IBM Research | Ponder This | October 2010 challenges

# Ponder This

## October 2010

<<September October November>>

Ponder This Challenge:

In the following story, can you fill in the values a, b, c, d,and e with integer numbers so as to make the story true? And what would be X?

Ponder: What is the area of the lake?
This: I can not tell since I do not know anything about it.
Ponder: It has the shape of a convex pentagon; its edges lengths (in kilometers) are integers.
This: Can you give me more details?
Ponder: Here are the integer lengths of the edges: a, b, c, d,and e. I sorted them for you: a<b<c<d<e.
This: Now we are getting somewhere, but I still do not know the area.
Ponder: Last hint: Two of the angles are right (90 degrees).
This: Thank you. The lake area MUST be X square kilometers.

Update: October 4th: X, the area of the lake, does not have to be an integer.

Update: October 5th: Please specify, in your solution, the order of the edges.

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: 10/01/2010 @ 11:14 AM EST
Solution: 11/01/2010 @ 11:14 AM EST
List Updated: 30/01/2010 @ 11:14 AM EST

Mark Perkins (10/01/2010 06:48 PM EDT)
Chuck Carroll (10/02/2010 02:30 AM EDT)
János Kramár (10/02/2010 03:57 AM EDT)
Vladimir Sedach (10/03/2010 10:14 AM EDT)
Michael Brand (10/02/2010 04:30 PM EDT)
Daniel Bitin (10/03/2010 08:06 AM EDT)
Singularity Institute (10/03/2010 06:25 PM EDT)
Adam and Lael Daire (10/04/2010 04:44 PM EDT)
Joseph DeVincentis (10/04/2010 04:59 PM EDT)
Jason Crease (10/05/2010 12:23 PM EDT)
John Tromp (10/05/2010 02:40 PM EDT)
David Cole (10/05/2010 03:12 PM EDT)
John T. Robinson (10/05/2010 08:38 PM EDT)
Piet Orye (10/09/2010 12:48 PM EDT)
Todd Will (10/10/2010 03:09 PM EDT)
Albert Stadler (10/12/2010 01:12 PM EDT)
Donald T. Dodson (10/14/2010 06:34 PM EDT)
David Friedman (10/14/2010 07:28 PM EDT)
Lei Liu (10/15/2010 05:32 AM EDT)
Jeff Steele (10/16/2010 01:04 PM EDT)
John G. Fletcher (10/17/2010 09:11 PM EDT)
Liubing Yu (10/20/2010 06:35 AM EDT)
Hamidreza Bidar (10/21/2010 09:00 AM EDT)
Chris Shannon (10/21/2010 12:03 AM EDT)
Dan Dima (10/21/2010 02:58 PM EDT)
Jan Fricke (10/22/2010 09:50 AM EDT)
Sylvain Becker (10/25/2010 11:16 AM EDT)
Gale W. Greenlee (10/25/2010 12:54 PM EDT)
Brian Kemper (10/28/2010 09:47 PM EDT)
Qian Yang (10/31/2010 02:03 AM EDT)
Phil Benamy (10/31/2010 06:51 PM EDT)

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