Question 3
Let $n\ge2$ be an integer. An $n\times n$ board is empty. Each minute one may place stones in all three empty cells of a fixed-orientation L tromino (rotations not allowed), or remove all stones from a completely filled row, or from a completely filled column. The L consists of its bottom-left, bottom-right and top-left cells.
For which $n$ can a nonempty sequence of moves return the board to empty?
Proposed by Alex Zhai, Shaunak Kishore. Evan Chen’s third-party solution notes: https://aops.com/community/p21498538; source video https://youtu.be/9WNgDETHOlI?t=2325. One point is nonofficial editorial normalization; manual essay grading only.
For which $n$ can a nonempty sequence of moves return the board to empty?
Proposed by Alex Zhai, Shaunak Kishore. Evan Chen’s third-party solution notes: https://aops.com/community/p21498538; source video https://youtu.be/9WNgDETHOlI?t=2325. One point is nonofficial editorial normalization; manual essay grading only.