dice.cc

/**
 * This program answers a fundamental question to life:
 * 
 * Are there three dices A, B and C that satisfies P[A > B], P[B > C], P[C > A] > 5/9?
 *
 * It turns out there is.
 */

#include <cstdio>

int main() {
  for (int a1 = 1; a1 < 6; ++a1) for (int a2 = a1 + 1; a2 <= 6; ++a2) for (int ar = 1; ar < 6; ++ar)
    for (int b1 = 1; b1 < 6; ++b1) for (int b2 = b1 + 1; b2 <= 6; ++b2) for (int br = 1; br < 6; ++br)
      if ((a1 > b1) * ar * br + (a1 > b2) * ar * (6 - br) + (a2 > b1) * (6 - ar) * br + (a2 > b2) * (6 - ar) * (6 - br) > 20)
        for (int c1 = 1; c1 < 6; ++c1) for (int c2 = c1 + 1; c2 <= 6; ++c2) for (int cr = 1; cr < 6; ++cr)
          if ((b1 > c1) * br * cr + (b1 > c2) * br * (6 - cr) + (b2 > c1) * (6 - br) * cr + (b2 > c2) * (6 - br) * (6 - cr) > 20 &&
              (c1 > a1) * cr * ar + (c1 > a2) * cr * (6 - ar) + (c2 > a1) * (6 - cr) * ar + (c2 > a2) * (6 - cr) * (6 - ar) > 20) {
            printf("A: ");
            for (int i = 0; i < 6; ++i) printf("%d ", i < ar ? a1 : a2);
            printf("\nB: ");
            for (int i = 0; i < 6; ++i) printf("%d ", i < br ? b1 : b2);
            printf("\nC: ");
            for (int i = 0; i < 6; ++i) printf("%d ", i < cr ? c1 : c2);
            printf("\nA > B: %d/36, B > C: %d/36, C > A: %d/36\n\n",
                   (a1 > b1) * ar * br + (a1 > b2) * ar * (6 - br) + (a2 > b1) * (6 - ar) * br + (a2 > b2) * (6 - ar) * (6 - br),
                   (b1 > c1) * br * cr + (b1 > c2) * br * (6 - cr) + (b2 > c1) * (6 - br) * cr + (b2 > c2) * (6 - br) * (6 - cr),
                   (c1 > a1) * cr * ar + (c1 > a2) * cr * (6 - ar) + (c2 > a1) * (6 - cr) * ar + (c2 > a2) * (6 - cr) * (6 - ar));
          }
  return 0;
}