```Date: Thu, 07 Nov 1996 22:22:11 -0600
Sender: Sam
Subject: PENTOMINOE
```
What is a pentominoe? I need to understand the concept and how/why it is used? I have a 1st grader that is studying pentominoes and their symmetry. I can explain symmetry, but I don't understand exactly what a pentominoe is - besides "something" with five sides. I have heard, puzzle, games, etc. Please help!

Hi Sam:

A pentomino is a geometric shape formed by joining five unit squares edge to edge. There happen to be twelve possibilities.

A children's puzzle requiring one to place the 12 pentominoes in a 5 by 12 rectangle is produced commercially. They can actually be used to tile each of the rectangles 3 by 20, 4 by 15, 5 by 12, and 6 by 10. There are two ways to do the 3 by 20; in the accompanying picture the region shown in green can be rotated.

Pentominoes were first featured in

H.E. Dudeney's The Canterbury Puzzles, Dover, New York, 1958, pp.119-121.

Since then there have been a number of articles on pentominoes, notably in articles by Martin Gardiner:

• The Scientific american Book of Mathematical Puzzles and Diversions, Fireside Books, New York, 1959, pp 124-140
• New Mathematical Diversions from Scientific American, Fireside Books, New York, 1966, pp. 150-161
• Mathematical Magic Show, Math. Assoc. Amer., Washington, 1990, pp. 172-187.

An article that would be more of use in the elementary classroom is that by
Barry Onslow, Pentominoes Revisited, The Arithmetic Teacher, 1990, 37(9) pp. 5-9.
I believe The Arithmetic Teacher is, or was, an NCTM publication.

Cheers
Penny

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