In the halving problem with 305 numbers, what is the minimum number of halving operations required to reach 0?

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Multiple Choice

In the halving problem with 305 numbers, what is the minimum number of halving operations required to reach 0?

Explanation:
Each halving is floor division by 2, so after n halvings the value becomes floor(305 / 2^n). To reach zero, you need 2^n to exceed 305. Since 2^8 = 256 is not enough but 2^9 = 512 is, the smallest n that works is 9. You can also think in binary terms: 305 sits between 2^8 and 2^9, so it has 9 binary digits, and you need nine halvings to drop to zero. Therefore, the minimum number of halving operations is 9.

Each halving is floor division by 2, so after n halvings the value becomes floor(305 / 2^n). To reach zero, you need 2^n to exceed 305. Since 2^8 = 256 is not enough but 2^9 = 512 is, the smallest n that works is 9. You can also think in binary terms: 305 sits between 2^8 and 2^9, so it has 9 binary digits, and you need nine halvings to drop to zero. Therefore, the minimum number of halving operations is 9.

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