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| From | James Dow Allen <user4353@newsgrouper.org.invalid> |
|---|---|
| Newsgroups | rec.puzzles |
| Subject | Re: Two distances among Four Points |
| References | <1773774860-4353@newsgrouper.org> <10pjuar$1n96j$1@dont-email.me> |
| Date | 2026-03-20 17:11 +0000 |
| Message-ID | <1774026710-4353@newsgrouper.org> (permalink) |
"Carl G." <carlgnews@microprizes.com> posted:
> On 3/17/2026 12:14 PM, James Dow Allen wrote:
> > How many ways are there to arrange 4 points in the plane such that
> > only two inter-point distances occur?
> For me, the hardest of the six was the second arrangement that does not
> include an equilateral triangle.
And it is Carl G. who successfully completes the sextet.
This solution -- which Mr. G carefully leaves unspoiled -- is surely
the hardest to come up with.
Now: Solve the companion puzzle:
James Dow Allen <user4353@newsgrouper.org.invalid> posted:
> A closely related puzzle is to arrange FIVE distinct points such that
> only two inter-point distances occur.
... and describe the weird/wonderful relationship between this 5-point
companion puzzle and the question I asked earlier:
> Which of the six {4-point, 2-distances} arrangements is hardest to think of?
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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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