14 – pigeon hole principle

It’s Friday and my geometry kids finished working with “if-then” statements during the first hour; so in the second hour, I gave them this problem:

Five Couples

Jake and his wife recently attended a party at which there were four other married couples. Various handshakes took place. No one shook hands with himself (or herself) or with his (or her) spouse, and no one shook hands with the same person more than once. After all the handshakes were over, Jake asked each person, including his wife, how many hands he (or she) had shaken. To his surprise, each gave a different answer. How many hands did his wife shake?

(This problem makes use of the pigeon hole principle.)

Funny how they reached for the big whiteboards immediately without my directing them to. A group of 10 kids went outside to “act it out.” This is crazy, but I was a little sad that the bell rang because the kids were so into this problem —¬†they¬†didn’t want to leave class!

14

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