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2025 SSMO Relay Round 4 Problems/Problem 2

Revision as of 11:44, 9 September 2025 by Pinkpig (talk | contribs) (Created page with "==Problem== Let <math>T = TNYWR.</math> Jonathan and Kate are playing a game with <math>n</math> sticks. On each turn, a player may remove <math>1,</math> <math>2,</math> or...")
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Problem

Let $T = TNYWR.$ Jonathan and Kate are playing a game with $n$ sticks. On each turn, a player may remove $1,$ $2,$ or $3$ sticks. The player who picks up the last stick loses. Kate is first to remove sticks, and both players play optimally. For how many values of $n$ in the range $\left[T^3,2T^3\right]$ does Kate have a winning strategy?

Solution

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