perplexus.info :: Geometry : Only Isosceles

Only Isosceles (Posted on 2005-02-13)

Arrange 8 points in 3-space so that for each of the 56 triples of points that they determine, at least two of the three distances between points in the triple are equal.

Submitted by David Shin

Rating: 4.5000 (4 votes)

Solution: (Hide)

Start with a regular pentagon inscribed in the unit circle in the x-y plane, together with the origin; this places six of the points. Let the remaining points be (0,0,1) and (0,0,-1). In the comments, Charlies explains why this configuration works.

This problem is due to Paul Erdos. It is not known whether the 8-point set of the solution is unique.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Great problem	Charley	2005-05-12 16:56:46
re: solution	TomM	2005-02-14 07:03:37
solution	Charlie	2005-02-14 04:39:21
Second thoughts: an aborted repeat	TomM	2005-02-14 00:39:20
More ideas	Gamer	2005-02-13 20:58:46
First thoughts.	TomM	2005-02-13 17:22:25

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