IBM Research | Ponder This | July 2005 challenges
Skip to main content

Ponder This

July 2005

<<June July August>>

Ponder This Challenge:

Puzzle for July 2005. Solutions will not be solicited.

This puzzle was suggested by Alan O'Donnell.
We are not asking for solutions this month.

Upon a rectangular table of finite dimensions L by W, we place n identical, circular coins; some of the coins may be not entirely on the table, and some may overlap. The placement is such that no new coin can be added (with its center on the table) without overlapping one of the old coins. Prove that the entire surface of the table can be covered completely by 4n coins.

We invite visitors to our website to submit an elegant solution. Send your submission to the

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


Challenge: 07/01/2005 @ 08:30 AM EST
Solution: 08/01/2005 @ 08:00 AM EST
List Updated: 07/01/2005 @ 08:30 AM EST

(No "correct responses" list this month)

Attention: If your name is posted here and you wish it removed please send email to the