January 3, 2000
Problem of the Week

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?

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Q: Do you know why they never have beer at a math teacher's party?

A: Because you can't drink and derive!

Solution to the Problem:

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

Send any comments or questions to: David Pleacher