Originally Posted by

**datboitom** I have this question I need to complete but I'm not sure how to get started with it. Here is the question:

Let S be a set of ten distinct integers between 1 and 50. Use the pigeonhole principle to show that there are two different 5-element subsets of S with the same sum.

An example of that would be S= {1,2,3,4,5,30,31,32,33,34} and {30,2,3,4,5} and {31,1,3,4,5} have the same sum. And I need to prove this for any 10 elements.

I don't really know how to get started with this. The only thing I have right now is that given a set of 10 elements there are: 252 distinct subsets of 5.

And I think what I need to find out is the number of summations that do not yield the same result for a given subset of 5 elements, which would have to be under 252, which would then show some of them would have to be equal.