/*

    Problem151.java
    CIS 160
    David Klick
    2015-09-11

    Solves Project Euler problem 151
*/

public class Problem151 {
    static int count = 0;

    public static void main(String[] args) {
        System.out.printf("%8.6f\n", f(1,1,1,1));
    }
    
    private static double f(int a, int b, int c, int d) {
        if (a+b+c+d==1) {
            if (d==1) return 0.0;
            if (a==1) return 1.0 + f(0,1,1,1);
            if (b==1) return 1.0 + f(0,0,1,1);
            else return 1.0 + f(0,0,0,1);
        } else {
            double tot = a + b + c + d;
            double result = 0.0;
            if (a > 0) result += (a / tot) * f(a-1,b+1,c+1,d+1);
            if (b > 0) result += (b / tot) * f(a,b-1,c+1,d+1);
            if (c > 0) result += (c / tot) * f(a,b,c-1,d+1);
            if (d > 0) result += (d / tot) * f(a,b,c,d-1);
            return result;
        }
    }
}

/*  Output:

    0.464399
*/