IBM Research | Ponder This | September 2005 challenges

# Ponder This

## September 2005

<<August September October>>

Ponder This Challenge:

Puzzle for September 2005.

This puzzle was sent in by Alan O'Donnell.
It comes in three parts; solve as many as you can.

Part 1:
You have a frictionless pulley with a rope over it. On one side is a 3kg weight. On the other side is a weightless frictionless pulley with another rope over it. This second pulley has a 1kg weight on one side, and a 2kg weight on the other. You have a frictionless pulley with a rope over it; the pulley is attached to an immovable ceiling.

At what rate (in terms of g, the acceleration due to gravity) does the 3kg weight accelerate downwards when the system is released?

Part 2:
Suppose the system described in Part 1 is on one end of a rope over another pulley, with a 6kg weight on the other side. How fast does the 6kg weight accelerate in terms of g?

Part 3:
Suppose this sequence is continued with weights 1kg, 2kg, 3kg, 6kg, 12kg, 24kg, ..., 3*(2**m)kg. What is the general term for the acceleration of the heaviest object?

The first 100 people who answer all three parts correctly will be listed. The answer will be posted a week after the 100th is received, or at the end of the month.

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: 09/01/2005 @ 08:30 AM EST
Solution: 10/01/2005 @ 08:30 AM EST
List Updated: 09/01/2005 @ 08:30 AM EST

Joe BGI SF Fendel (09.01.2005 @01:12:22 PM EDT)
Dharmadeep Muppalla (09.01.2005 @01:35:34 PM EDT)
Raicho Tchalkov (09.01.2005 @02:16:57 PM EDT)
Xinzhou Wu (09.01.2005 @03:39:36 PM EDT)
Sunil Nandihalli (09.02.2005 @01:09:22 AM EDT)
Max Alekseyev (09.02.2005 @01:29:18 AM EDT)
Vladimir Sedach (09.02.2005 @07:27:02 AM EDT)
Edmond Bernardy (09.02.2005 @07:48:06 AM EDT)
Eugene Vasilchenko (09.02.2005 @12:01:44 PM EDT)
Konstantin Ilyashenko (09.02.2005 @12:43:09 PM EDT)
Christopher Howe (09.02.2005 @01:13:59 PM EDT)
Andre Rzym (09.02.2005 @03:48:38 PM EDT)
Robert Benea (09.03.2005 @10:19:55 PM EDT)
Karl D'Souza (09.05.2005 @02:25:40 PM EDT)
Kalyana Chakravarthy (09.06.2005 @10:31:25 AM EDT)
Sridharakumar Narasimhan & R. Madhusudana Rao (09.06.2005 @12:44:50 PM EDT)
Geert Jan Ruiter (09.07.2005 @11:53:31 AM EDT)
Mark Pilloff and Patrick J. LoPresti (09.07.2005 @03:25:58 PM EDT)
Dion Kane Harmon (09.07.2005 @05:13:55 PM EDT)
Balakrishnan V (09.07.2005 @11:43:46 PM EDT)
Krishna Chaitanya Ammanabrolu (09.08.2005 @02:55:04 AM EDT)
Dan Dima (09.08.2005 @09:52:19 AM EDT)
Yong Liu (09.08.2005 @10:43:40 AM EDT)
John G. Fletcher (09.08.2005 @07:20:37 PM EDT)
Chang-Seo Park (09.09.2005 @02:39:13 AM EDT)
John Ritson (09.09.2005 @03:24:17 AM EDT)
Daniel Bitin (09.09.2005 @08:18:40 AM EDT)
Devin Myers (09.09.2005 @09:13:50 AM EDT)
Ramanjit Ahuja (09.09.2005 @10:00:27 AM EDT)
Sriraman Tallam (09.09.2005 @06:14:21 PM EDT)
Bengu Li (09.09.2005 @08:19:13 PM EDT)
Sunil Srivastava (09.09.2005 @09:12:53 PM EDT)
Jerold Lewandowski (09.11.2005 @03:39:02 PM EDT)
Harsha (09.12.2005 @12:06:56 PM EDT)
IQSTAR (09.12.2005 @12:34:08 PM EDT)
Frank Vernaillen (09.12.2005 @07:27:19 PM EDT)
aman_cc (09.13.2005 @01:07:38 AM EDT)
Leonardo Liang (09.13.2005 @08:16:00 AM EDT)
Frank Mullin (09.13.2005 @09:08:32 AM EDT)
Qiqi Yan (09.13.2005 @11:32:00 AM EDT)
Michael Brand (09.13.2005 @01:46:19 PM EDT)
Joseph DeVincentis (09.13.2005 @02:10:38 PM EDT)
Yoav Raz (09.13.2005 @08:38:34 PM EDT)
Suryaprasad Kareenahalli (09.15.2005 @12:52:10 AM EDT)
Forrest McClellan (09.15.2005 @04:09:16 AM EDT)
Shashikiran Kolar (09.15.2005 @07:49:18 AM EDT)
Steve Plate (09.15.2005 @01:44:18 PM EDT)
Se Kwon Kim (09.16.2005 @02:53:50 AM EDT)
Gurpreet Singh Pahwa (09.16.2005 @11:41:00 AM EDT)
Udo Klein (09.19.2005 @01:15:59 AM EDT)
Shmuel Spiegel (09.20.2005 @04:53:32 AM EDT)
Prasad JVV (09.20.2005 @05:31:54 AM EDT)
Sunil Bothra (09.20.2005 @09:56:41 AM EDT)
John Tromp (09.21.2005 @05:27:03 AM EDT)
Vinay Mogulothu (09.21.2005 @06:52:13 PM EDT)
Dave Biggar (09.22.2005 @07:32:47 AM EDT)
Debo Olaosebikan (09.22.2005 @07:50:00 PM EDT)
Jinhui Li (09.24.2005 @12:54:53 PM EDT)