# COMBINATORICS at its PEAK...

**Discrete Mathematics**Level 2

A "domino" is a 1 by 2 or a 2 by 1 rectangle.

A 'domino tiling' of a region of the plane is a way of covering it (and only it) completely by non-overlapping dominoes. For example: There's 1 domino tiling of a 2 by1 rectangle & 2 tilings of a 2 by 2 rectangle. (1 consisting of 2 horizontal dominoes & 1 containing of 2 vertical ones) How many domino tilings of a 2 by 10 rectangle are there?

A 'domino tiling' of a region of the plane is a way of covering it (and only it) completely by non-overlapping dominoes. For example: There's 1 domino tiling of a 2 by1 rectangle & 2 tilings of a 2 by 2 rectangle. (1 consisting of 2 horizontal dominoes & 1 containing of 2 vertical ones) How many domino tilings of a 2 by 10 rectangle are there?

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