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anthropic

claude-opus-4

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Our most capable and intelligent model yet. Claude Opus 4 sets new standards in complex reasoning and advanced coding

Input:$15 / 1M tokens
Output:$75 / 1M tokens
Context:200K tokens
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image
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6 available
include_reasoning
max_tokens
stop
temperature
012
tool_choice
tools
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    Bob wins when n ≡ 0 or 2 (mod 5), n > 0 Count n ≤ 2024 satisfying this: - Multiples of 5 up to 2024 (excluding 0): From 5 to 2020 → (2020/5) = 404 numbers - Numbers ≡ 2 mod 5 up to 2024: Sequence: 2, 7, 12, ..., 2022 Count = ((2022 - 2) / 5) + 1 = (2020/5) + 1 = 404 + 1 = 405 Total = 404 + 405 = 809 **Final answer:** **Bob has a forced winning strategy for 809 values of n ≤ 2024.**
    about 1 month ago
    Bob has a winning strategy exactly when n ≡ 0 or 2 (mod 5); for positive n ≤ 2024, there are 809 such values.
    combinatorial game theory
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