Backtracking

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

// Exercise description:
// The numbers 1-8 are distributed over a cube with the corners a, b, c, d, e, f, g, h.
// The sum of the corners of every surface must be 18.
// Write a method in C# - using backtracking - to create a list of all possible cube configurations.

namespace TentProg3 {
    class Program {
        public static List<List<int>> magicCube() {
            List<List<int>> cubes = new List<List<int>>();
            for (int a = 1; a < 9; a++) {
                for (int b = 1; b < 9; b++) {
                    if (a != b) {
                        for (int c = 1; c < 9; c++) {
                            if ((c != a) && (c != b)) {
                                for (int d = 1; d < 9; d++) {
                                    if ((d != a) && (d != b) && (d != c)) {
                                        if (a + b + c + d != 18)
                                            continue;
                                        for (int e = 1; e < 9; e++) {
                                            if ((e != a) && (e != b) && (e != c) && (e != d)) {
                                                for (int f = 1; f < 9; f++) {
                                                    if ((f != a) && (f != b) && (f != c) && (f != d) && (f != e)) {
                                                        if (a + b + e + f != 18)
                                                            continue;
                                                        for (int g = 1; g < 9; g++) {
                                                            if ((g != a) && (g != b) && (g != c) && (g != d) && (g != e) && (g != f)) {
                                                                if (b + c + f + g != 18)
                                                                    continue;
                                                                for (int h = 1; h < 9; h++) {
                                                                    if ((h != a) && (h != b) && (h != c) && (h != d) && (h != e) && (h != f) && (h != g)) {
                                                                        if ((e + f + g + h != 18) && (a + d + h + e != 18) && (c + d + h + g != 18))
                                                                            continue;
                                                                        List<int> cube = new List<int>();
                                                                        cube.Add(a);
                                                                        cube.Add(b);
                                                                        cube.Add(c);
                                                                        cube.Add(d);
                                                                        cube.Add(e);
                                                                        cube.Add(f);
                                                                        cube.Add(g);
                                                                        cube.Add(h);
                                                                        cubes.Add(cube);
                                                                    }
                                                                }
                                                            }
                                                        }
                                                    }
                                                }
                                            }
                                        }
                                    }
                                }
                            }
                        }
                    }
                }
            }

            return cubes;
        }
    }
}