Using the mathod of mathematical induction

[cocobaby]

Homework Statement

Let H be a ten- element set of potive integers ranged from 1 to 99. Prove that H has two disjoint subsets A and B so that the sum of the elements of A is equal to the sum of the elements of B.

 

[boboYO]

This is a pigeonhole question, not an induction question.
hint:

If you have 10 different numbers, how many different ways can you choose a subset of them? (to make a sum)and also,

what is the range of answers you can possibly get? (numbers chosen from 1-99 and up to a maximum of 10 numbers)