## Problem:

Let S(A) represent the sum of elements in set A of size n. We shall call it a special sum set if for any two non-empty disjoint subsets, B and C, the following properties are true:

1. S(B) [≠] S(C); that is, sums of subsets cannot be equal.
2. If B contains more elements than C then S(B) [>] S(C).

For this problem we shall assume that a given set contains n strictly increasing elements and it already satisfies the second rule.

Surprisingly, out of the 25 possible subset pairs that can be obtained from a set for which n = 4, only 1 of these pairs need to be tested for equality (first rule). Similarly, when n = 7, only 70 out of the 966 subset pairs need to be tested.

For n = 12, how many of the 261625 subset pairs that can be obtained need to be tested for equality?

NOTE: This problem is related to problems 103 and 105.

25164150

## Code:The solution may include methods that will be found here: Library.java .

public interface EulerSolution{public String run();}
/*  * Solution to Project Euler problem 6 * By Nayuki Minase *  * http://nayuki.eigenstate.org/page/project-euler-solutions * https://github.com/nayuki/Project-Euler-solutions */public final class p006 implements EulerSolution {		public static void main(String[] args) {		System.out.println(new p006().run());	}			private static final int N = 100;			public String run() {		int sum = 0;		int sum2 = 0;		for (int i = 1; i <= N; i++) {			sum += i;			sum2 += i * i;		}		/* 		 * For the mathematically inclined:		 *   sum  = N(N + 1) / 2.		 *   sum2 = N(N + 1)(2N + 1) / 6.		 */		return Integer.toString(sum * sum - sum2);	}	}