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.**
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Discussion about 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.**
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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.**
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