AMO-Bench 2025 Problem 46

Answer

There are $n\times n\times n$ mud blocks on the ground. A miner starts digging through one of the blocks. Each time, he can only dig a face-adjacent block until all blocks are dug out. If he digs the blocks consecutively and for $n$ times these blocks are all in a line, then the miner is described as to have dug a straight line'' once. Find the maximum possible number the miner can dig a straight line''.

Dataset text AMO-Bench. Open licence.

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When $n = 2$ , the number is 7; When $n \geq 3$ , the number is ${n}^{2} + 2$

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