Question4390194b.java

import java.util.Random;

public class Question4390194b {
    final static Random random = new Random();
    
    final static int ntrials = 100000000;
    
    final static int [] [] families = {
            {2,4,6},
            {2,3,5},
            {1,4},
    };
    
    final static int [] [] permutations = {
            {0,1,2},
            {0,2,1},
            {1,0,2},
            {1,2,0},
            {2,0,1},
            {2,1,0},
    };
    
    final static int [] bits = new int [families.length];
    
    static {
        for (int i = 0;i < families.length;i++)
            for (int roll : families [i])
                bits [i] |= 1 << (roll - 1);
    }
    
    public static void main(String [] args) {
        long nrolls = 0;
        for (int n = 0;n < ntrials;n++) {
            int [] seen = new int [6];
            outer:
            for (;;) {
                int roll = 1 << random.nextInt(6);
                nrolls++;
                for (int p = 0;p < 6;p++)
                    if ((bits [permutations [p] [seen [p]]] & roll) != 0)
                        if (++seen [p] == 3)
                            break outer;
            }
        }
        System.out.println(nrolls / (double) ntrials);
    }
}