Classic olympiad problem · Combinatorics
There are 100 lockers, all closed. Student k toggles every k-th…
There are 100 lockers, all closed. Student toggles every -th locker, for . Prove exactly the perfect-square lockers end open.
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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