IBM Research | Ponder This | November 2001 challenges

# Ponder This

## November 2001

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Ponder This Challenge:

This month's puzzle comes from Evan Morton.

Suppose you decide to make a PB&J sandwich, and start with two identical asymmetrical slices of bread. You put the peanut butter on one, and the jelly on the other. Then you realize you've made a mistake; you've put the spreads on the corresponding side of the two slices, rather than on mirror image sides. Since you don't want a half-open-faced sandwich, nor do you want to waste food, you put the two slices together as best you can, meaning you minimize the overhang (maximize the overlap). Let's define the "asymmetry" of the slice as the proportion of each slice that doesn't match the other, when that percentage is minimized. So a symmetric slice would have an asymmetry of 0, and nothing could have an asymmetry more than 1.

Questions:

1. What's the maximum asymmetry a shape can have? That is, what's the worst shape of bread slice with which to make the above mistake?

2. What's the maximum asymmetry a convex shape can have?

3. What's the maximum asymmetry a triangle can have?

Puzzlemaster confesses that he does not know all three answers.
Consideration will be given to partial responses, of the form
"The answer to (3) is at least 0.94, because..." or
"The answer to (2) is at most 0.73, because...".

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 webmaster.

If you have any problems you think we might enjoy, please send them in. All replies should be sent to: webmster@us.ibm.com

Challenge: 11/01/2001 @ 9:30 AM EST
Solution: 11/30/2001 @ 3:00 PM EST
List Updated: 11/30/2001 @ 2:40 PM EST

Vladimir Sedach (11.01.2001 @ 6:14 PM EDT)
Henry Bottomley (11.01.2001 @ 7:39 PM EDT)
Jacques Willekens (11.04.2001 @ 9:03 AM EDT)
Bill Roscoe (11.05.2001 @ 8:59 AM EDT)
Dick Saunders Jr. (11.05.2001 @ 9:30 PM EDT)
Alan O'Donnell (11.09.2001 @ 11:57 AM EDT)
Nagendra.G.D (11.12.2001 @ 8:53 AM EDT)
Surendar Reddy Nanchary (11.14.2001 @ 2:54 AM EDT)
Amos Guler (11.14.2001 @ 1:44 PM EDT)
Christopher Howe (11.15.2001 @ 11:12 AM EDT)
John G. Fletcher (11.18.2001 @ 3:36 PM EDT)
Alexey Vorobyov (11.20.2001 @ 2:49 AM EDT)
Vincent Lynch (11.25.2001 @ 12:55 PM EDT)
Algirdas Rascius (11.29.2001 @ 3:33 PM EDT)

Attention: If your name is posted here and you wish it removed please send email to the webmaster.