Thursday, October 1, 2015

Building Shapes out of Polyominoes - HW2

Link to PSet
Link to Answer Key

Now that we've learned what polyominoes are in HW1, the questions in HW2 ask us to try building some different shapes out of them. We also start talking about how you can actually prove whether or not you can make a particular shape out of specific polyominoes.

The goal for these questions is two-fold: In the early questions, I wanted to encourage experimentation. The value of false starts, dead ends, and general mucking about is a good thing to learn about mathematical thinking. In the later questions, however, I wanted to try and introduce the idea that sometimes you can work something out without having to try lots of experiments. I do this here using the classic "Mutilated Chessboard" problem, which I hope is a clear enough example of a simple proof for kids to get the idea.

If you're still loving the polyominoes, you really need to get a copy of Solomon Golomb's book "Polyominoes: Puzzles, Patterns, Problems and Packings."

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