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AMO-Bench 2025 Problem 48

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A city is going to be built as a 10×1010\times 10 square grid of blocks. Now, the city is planning to set up security booths in some blocks. To ensure the safety of the entire city, city safety regulations require that for any block (regardless of whether it has a security booth itself), at least one of its four adjacent blocks (up, down, left, right) must have a security booth. How many security booths are needed at a minimum to satisfy the safety regulations?

Dataset text AMO-Bench. Open licence.

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