Question4390194a.java

import java.util.ArrayList;
import java.util.List;
import java.util.Random;

public class Question4390194a {
    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 List<Integer> triples = new ArrayList<>();
    
    static {
        for (int a : families [0])
            for (int b : families [1])
                if (b != a)
                    for (int c : families [2])
                        if (c != a && c != b)
                            triples.add ((1 << a) | (1 << b) | (1 << c));
    }
    

    public static void main(String [] args) {
        int s = triples.size();
        int [] c = new int [7];
        for (int bits = 1;bits < 1 << s;bits++) {
            int b = 0;
            int sign = -1;
            for (int i = 0;i < s;i++)
                if ((bits & (1 << i)) != 0) {
                    b |= triples.get(i);
                    sign = -sign;
                }
            int count = 0;
            for (int i = 1;i <= 6;i++)
                if ((b & (1 << i)) != 0)
                    count++;
            c [count] += sign;
        }

        for (int i = 3;i < 7;i++)
            System.out.println(i + " : " + c [i]);
        System.out.println();
        
        long nrolls = 0;
        for (int n = 0;n < ntrials;n++) {
            int seen = 0;
            outer:
            for (;;) {
                int roll = random.nextInt(6);
                nrolls++;
                seen |= 1 << (roll + 1);
                for (int t : triples)
                    if ((seen & t) == t)
                        break outer;
            }
        }
        System.out.println(nrolls / (double) ntrials);
    }
}