IBM Research | Ponder This | October 2000 challenges

# Ponder This

## October 2000

<<September October November>>

Ponder This Challenge:

This puzzle is due to a suggestion by Denis Borris.
(Thanks, Denis.)

Part A:
There are three participants: a Host, a Partner, and a Volunteer.
The Partner is in a soundproof room.
The Host gives the Volunteer six blank cards, five white and one blue.
The Volunteer writes a different integer from 1 to 125 on each card, as the Host is watching.
The Volunteer keeps the blue card.
The Host arranges the five white cards in some order and passes them to the Partner.
The Partner then announces the number on the blue card.
How?

Part B:
Same set-up, except:
The integers now range from 1 to N, where N=190.
The Host can either pass all five white cards, as before, or discard one and just pass four cards.

Part B is much harder than Part A. Special mention will be given to the first person to give a justifiable procedure that works when N is at least 190; and to the first person to give a justifiable procedure for the largest value of N submitted (even if that's smaller than 190).

Notes:
There are no tricks like upside-down cards; the only information that the Partner gets is the cards and their ordering.

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: 10/02/00 @ 9:00 AM
Solution: 10/31/00 @ 1:28 PM
List Updated: 10/31/00 @ 1:28 PM

Part A:
Olivier Miakinen (10.02.2000 @ 12:42 PM EDT)
Mat Newman (10.02.2000 @ 1:23 PM EDT)
Ether Jones (10.02.2000 @ 2:23 PM EDT)
Ravishankar Arunachalam (10.02.2000 @ 2:30 PM EDT)
Michael Malak (10.02.2000 @ 3:26 PM EDT)
Prithu (10.03.2000 @ 9:14 AM EDT)
David J McKee (10.03.2000 @ 9:14 AM EDT)
Muralidhar Seshadri (10.03.2000 @ 7:47 AM EDT)
Guenter Mair (10.03.2000 @ 7:55 AM EDT)
Daniel Li (10.03.2000 @ 2:05 PM EDT)
Ashish Kadakia (10.03.2000 @ 2:05 PM EDT)
Ming Song (10.03.2000 @ 4:10 PM EDT)
Alec Spiegelman (10.03.2000 @ 4:14 PM EDT)
Joseph DeVincentis (10.03.2000 @ 5:10 PM EDT)
Alexey Vorobyov (10.03.2000 @ 9:56 PM EDT)
Amos Guler (10.04.2000 @ 2:43 AM EDT)
Ashutosh Misra (10.04.2000 @ 7:44 AM EDT)
Thomas Rohr (10.04.2000 @ 10:45 AM EDT)
Alexis Megas (10.04.2000 @ 2:44 PM EDT)
Manikantan Srinivasan (10.04.2000 @ 5:35 AM EDT)
Jim Schnelker (10.04.2000 @ 11:07 PM EDT)
Simon Andersson (10.05.2000 @ 12:07 AM EDT)
Tim Edmonds (10.05.2000 @ 10:50 AM EDT)
Khaled Fayed (10.05.2000 @ 11:11 AM EDT)
Gustavo Durand (10.05.2000 @ 2:59 PM EDT)
Vic Monell (10.05.2000 @ 4:43 PM EDT)
William Mather (10.05.2000 @ 8:55 PM EDT)
Trevor Strohman (10.05.2000 @ 11:11 PM EDT)
Ian Lovely (10.06.2000 @ 9:14 AM EDT)
Bhuvan Urgaonkar (10.06.2000 @ 5:35 PM EDT)
Dmitri Asonov (10.07.2000 @ 1:43 PM EDT)
Jessica Jo Lang (10.10.2000 @ 2:26 PM EDT)
Philip Nanni (10.08.2000 @ 3:41 AM EDT)
Eduard Tita (10.09.2000 @ 4:33 AM EDT)
Jonathan Wildstrom (10.09.2000 @ 4:36 PM EDT)
Murali Prakash (10.11.2000 @ 9:26 AM EDT)
Francis Golding (10.11.2000 @ 5:52 PM EDT)
Mohit Sauhta (10.12.2000 @ 12:25 PM EDT)
Shmuel Spiegel (10.12.2000 @ 9:28 PM EDT)
Christie Bolton (10.14.2000 @ 12:20 PM EDT)
Samy Tawab (10.14.2000 @ 10:37 PM EDT)
Robert Danek (10.15.2000 @ 1:47 PM EDT)
Subrahmanyam Devulapalli (10.16.2000 @ 9:31 PM EDT)
Senthil Nathan G (10.17.2000 @ 2:49 AM EDT)
Paul Gover (10.20.2000 @ 11:19 AM EDT)
Robin Munn (10.22.2000 @ 5:20 PM EDT)
Jonathan Hayward (10.22.2000 @ 5:20 AM EDT)
Stephen Merriman (10.23.2000 @ 10:55 AM EDT)
Anand Rangarajan (10.23.2000 @ 2:44 AM EDT)
George Tolley (10.24.2000 @ 11:47 AM EDT)
Dieter Verhofstadt (10.26.2000 @ 6:21 AM EDT)
Laura Apostoloiu (10.27.2000 @ 1:26 PM EDT)
Bernd Beimel (10.28.2000 @ 5:04 PM EDT)
Sujith Vijay
(10.31.2000 @ 7:50 AM EDT)
Nagendra (10.31.2000 @ 8:08 AM EDT)

Part B:

Eureka! We have a correct respondent @ N=200
Olivier Miakinen

Correct respondent @ N=172:
Prithu

Correct respondents @ N=148:
Daniel Li
Thomas Rohr
Michael Malak & Brian Murphy

Ming Song
Jim Schnelker
Manikantan Srinivasan
Alexey Vorobyov
Tim Edmonds
Vic Monell
Trevor Strohman
"&"
Ian Lovely
Dmitri Asonov
Jessica Jo Lang
Jonathan Wildstrom
Francis Golding
Mohit Sauhta
Christie Bolton
Samy Tawab
Senthil Nathan G
Paul Gover
Jonathan Hayward (@ N=147)
Stephen Merriman