Let S be a set of ten integers chosen from 1 through 50. Show that the

set has at least two different (but not necessarily disjoint) subsets

of exactly four integers each that add up to the same number. (For

instance, if S = {3,8,9,18,24,34,35,41,44,50} then the subsets can be

taken to be {8,24,34,35} and {9,18,24,50}; these borth have sums of

101.Show this using the pigeonhole principle.

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