about 1 month ago
Bob can force a win if n ≡ 0 or 2 (mod 5); up to 2024, there are 809 such n where Bob has a winning strategy.
combinatorial game theory
winning and losing positions
modular pattern
token removal game
P-positions: n ≡ 0 or 2 (mod 5); Count n ≤ 2024 with n mod 5=0 → 404 values, n mod 5=2 → 405 values; Total = 404 + 405 = **809**.
Cost
$0
Input
0tokens
Output
0tokens
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