Count the number of surface paths from a vertex to the opposite vertex of a Rubik's Cube; see http://math.stackexchange.com/questions/317288.

Question317288.java

public class Question317288 {
    final static int d = 3;
    final static int n = 3;

    final static int [] state = new int [d];

    static int count;

    public static void main (String [] args) {
        recurse ();
        System.out.println (count);
    }

    static void recurse () {
        int count0 = 0;
        int countn = 0;
        
        for (int i = 0;i < d;i++) {
            if (state [i] == 0)
                count0++;
            else if (state [i] == n)
                countn++;
        }

        if (countn == d)
            count++;
        else if (count0 + countn > 0)
            for (int i = 0;i < d;i++)
                if (state [i] < n) {
                    state [i]++;
                    recurse ();
                    state [i]--;
                }
    }
}