about 2 months ago
Bob can force a win if and only if \(n\) is divisible by 8; there are 252 such positive integers \(\leq 2024\).
combinatorial game theory
winning and losing positions
modular pattern analysis
counting losing positions
Losing (Bob-win) positions: \(n \equiv 0 \pmod{8}\) Count of \(n \leq 2024\) with \(n \equiv 0 \pmod{8}\), \(n > 0\): 252
Cost
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Output
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