S25, S35, S45, S55, S65, S75, S85, S95],
  Col6 = [S16, S26, S36, S46, S56, S66, S76, S86, S96],
  Col7 = [S17, S27, S37, S47, S57, S67, S77, S87, S97],
  Col8 = [S18, S28, S38, S48, S58, S68, S78, S88, S98],
  Col9 = [S19, S29, S39, S49, S59, S69, S79, S89, S99],

  Square1 = [S11, S12, S13, S21, S22, S23, S31, S32, S33],
  Square2 = [S14, S15, S16, S24, S25, S26, S34, S35, S36],
  Square3 = [S17, S18, S19, S27, S28, S29, S37, S38, S39],
  Square4 = [S41, S42, S43, S51, S52, S53, S61, S62, S63],
  Square5 = [S44, S45, S46, S54, S55, S56, S64, S65, S66],
  Square6 = [S47, S48, S49, S57, S58, S59, S67, S68, S69],
  Square7 = [S71, S72, S73, S81, S82, S83, S91, S92, S93],
  Square8 = [S74, S75, S76, S84, S85, S86, S94, S95, S96],
  Square9 = [S77, S78, S79, S87, S88, S89, S97, S98, S99],

  valid([Row1, Row2, Row3, Row4, Row5, Row6, Row7, Row8, Row9]),
  valid([Col1, Col2, Col3, Col4, Col5, Col6, Col7, Col8, Col9]),
  valid([Square1, Square2, Square3,
         Square4, Square5, Square6,
         Square7, Square8, Square9]).

print_sudoku(List) :-
    length(List, 81),
    print_rows(List, 0).
print_rows([], _).
print_rows([Head|Tail], Count) :-
    write('    '),
    write(Head),
    (Count mod 9 =:= 8 -> nl ; tab(3)),
    NewCount is Count + 1,
    print_rows(Tail, NewCount).

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