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, 2003

Combinatorics Difficulty 3.0 AMC 10/12 Prove it Canada

In a game, Xavier and Yolanda take turns calling out whole numbers. The first number called must be a whole number between and including $1$ and $9$ . Each number called after the first must be a whole number which is $1$ to $10$ greater than the previous number called. The first time the game is played, the person who calls the number $15$ is the winner. Explain why Xavier has a winning strategy if he goes first and calls $4$ .

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.