Math Forum - Project of the Month, October 1996

# October POM - Annie's Comments

This is a problem that relies on a little bit of perseverance - while you can be somewhat systematic about figuring out the 12 pentominoes, there isn't one system that will work for figuring out how to place the pieces in the various rectangles.

We got nine solutions this month, and all of them got the 12 pentominoes correct. Five teams got at least one rectangle. I had fun playing with the rectangles, but that's partly because I have some cool wooden pentominoes that make work seem like play!

Here's how I picked the winner. Teams could earn two points for getting all the pentominoes, one point for each rectangle, two points for a good explanation of the sizes of the rectangles and the limits placed on those sizes, and another point for trying out any of the "extra" parts.

Our winners scored 8 points, and their solution was the most thorough. They did the pentominoes, figured out the rectangles, and explained why the rectangles had to be at least three wide and figured out what the possible sizes could be. They drew some pretty good pictures using just ascii! Congratulations to Hayley, April, and Juli.

The honorable mention winners, Wade and Annie, drew the pentominoes and also did the four rectangles. They didn't provide much of an explanation, but they did score 6 points.

This could be a time-consuming problem! There are 2339 solutions to the 6x10 rectangle alone! The 3x20 is actually the hardest, because there are only two ways to do it (and both solutions were sent in this month).