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DANUBE 2015 Problem 5

    A lantern needs exactly 22 charged batteries in order to work.We have available nn charged batteries and nn uncharged batteries, n≥4n\ge 4 (all batteries look the same). A try consists in introducing two batteries in the lantern and verifying if the lantern works.Prove that we can find a pair of charged batteries in at most n+2n+2 tries.

    Dataset text AI-MO AoPS. Quoted with source.

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