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Friday, February 22, 2013

Semicircles and 13s

Here are two puzzles:

1. Mr. Farmer has two goats, Abel and Betty. Each is tied to hooks on the center of separate walls.  The area over which one goat can graze is a semicircle. The combined area over which the goats can graze is 8 2/4 π m2. Mr. Farmer has decimalophobia, meaning that he doesn't like decimals. In fact, he only agreed to the 8 2/4 π m2 because there was no more land to spare, and Mrs. Farmer assured him that the wall measurements are integers.  

What is the sum of the wall's measurements?

2.  How do you make 13 using 7, 9, 2, and 5? Note that you may use the 2 three times.

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