Problem 6

A vegetable patch is a square grid of $n$ by $n$ uncleared cells with $n \ge 3$ and $n$ odd. Mo the mole is in the centre cell and digs it up to clear it.

Mo then digs up cells one at a time according to the following rule. Mo can dig up an uncleared cell that is both adjacent horizontally or vertically to a cleared cell and in the middle of a line of three uncleared cells in the vegetable patch.

After digging up $M$ squares, Mo can dig no further. Find in terms of $n$ the smallest $M$ for which this can happen and prove there is no smaller value.