i am coding a simple game. it consists of a balance (as in, a set of scales) and a set of items that may be placed on it.

the object is to place the correct items on the scale, such that it balances. there is only one possible solution to the problem.

what i'm looking for, then, is a set of numbers with two (and only two) subsets whose sums are equal. i realize how important linguistic precision is with respect to mathematical discussions, so if my meaning isn't clear, let me know.

how do i approach this problem logically? the set in this instance is quite small, but i'd llike to be able to apply what i learn here - if anything - to similar problems in the future.