about 1 month ago
Pattern of losing (P) positions are those where \( n \equiv 0, 2, \text{ or } 5 \pmod{6} \); counting these up to 2024 gives 1013 integers where Bob can force a win.
combinatorial game theory
winning and losing positions
modular pattern
forced winning strategy
Bob’s winning positions: \(n \equiv 0, 2, 5 \pmod{6}\); total count for \(n \leq 2024\) is \(\boxed{1013}\).
Cost
$0
Input
0tokens
Output
0tokens
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