olymmath

RU-ALLRUSSIAN 1973 Problem 6

    Players numbered 1 to 1024 play in a knock- out tournament. There are no draws, the winner of a match goes through to the next round and the loser is knocked- out, so that there are 512 matches in the first round, 256 in the second and so on. If m plays n and m<n−2\mathrm{m}< \mathrm{n} - 2 then m always wins. What is the largest possible number for the winner?

    Dataset text NuminaMath olympiads. Quoted with source.

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