# Thread: Covering board with dominoes

1. ## Covering board with dominoes

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.

Any help would be appreciated.

2. Originally Posted by 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.

Any help would be appreciated.
I think you need to be clearer about what properties this line is to posses (is it a straight line, and what does separate the squares mean?)

CB

3. 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
|       |   |   |       |
*-------*   |   *-------*
|       |   |   |       |
*-------*---*---*-------*