Let S be a set of 10 distinct integers between −10 and 10 (inclusive). Prove that there exist four distinct integers in S whose average is the same as the average of just two of the four.
2026-04-01 00:25:32.1775003132
Pigeonhole Principle - prove that average of 4 integers = average of 2
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HINT: The key is to realize that it’s enough to prove that there are two different pairs of integers from $S$ that have the same average. Now you have to figure out