olymmath

BALKAN-SL 2021 C3

    In an exotic country, the National Bank issues coins that can take any value in the interval [0,1][0,1]. Find the smallest constant c>0c>0 such that the following holds, no matter the situation in that country:

    Any citizen of the exotic country that has a finite number of coins, with a total value of no more than 1000, can split those coins into 100 boxes, such that the total value inside each box is at most c.

    Dataset text NuminaMath olympiads. Quoted with source.

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