Answer to the Problem of the Week
for the week of January 2, 2006

Whole Lotta Shakin' Goin' On
  From Car Talk

In honor of Elvis' birthday this week, the problem of the week is a tribute to his song, Whole Lotta Shakin' Goin' On.

Elvis and Priscilla are married. They agree to go out to dinner with four other married couples. So, there are five couples, or ten people, altogether.

They arrive at the restaurant, and, because there are some people who don't know other people, there are some handshakes that take place, and introductions. Anyone who doesn't know somebody will shake hands with that person. People will not shake hands with anyone they already know, and, of course, you don't shake hands with your own spouse.

At the end of the dinner, Elvis asks all the people there, including his own wife, how many hands each of them shook.

He gets the following answers: 0,1,2,3,4,5,6,7, and 8.

There are 9 other people there, and they give him 9 different answers.

Here's the question: How many hands did Elvis' wife Priscilla shake?

Now it may seem that you don't have enough information to solve this problem. But you do.


 

Solution to the Problem:

Priscilla shook hands with four people.

Click here for an explanation.



Correctly solved by:

1. James Alarie University of Michigan--Flint
Flint, Michigan
2. Jeffrey Gaither University of Virginia
Charlottesville, Virginia
3. Arin Smith University of Virginia
Charlottesville, Virginia
4. David and Judy Dixon Bennettsville, South Carolina
5. Stephen O'Hara Winchester, Virginia
6. Nathan Stoddard ----------
7. Keith Mealy Cincinnati, Ohio
8. Bob Bardsley Phoenixville, Pennsylvania
9. TJ Yarbrough Mountain View, Wyoming
10. Andrew Tucker Mountain View, Wyoming
11. Paden Atkins Mountain View, Wyoming
12. Mary Bailey Wickham Columbus, Georgia
13. Mary Frances Flowers ----------
14. Blake Hudson Columbus, Georgia
15. Carter Galbraith Columbus, Georgia
16. Russell Beaty Columbus, Georgia
17. Chance Tillotson ----------
18. Karl Jaeger ----------