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.

Printable View

- Feb 27th 2011, 12:09 PMdougCovering 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 PMCaptainBlack
- Feb 27th 2011, 06:19 PMSoroban
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

| | | | |

*-------* | *-------*

| | | | |

*-------*---*---*-------*