Five couples were at a party. If each person shook hands exactly once with everyone else except his/her spouse, how many handshakes were exchanged?
You may be scratching your head over that puzzler, but to several Trottier eight graders it’s a piece of cake. The students are part of the Trottier Math Team which recently came in sixth place in the annual MathCounts Chapter Competition.
Students Tommy Yu, Chad Kalil, Helen Hsia, and Shaun Tan make up the team, and with their performance in the chapter competition, they’ll be heading to the state competition next month.
About 200 kids on twenty-six teams competed. Trottier’s Tommy Yu placed an impressive 14th in the individual competition.
Math team coach and Trottier teacher Tom Griffin called the team’s performance “outstanding.” “This is the second year that some of these kids have made the state competition. It is extremely competitive and we were one of only two public schools to make the top six teams.”
The Trottier team meets once a week throughout the school year to hone their math skills. They’ll compete in the state competition on March 7 at Wentworth Institute of Technology.
… And in case you’re wondering, the answer is 40.
Hmm. I’m not smarter than an eighth-grader. I assumed that each of the 10 people at the party shook hands with 8 others (everyone but themselves and their spouse). 80 handshakes. Darn.
I cheated and went to the answer key. Here’s the solution:
If spouses shook hands too, then there would be 10 × 9 = 90 handshakes. But, remember that person X shaking hands with person Y is the same as person Y shaking hands with person X. So there are only half the number of handshakes or 45. Now how many handshakes do we remove for the spouses not shaking hands. Since there are 5 couples there are 5 handshakes to be removed. 45 – 5 = 40
Of course! D’oh.
Nice job on the blog, by the way. My wife and I have been following you for about a month now.
My daughter (7 yo), on her third try, figured it out this way: http://woodgroove.com/answer.jpg