Hello, doug!
A 6x6 board is covered with 2x1 dominoes.
Show that we can find a line which seperate the squares
that does not divide any dominoes.
Go a Goodle seartch on "fault-free rectangles".
The statement says: If we tile a 6x6 board with 2x1 dominoes,
there will always be a straight line formed by the sides of the dominoes
that goes from one side of the board to the opposite side.
(If it were a matzo, it can be broken along a straight line.)
Here is one such tiling:
Code:
*---*-------*-------*---*
| | | | |
| *---*---*---*---* |
| | | | | |
*---* *-------* *---*
| | | | | |
| *---*---*---*---* |
| | | | |
*---*---*---*---*---*---* ← fault
| | | | |
*-------* | *-------*
| | | | |
*-------*---*---*-------*