2018 年刑偵科推理試題 https://photos.app.goo.gl/suY5DO8ozd8HtvGj1

solver.m

lis = {1, 2, 3, 4};
all = Flatten[ 
  Outer[ List,
    lis, lis, lis, lis, lis,
    lis, lis, lis, lis, lis
  ], 9
];

q2[l_] := 
  l[[2]] == 1 && l[[5]] == 3 || 
  l[[2]] == 2 && l[[5]] == 4 ||
  l[[2]] == 3 && l[[5]] == 1 || 
  l[[2]] == 4 && l[[5]] == 2;

q3[l_] := 
  l[[3]] == 1 && (l[[6]] == l[[2]] == l[[4]] != l[[3]]) ||
  l[[3]] == 2 && (l[[3]] == l[[4]] == l[[2]] != l[[6]] ) ||   
  l[[3]] == 3 && (l[[3]] == l[[6]] == l[[4]] != l[[2]] ) || 
  l[[3]] == 4 && (l[[3]] == l[[2]] == l[[6]] != l[[4]]);

q4[l_] :=
  l[[4]] == 1 && l[[1]] == l[[5]] ||
  l[[4]] == 2 && l[[2]] == l[[7]] ||
  l[[4]] == 3 && l[[1]] == l[[9]] ||
  l[[4]] == 4 && l[[6]] == l[[10]];

q5[l_] :=
  l[[5]] == 1 == l[[8]] ||
  l[[5]] == 2 == l[[4]] ||
  l[[5]] == 3 == l[[9]] ||
  l[[5]] == 4 == l[[7]];

q6[l_] :=
  l[[6]] == 1 && (l[[8]] == l[[2]] == l[[4]]) ||
  l[[6]] == 2 && (l[[8]] == l[[1]] == l[[6]]) ||
  l[[6]] == 3 && (l[[8]] == l[[3]] == l[[10]]) ||
  l[[6]] == 4 && (l[[8]] == l[[5]] == l[[9]]);

q7[l_] := Module[{cnt, mi},
  cnt = BinCounts[l, {1, 5, 1}];
  mi = MinimalBy[Range[4], cnt[[#]] &] // First;
  l[[7]] == 1 && mi == 3 ||
  l[[7]] == 2 && mi == 2 ||
  l[[7]] == 3 && mi == 1 ||
  l[[7]] == 4 && mi == 4
];

q8[l_] :=
  l[[8]] == 1 && Abs[l[[7]] - l[[1]]] > 1 ||
  l[[8]] == 2 && Abs[l[[5]] - l[[1]]] > 1 ||
  l[[8]] == 3 && Abs[l[[2]] - l[[1]]] > 1 ||   
  l[[8]] == 4 && Abs[l[[10]] - l[[1]]] > 1;

q9[l_] := 
  l[[9]] == 1 && Xor[l[[1]] == l[[6]], l[[6]] == l[[5]]] ||
  l[[9]] == 2 && Xor[l[[1]] == l[[6]], l[[10]] == l[[5]]] ||
  l[[9]] == 3 && Xor[l[[1]] == l[[6]], l[[2]] == l[[5]]] ||
  l[[9]] == 4 && Xor[l[[1]] == l[[6]], l[[9]] == l[[5]]];

q10[l_] := Module[{cnt, mx, mi},
  cnt = BinCounts[ l, {1, 5, 1}];
  mx = Max[cnt];
  mi = Min[cnt];
  l[[10]] == 1 && mx - mi == 3 ||
  l[[10]] == 2 && mx - mi == 2 ||
  l[[10]] == 3 && mx - mi == 4 ||
  l[[10]] == 4 && mx - mi == 1
]

sat[lis_] := Module[{},
  q2[lis] && 
  q5[lis] &&
  q3[lis] && 
  q4[lis] &&  
  q6[lis] &&
  q7[lis] &&
  q8[lis] &&
  q9[lis] &&
  q10[lis]
];

ans = Select[all, sat]
(* {{2, 3, 1, 3, 1, 3, 4, 1, 2, 1}} *)