:- use_module(library(clpfd)).

magique3(C):-
    length(C,9),
    C ins 1..9,
    all_distinct(C),
    contraintes(C),
    label(C).

contraintes(C):-
    C = [C11,C12,C13,C21,C22,C23,C31,C32,C33],
    SL1 #= C11+C12+C13,
    SL1 #= C21+C22+C23,
    SL1 #= C31+C32+C33,
    
    SL1 #= C11+C21+C31,
    SL1 #= C12+C22+C32,
    SL1 #= C13+C23+C33,

    SL1 #= C11+C22+C33,
    SL1 #= C13+C22+C31.

machine(T,P,L,R) :-
    L = [E2,E1,C50,C20,C10],
    R = [R2,R1,R50,R20,R10],
    RV #= T - P,
    R2 * 200 + R1 * 100 + R50 * 50 + R20 * 20 + R10*10 #= RV,
    R2 in 0..E2,
    R1 in 0..E1,
    R50 in 0..C50,
    R20 in 0..C20,
    R10 in 0..C10,
    label(R).

puzzle([C,R,O,S,S] + [R,O,A,D,S] = [D,A,N,G,E,R]
) :-
    C in 1..9,
    R in 1..9,
    D in 1..9,
    O in 0..9,
    S in 0..9,
    A in 0..9,
    N in 0..9,
    E in 0..9,
    G in 0..9,
    all_distinct([C,R,D,O,S,A,N,E,G]),
    C*10000 + R*1000 + O*100 + S*10 +S+ R*10000+ O*1000+ A*100+ D*10+ S #= D*100000+ A*10000+ N*1000+ G*100+ E*10 +R,
    label([C,R,D,O,S,A,N,E,G]).