IMO 1972, Problem 1 · Combinatorics
IMO 1972, Problem 1
Prove that from a set of ten distinct two-digit numbers, one can always choose two disjoint non-empty subsets whose members have the same sum.
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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This problem sits in the Olympiad Set: 89 proof problems (real IMO problems and the classics) with progressive hints, full walkthroughs and marking rubrics. 125 lessons, 1206 curated problems and unlimited generated practice at six difficulties. Free to start, no card, and every paid plan opens with 3 free days.
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