ISL 2023 C5
- Answer
Elisa has 2023 treasure chests, all of which are unlocked and empty at first. Each day, Elisa adds a new gem to one of the unlocked chests of her choice, and afterwards, a fairy acts according to the following rules: - if more than one chests are unlocked, it locks one of them, or - if there is only one unlocked chest, it unlocks all the chests. Given that this process goes on forever, prove that there is a constant with the following property: Elisa can ensure that the difference between the numbers of gems in any two chests never exceeds , regardless of how the fairy chooses the chests to lock. (Israel)
Official text Transcription from NuminaMath olympiads, checked word for word against the official paper. Quoted with source.
Official text: IMO 2023 Shortlist booklet, page 8.
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3 n(n-1)+n
Solutions
Official solution Solution 1 by the IMO Problem Selection Committee
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