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.
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?
What's the maximum asymmetry a convex shape can have?
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...".
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11/01/2001 @ 9:30 AM EST
Solution: 11/30/2001 @ 3:00 PM EST
List Updated: 11/30/2001 @ 2:40 PM EST
People who answered correctly:
(total or partial solutions received)
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)
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