valid([]).

valid([Head|Tail]) :-

fd_all_different(Head),

valid(Tail).

coloring(Puzzle, Solution) :-

Solution = Puzzle,

Puzzle = [A1, A2, A3, A4, A5, A6,

B1, B2, B3, B4, B5, B6,

C1, C2, C3, C4, C5, C6,

D1, D2, D3, D4, D5, D6,

E1, E2, E3, E4, E5, E6,

F1, F2, F3, F4, F5, F6],

fd_domain(Puzzle, 1, 6),

RowA = [A1, A2, A3, A4, A5, A6],

RowB = [B1, B2, B3, B4, B5, B6],

RowC = [C1, C2, C3, C4, C5, C6],

RowD = [D1, D2, D3, D4, D5, D6],

RowE = [E1, E2, E3, E4, E5, E6],

RowF = [F1, F2, F3, F4, F5, F6],

Col1 = [A1,B1,C1,D1,E1,F1],

Col2 = [A2,B2,C2,D2,E2,F2],

Col3 = [A3,B3,C3,D3,E3,F3],

Col4 = [A4,B4,C4,D4,E4,F4],

Col5 = [A5,B5,C5,D5,E5,F5],

Col6 = [A6,B6,C6,D6,E6,F6],

Ones = [A1,B5,C2,E6,F4],

Twos = [A5,B1,C4,D6,E2,F3],

Threes = [A2,B6,C3,D4,E5,F1],

Fours = [A3,B4,C6,D2,E1,F5],

Fives = [A4,B2,C5,D1,E3,F6],

Zeros = [A6,C1,D5,E4,F2],

valid([RowA, RowB, RowC,RowD, RowE, RowF,Col1, Col2, Col3, Col4, Col5, Col6, Ones, Twos, Threes, Fours, Fives, Zeros]),

fd_labeling(Puzzle).