IBM Research | Ponder This | March 2010 challenges

# Ponder This

## March 2010

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Ponder This Challenge:

Three people named Erne, Neer, and Rene are standing in a circle. Two of them hold a phone and talk to one another -- Neer is holding the first phone and Erne is holding the second phone. After they talk, Erne passes his phone to Rene and now Neer talks to Rene. After that, Neer passes his phone to Erne and the last pair, Rene and Erne, speak to one another. At this point, all three pairs have talked, each one exactly once. If we write the initial letter of the people who talked in order by phone, it looks like this:

1. The initial holder of the first phone (Neer) = N
2. The initial holder of the second phone (Erne) = E
3. The final holder of the first phone (Erne) = E
4. The final holder of the second phone (Rene) = R

We get NEER, one of the names in the list. It's easy to verify that Rene can not be a solution while Erne can be; and there is only one possible scenario of phone-passing for each of the two names.

Now consider the list of 21 people below, who are all standing in a circle, when moving clockwise their names are sorted in alphabetical order. Our riddle this month is to find out how many possible scenarios of 209 phone passes exist that spell out each name in that list, based on the initial letter of the names of the four people who speak -- the initial holders of the first and second phone, and the final holders of the first and second phone, in that order. On each phone pass, one phone is passed to one of a person's two neighbors in the alphabetically ordered cycle. In each scenario of 209 passes, every pair of people talks exactly once.

The 21 names are Adam, Boga, Dave, Eric, Fred, Gale, Ioan, John, Karl, Luke, Mark, Nick, Oded, Phil, Rani, Siva, Tony, Udit, Wolf, Yury, and Zhou.

Bonus question - what is common to all these names?

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: 03/01/2010 @ 03:00 PM EST
Solution: 04/01/2010 @ 03:00 PM EST
List Updated: 04/15/2010 @ 03:00 PM EST

David Friedman (03/02/2010 03:08 PM EDT)
Liubing Yu
(03/04/2010 08:42 AM EDT)
T
om Sirgedas (03/05/2010 02:30 PM EDT)
B
rian Chen (03/06/2010 12:19 AM EDT)
Chuck Carroll (03/06/2010 12:37 AM EDT)
Dan Dima (03/07/2010 08:21 AM EDT)
Alex Shnaidman (03/07/2010 12:06 PM EDT)
Lachezar Hristov (03/08/2010 07:21 AM EDT)
Alexander Ivrii / Sergey Novikov (03/08/2010 09:46 AM EDT)
Ben Tarlow (03/08/2010 02:14 PM EDT)
Phil Muhm (03/09/2010 01:02 PM EDT)
Adam Daire (03/09/2010 05:49 PM EDT)
Nagy Zoltan (03/11/2010 11:09 AM EDT)
Jeff Steele (03/12/2010 01:24 AM EDT)
John T. Robinson (03/12/2010 11:34 PM EDT)
Daniel Bitin
(03/16/2010 01:36 PM EDT)
Clive Tong (03/17/2010 06:15 PM EDT)
Mark Mixer (03/17/2010 11:47 PM EDT)
Anurag Anshu (03/19/2010 01:39 PM EDT)
Alan Murray (03/21/2010 07:00 PM EDT)
Aliaksei Sanko (03/23/2010 02:36 PM EDT)
Dan Ignatoff (03/24/2010 05:07 AM EDT)
Hongcheng Zhu (03/27/2010 12:03 AM EDT)
John G Fletcher (03/30/2010 09:09 PM EDT)
Nyles Heise (03/31/2010 09:36 AM EDT)

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