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There are 300 matches in a box. On a turn, it is allowed to take no more than half of the matches in the box. The player who cannot make a move loses.

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Official solution

The first player wins. Winning positions are those in which there are $2^{n}$ - 1 matches left in the box.

The first move is to leave 255 matches.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.