sol.cs

using System;
using System.Collections.Generic;

public class Program {
  public static void Main(string[] args) {
    var K = 3;
    var A = new[]{8, 7, 5, 6, 10};
    //var A = new[]{9, 6};
    var res = Sol.Solution(A, K);

    Console.WriteLine($"Solution: {res}");
  }
}
public static class Sol {
  public static int Solution(int[] rolls, int k)
  {
    var counter = 0;
    void bt(int curIndex, int size, List<int> cur, HashSet<int> friends)
    {
      if (cur.Count == size)
      {
        foreach (var c in cur)
          Console.Write($"{c}, ");
        Console.WriteLine();
        counter++;
        return;
      }

      for (var i = curIndex; i < rolls.Length; ++i)
      {
        if (friends.Contains(rolls[i]))
          continue;
        friends.Add(rolls[i] + k);
        friends.Add(k - rolls[i]);
        friends.Add(rolls[i] - k);
        cur.Add(rolls[i]);
        bt(i + 1, size, cur, friends);
        if (cur.Count == 0)
          continue;
        cur.RemoveAt(cur.Count - 1);
        friends.Remove(rolls[i] + k);
        friends.Remove(k - rolls[i]);
        friends.Remove(rolls[i] - k);
      }
    }

    for (var s = 1; s <= rolls.Length; ++s)
      bt(0, s, new(), new());
    return counter;
  }
}
/*
(5,7,6,8,10),(6,10),(6,5),(8,5),(10,5),(6,7), (8,7), (10,7), (6,10,5), (6,10,7)

[8,7,5,6,10] 
8     x
7     x
5     x
6     x
10    x
-------
8,7   x
8,5   x
[8,6]
[8,10]
[7,5]
7,6   x
7,10  x
5,6   x
5,10  x
6,10  x
-------
[8,7,5]
[8,7,6]
[8,7,10]
[8,5,6]
[8,5,10]
[8,6,10]
[7,5,6]
[7,5,10]
7,6,10 x
5,6,10 x
--------
[8,7,5,6]
[8,7,5,10]
[7,5,6,10]
---------
[8,7,5,6,10]
*/