# Qn on Pigeon-Hole Principle

Let S be a set of 10 positive integers ≤ 50. Show that there two different (but not necessarily disjoint) subsets of four integers such that the sums of the 4 integers in the sets are equal.

Having problems identifying which should be the pigeon-hole. Would appreciate some help here.. Thanks

Hint: There are $\binom{10}{4}$ different subsets of size four but only $200$ possible sums.

• why will there be only 200 possible sums? – qwerty23 Sep 27 '14 at 5:36
• Min sum is $4$, max sum is $200$, the possible sums cannot exceed $200$. Note we don't need the exact count. – Macavity Sep 27 '14 at 5:42