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The Fur Dresser's Mistake (Posted on 2004-05-28) Difficulty: 2 of 5
A fur dresser had to put a patch shaped like a scalene triangle on a piece of fur. Suddenly he realized he had made a terrible mistake. The patch fitted the hole but the fur side faced the wrong way.

The fur dresser, after some thought, cut the triangular patch into 3 parts, each of which would be unchanged when turned over. How?

  Submitted by Victor Zapana    
Rating: 4.0000 (6 votes)
Solution: (Hide)
My Solution: Without loss of generality, let angle B be the largest angle. Let ABC be the patch to be turned over. Let D be the point of intersection between AC and its perpendicular through point B. Let E be the midpoint of BC. Let F be the midpoint of AB. The fur dresser cuts along DE and DF (which bisect BC and AB, respectively), and turns the 3 resulting parts over - the triangles around vertical axes and the quadrilateral around EF. When he sewed them together, patch ABC was reversed but preserved its shape.

rixar's solution: Construct the incenter of triangle ABC on the hide side. Call that point I. Connect I to AB, AC, and BC at points E, F, G, respectively, such that IE is perpendicular to AB, IF is perpendicular to AC, and IG is perpendicular to BC. The fur dresser cuts along IE, IF, and IG. He is left with three symmetrical quadrangles, which are the same shape when flipped on the axes created by lines constructing the incenter.

Kudos to Brian Smith to being the first to get my solution, and rixar for getting his own solution. There might be others :)

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Possible Solution?Ouchy the Klown2004-06-01 21:36:48
Both Brian Smith's and rixar's workJer2004-05-29 15:53:26
Solutionsolution?rixar2004-05-29 10:53:15
SolutionSolutionBrian Smith2004-05-29 09:45:27
re(3): Half an answer - to FKSilverKnight2004-05-28 15:09:48
re(3): Half an answer - to RichardSilverKnight2004-05-28 14:59:50
No SubjectJer2004-05-28 14:48:08
Some Thoughtsre(3): Half an answerFederico Kereki2004-05-28 14:41:42
Some Thoughtsre(2): Half an answerFederico Kereki2004-05-28 14:39:33
re(2): Half an answerRichard2004-05-28 14:34:53
re: Half an answerSilverKnight2004-05-28 14:23:09
Some ThoughtsHalf an answere.g.2004-05-28 13:55:25
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