Prolog密码算术拼图

我被要求用Prolog解决一个Cryptarithmetic Puzzle:

GIVE
* ME 
------
MONEY

以上是谜题,我无法弄清楚问题出在哪里,结果总是返回false.另外,我不允许在SWI-Prolog中使用任何库.

solve(Z) :-
    assign(Z,[0,1,2,3,4,5,6,7,8,9]),
    check(Z).

find( VAL , G,I,V,E  ) :- VAL  is G * 1000 + I * 100 + V * 10 + E.
find2(VALR, M,E      ) :- VALR is M * 10 + E.
find3(VALA, M,O,N,E,Y) :- VALA is M * 10000 + O * 1000 + N * 100 + E * 10 + Y.

check(Z) :- 
    G #>= 1, 
    M #>= 1,
    find( VAL,  G,I,V,E), 
    find2(VALR, M,E), 
    find3(VALA, M,O,N,E,Y), 
    VAL * VALR =:= VALA.

assign(Z,L) :-
    permute(L,Z).

/* permute is similar to all_different in swi-prolog */
addany(X,K,[X|K]).
addany(X,[F|K],[F|L1]) :-
    addany(X,K,L1).

permute([],[]).
permute([X|K],P) :- 
    permute(K,L1),
    addany(X,L1,P).

示例查询:

?- solve([G,I,V,E,M,O,N,Y]).
false.                          % fails unexpectedly

最佳答案 以下
article由Eric Weisstein和Ed Pegg将是有用的.它为Mathematica中的类似问题提供了几种解决方案.

使用非常强力的方法,有两种解决方案:1072 * 92 = 98624和1092 * 72 = 78624.我使用的代码:

In[16]:= Cases[
 Permutations[
  Range[0, 9], {5}], {g_, i_, v_, e_, m_} /; g > 0 && m > 0 :> 
  With[{dig = IntegerDigits[(g*10^3 + i*10^2 + v*10 + e) (10 m + e)]},
   Join[{g, i, v, e, m}, dig[[{2, 3, 5}]]] /; 
    And[Length[dig] == 5, Unequal @@ dig, dig[[{1, 4}]] == {m, e}, 
     Intersection[dig[[{2, 3, 5}]], {g, i, v, e, m}] === {} ]
   ]]

Out[16]= {{1, 0, 7, 2, 9, 8, 6, 4}, {1, 0, 9, 2, 7, 8, 6, 4}}
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