Today’s Problem: Greener Pastures

pasture-fencing_0_0_2hfs

Materials needed: Paper and pencil.

Randomly place between 8 and 16 dots on a piece of paper. These will be your “fence posts.”

Next, draw “fences” between your fence posts to make several “pastures.” Make sure you use every fence post and that have lots of open space for your livestock. Also, make sure your fences don’t cross.

Count the number of fences and pastures. exm

Add the number of fence posts to the number of pastures and subtract the number of fences. Your answer should be the same as your classmates, even if they used a different number of fenceposts, drew a different number of fences and had a different number of pastures.

Using this fact (related to something called the Euler Characteristic), how many fences will a farmer need if he wants 5 pastures and uses 51 fence posts?

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