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# Ponder This

## August 1999

<<July August September>>

Ponder This Challenge:

This puzzle is from Evan Morton.

Recently I went on a vacation with my wife and her extended family. The dining room staff at the resort said that the 14 of us could not be seated at the same table, so they put us at two tables, of 8 and 6 seats respectively. So I wondered, if everyone wants to sit at least once with everyone else, how many meals do we need to accomplish this?

When I say "sit with," I don't mean "sit next to", I just mean sit at the same table.

This leads to a more general question. Given any two numbers M and N, if M+N people are seated at tables of M and N respectively, how many meals does it take?

This is not a trick question. At a given meal you have to sit in one seat throughout the meal, the tables do not overlap, etc.)
It turns out to be a reasonably hard problem.

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: 08/01/99 @ 12:00 AM EST
Solution: 09/01/99 @ 12:00 AM EST
List Updated: 09/01/99 @ 12:00 AM EST

### People who answered correctly:

Kunal Shroff (8.4.1999 @ 4:57 PM EST)
Ludger Weber (8.5.1999 @ 2:52 AM EST)
Glen Hattrup (8.5.1999 @ 4:36 PM EST)
Tom Bradford (8.5.1999 @ 6:50 PM EST)
Alamuru Krishal (8.5.1999 @ 9:20 PM EST)
Chris Lusby-Taylor (8.5.1999 @ 10:23 AM EST)
David MacMahon (8.5.1999 @ 10:31 PM EST)
Dieter Verhofstadt (8.6.1999 @ 2:59 AM EST)
Donna Byrne (8.6.1999 @ 7:16 AM EST)
Sachin Desai (8.6.1999 @ 7:22 AM EST)
Ming-Wei Wang (8.8.1999 @ 8:09 PM EST)
Bruce Hoff (8.9.1999 @ 3:51 PM EST)
Joseph Devincentis (8.11.1999 @ 9:49 AM EST)
Ernst Munter (8.11.1999 @ 2:26 AM EST)
Peter Huesken (8.14.1999 @ 9:26 AM EST)
Bart VanSteirteghem (8.17.1999 @ 2:17 PM EST)
Dan Peleg (8.23.1999 @ 3:10 AM EST)
Cheryl Patrick (8.24.1999 @ 8:24 AM EST)
Vivek Agrawal (8.24.1999 @ 12:36 PM EST)
Petr Broz (8.30.1999 @ 5:33 AM EST)
Manish C Tayal (9.1.1999 @ 11:26 AM EST)

Attention: If your name is posted here and you wish it removed please send email to the ponder@il.ibm.com.