about 1 month ago
Bob has a winning strategy if and only if \( n \equiv 0 \) or \( 2 \pmod{5} \); counting these \( n \leq 2024 \) gives \(808 + 1 = 809\) such integers.
combinatorial game theory
forced winning strategy
p and n positions
modular pattern analysis
Bob wins exactly when \(n \equiv 0 \text{ or } 2 \pmod{5}\). Up to 2024, this occurs for 809 values of \(n\).
Cost
$0
Input
0tokens
Output
0tokens
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