Answer to the Problem of the Week

for the week of January 3, 2000

Solve the following problem between Monday and Friday. Then click on the icon below to e-mail your solution along with your name, city, and state.

The New Year's Eve Problem
At a recent hilarious Math Teacher's New Year's Eve Party, consisting of three people, there were 21 bottles of apple juice on hand (to find out why beer was not served at the party, see below). Unfortunately, seven of these bottles were empty, seven only half full, and seven completely full.

In order to be completely fair, the host decided to give each of his three guests the same quantity of apple juice and the same number of bottles.

How can this be done without pouring any apple juice?

Q: Do you know why they never have beer at a math teacher's party?
A: Because you can't drink and derive!


Solution:

There are two solutions to this problem:

Guest Full Bottles Half-Full Bottles Empty Bottles Total Amount of Juice
Guest #1 2 3 2 3.5 bottles
Guest #2 3 1 3 3.5 bottles
Guest #3 2 3 2 3.5 bottles
Total 7 7 7 10.5 bottles

Guest Full Bottles Half-Full Bottles Empty Bottles Total Amount of Juice
Guest #1 3 1 3 3.5 bottles
Guest #2 3 1 3 3.5 bottles
Guest #3 1 5 1 3.5 bottles
Total 7 7 7 10.5 bottles

Correctly solved by:

1. Chris Moats Winchester, VA
2. Tom Marino Winchester, VA
3. Michael Webber Winchester, VA
4. Sam Stiebel Winchester, VA
5. Chip Crawford Winchester, VA
6. Jon Pence Winchester, VA
7. Josh Grewal Winchester, VA
8. Brandon Jaycox Winchester, VA
9. Bob Hearn Winchester, VA
10. Court Pifer Winchester, VA