Question 176
On an infinite chessboard, two squares are said to touch if they share at least one vertex and they are not the same square. Suppose that the squares are colored black and white such that
- there is at least one square of each color;
- each black square touches exactly $m$ black squares;
- each white square touches exactly $n$ white squares
where $m$ and $n$ are integers. Must $m$ and $n$ be equal?
- there is at least one square of each color;
- each black square touches exactly $m$ black squares;
- each white square touches exactly $n$ white squares
where $m$ and $n$ are integers. Must $m$ and $n$ be equal?