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The Counting Game

Unreviewed import — a classic from the public domain; its solution has not been machine-checked yet.

math
Two players take turns saying numbers starting from 1, where the highest number they can say is 10. Each player must add numbers that total up to exactly 100. The player who says the number that makes the total exactly 100 wins. If you start the game by saying 1, can you always guarantee a win?

Solution

Commit an attempt to unseal the proof. Write your answer — right or wrong, thinking it through is the point.

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