IBM Research | Ponder This | July 1998 challenges

# Ponder This

## July 1998

<<June July August>>

Ponder This Challenge:

Wimbledon has just ended, and your job is to store the remaining tennis balls in buckets. The storage area will only hold rows of three buckets, but will hold an undetermined number of rows. You must follow three inviolable rules in storing the tennis balls:

• Each bucket must have a different positive number of balls.
• Each row must have the same total number of balls in its three buckets.
• The total number of balls in each row is as small as possible.

For example, if you were given only two rows of buckets, the setup:

achieves a row total of 11. This is the best possible arrangement for two rows.
Problem: Can you give a construction that gives an optimal arrangement that works for an arbitrary number k of rows?

We will post the names of those who submit a correct, original solution! If you don't want your name posted then please include such a statement in your submission!

We invite visitors to our website to submit an elegant solution. Send your submission to the ponder@il.ibm.com.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: ponder@il.ibm.com

Challenge: 07/01/98 @ 12:00 AM EST
Solution: 08/01/98 @ 12:00 AM EST
List Updated: 12/01/01 @ 10:00 AM EST