Classic olympiad problem · Combinatorics
Prove that in any sequence of mn+1 distinct reals, there is an…
Prove that in any sequence of distinct reals, there is an increasing subsequence of length or a decreasing one of length .
This is a proof problem. The answer is an argument, not a number. The solution is deliberately not posted here: reading a solution you didn't fight for teaches almost nothing. On Lemma you attempt it cold, take one of the 3 progressive hints only when genuinely stuck, then compare your proof against a full walkthrough and mark yourself with the same rubric a competition coordinator would use.
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