Consider a checkerboard that extends infinitely towards the up and right directions. On the bottom-left cell (that we'll call the origin), place a single smarties.
You are allowed to perform repeatedly the following action:
- if there is a smarties on a cell and the up and right neighboring cells are empty, you can remove the smarties from the considered cell, and add a new smarties on each of the up and right neighboring cells, as illustrated by the following figure.
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| The transformation rule. |
Question: Is it possible, from the initial starting position with a single smarties in the origin cell, to apply the transformation rule so that the 6 cells corresponding to the first 3 diagonals are completely empty.
The goal is to remove all smarties from the white cells.
The following figure shows a sequence of consecutive valid transformations from the initial configuration:
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