Bob wins when the initial \(n \equiv 0 \text{ or } 2 \pmod{5}\); there are 404 multiples of 5 and 405 numbers \( \equiv 2 \pmod{5} \) up to 2024, totaling 809 such \(n\).
combinatorial game theory
winning strategy
modular pattern
token removal game
Bob wins for \( n \equiv 0 \text{ or } 2 \pmod{5} \); total count up to 2024 is **809**.
Cost
$0
Input
0tokens
Output
0tokens
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