random - Given 4 numbers of array of 1 to 10 elements. Find 3 numbers whose sum can generate all the four numbers? -

i given array containing list of 4 random numbers (1 10 inclusive). supposed generate list of 3 numbers (1 10 inclusive) can generate 4 numbers of initial list adding 3 numbers of generated list.

someone please provide algorithm doing this.

since solution contains 3 numbers in 1..10 range, brute force effective algorithm here (at 1000 possibilities check in naive implementation). c# code be

public static int[] bruteforce(int[] data) {   hashset<int> hs = new hashset<int>();    (int x = 1; x <= 10; ++x)     (int y = x; y <= 10; ++y)       (int z = y; z <= 10; ++z) {         hs.clear();          (int = 0; < data.length; ++i)           hs.add(data[i]);          hs.remove(x);         hs.remove(y);         hs.remove(z);          hs.remove(x + y);         hs.remove(x + z);         hs.remove(y + z);          hs.remove(x + y + z);          if (hs.count <= 0)            return new int[] { x, y, z }; // <- solution       }    return new int[] {}; // <- no solution found } 

some test cases:

1. bruteforce(new int[] {1, 3, 7, 8}); // <- [1, 2, 5]
2. bruteforce(new int[] {1, 3, 7, 9}); // <- [1, 2, 6]
3. bruteforce(new int[] {1, 6, 7, 9}); // <- [1, 2, 6]; same previous case
4. bruteforce(new int[] {4, 6, 7, 9}); // <- [1, 3, 6]
5. bruteforce(new int[] {5, 6, 7, 9}); // <- [2, 3, 4]
6. bruteforce(new int[] {1, 2, 4, 8}); // <- no solution found

even problem set (all possible lists of 4 items in 1..10 range) small enough (10000 items) solved brute force algorithm implemented above. can find out 768 4-items lists 10000 can't generated 3-items lists.