C#-Code

using System;
using System.IO;
using System.Collections.Generic;
using System.Linq;

namespace trainYourProgrammer
{
	class MainClass
	{
		static void Main(string[] args)
		{
			solutions = 0;
			Console.Write ("Anzahl der Kinder: ");
			int k = int.Parse (Console.ReadLine ());
			Console.Write ("Anzahl der Torten: ");
			int t = int.Parse (Console.ReadLine ());
			int[] pieces = new int[t];
			for (int i = 0; i < t; i++)
				pieces [i] = k;
			TakePieces (k, t, pieces, new List<int[]>());
			Console.WriteLine ("\n{0} Lösungen gefunden", solutions);
		}

		static int solutions;
		static void TakePieces(int childs, int pieces, int[] remaining, List<int[]> previous) {
			if (childs == 0) {
				Console.WriteLine (String.Join ("    ", previous.Select (x => String.Join (", ", x))));
				solutions++;
				return;
			}
			foreach (int[] take in Take(remaining, pieces)) {
				TakePieces (childs - 1, pieces, 
				            Enumerable.Range (0, remaining.Length).
				            Select (i => remaining [i] - take [i]).
				            ToArray (),
				            new List<int[]>(previous) {take}
				);
			}
		}

		//nimm genau pieces Stücke aus den verfügbaren, gib alle Möglichkeiten zurück
		static List<int[]> Take(int[] remaining, int pieces) {
			List<int[]> result = new List<int[]>();
			int[] current = new int[remaining.Length];
			TakeRecurs (remaining, pieces, current, 0, result);
			return result;
		}

		static void TakeRecurs(int[] remaining, int pieces, int[] taken, int index, List<int[]> result) {
			if (index == remaining.Length) {
				if (pieces == 0)
					result.Add (taken);
				return;
			}
			for (int take = 0; take <= Math.Min(pieces, remaining[index]); take++) {
				int[] takenNew = (int[])taken.Clone ();
				takenNew [index] = take;
				TakeRecurs (remaining, pieces - take, takenNew, index + 1, result);
			}
		}
	}
}