# Covering board with dominoes

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• Feb 27th 2011, 12:09 PM
doug
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.
• Feb 27th 2011, 12:54 PM
CaptainBlack
Quote:

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
• Feb 27th 2011, 06:19 PM
Soroban
Hello, doug!

Quote:

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       |      |  |  |      |       *-------*  |  *-------*       |      |  |  |      |       *-------*---*---*-------*```