using System;

using System.Collections;

​

public class Program

{

    public static ArrayList combos(int nDice, int tot, int max)

    {

        var res = new ArrayList();

        combos(res, "", nDice, tot, max);

        return res;

    }

​

    private static void combos(ArrayList res, String sol, int nDice, int tot, int max)

    {

        if(tot == 0)

        {

            res.Add(sol);

            return;

        }

        for(int side = 1+(tot-1)/nDice; side <= Math.Min(tot, max); side++)

            combos(res, sol+side, nDice-1, tot-side, side);

    }

​

    public static void Main (string[] args) {

        int nDice = 3;

        int nFaces = 4;

        for(int tot=1; tot<=nDice*nFaces+1; tot++)

        {

            Console.WriteLine ("\ntot: " + tot);

            foreach (var combo in combos(nDice, tot, nFaces)) {

                Console.WriteLine (combo);

            }

        }

    }

}