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Re: Two distances among Four Points

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Charlie Roberts <croberts@gmail.com> posted:

> On Tue, 17 Mar 2026 19:14:20 GMT, James Dow Allen
> <user4353@newsgrouper.org.invalid> wrote:
> 
> >
> >Pondering the Eight Location Puzzle reminded me of a nice Geometric Gem.
> >
> >How many ways are there to arrange 4 points in the plane such that
> >only two inter-point distances occur.  For example, one solution is the

I should have specified that the points must be DISTINCT.
Otherwise there are four solutions where one of the distances is zero!

A closely related puzzle is to arrange FIVE distinct points such that
only two inter-point distances occur.

(SIX points with THREE distances? No. NO-NO-NO.
At some point fun becomes masochism.
Fbzr lbhat ynqvrf va Oreyva gnhtug zr gung.)

> I came up with two more ...... but cannot think of any others.
> 
> 
> The two have to do with rather rudimentary logic.
> What if one starts with three points equidistant 
> from each other -- an equilateral triangle. 
> 
> One solution instantly falls out. The other one
> is a variant of the same. It plays on the old
> geometry things of points "within" and "without"
> a closed figure.
> 
> Now, to rack my brains some more!

Come on, folks:  Help Charlie here!
(I'm beginning to think r.p is moribund.)

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Thread

Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-17 19:14 +0000
  Re: Two distances among Four Points Charlie Roberts <croberts@gmail.com> - 2026-03-18 16:36 -0400
    Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-20 06:03 +0000
      Re: Two distances among Four Points  Charlie Roberts <croberts@gmail.com> - 2026-03-20 12:50 -0400
    Re: Two distances among Four Points Charlie Roberts <croberts@gmail.com> - 2026-03-20 11:04 -0400
      Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-20 16:22 +0000
        Re: Two distances among Four Points Phil Carmody <pc+usenet@asdf.org> - 2026-05-19 20:01 +0300
  Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-20 09:58 -0700
    Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-20 17:11 +0000
      Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-21 15:55 +0000
        Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-22 07:20 +0000
          Re: Two distances among Four Points HenHanna@NewsGrouper <user4055@newsgrouper.org.invalid> - 2026-03-23 16:16 +0000
            Re: Two distances among Four Points Mike Terry <news.dead.person.stones@darjeeling.plus.com> - 2026-03-25 02:40 +0000
              Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-25 11:44 +0000
                Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-25 09:17 -0700
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-26 07:58 +0000
                Re: Two distances among Four Points "Carl G." <carlgnews@microprizes.com> - 2026-03-26 10:26 -0700
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-27 10:25 +0000
                Re: Two distances among Four Points James Dow Allen <user4353@newsgrouper.org.invalid> - 2026-03-27 20:27 +0000

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