
The Four Points Puzzle - ColinWright
http://www.solipsys.co.uk/new/TheFourPointsPuzzle.html?HN_rh08
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romwell
I've found all the possible configurations by case-by-case analysis. I don't
know whether my approach would be considered elegant by the author, but it
wasn't exhausting (while being exhaustive).

My cases (or, rather, considerations) were:

1)Three points can form either an equilateral triangle, or an isosceles one;

2)The fourth point must lie on the perpendicular bisector of one of the edges
of that triangle;

3)The fourth point may on one of the two sides of that edge.

Given the constraints, that doesn't leave too many cases to consider.

But I, too, wonder what other approaches to the problem there are.

~~~
jobigoud
Haven't looked for solutions but 3 points can also form a line. Maybe there is
a configuration where 3 or even 4 points are colinear?

~~~
romwell
Three collinear points is just a degenerate obtuse triangle, so this falls
under one of the cases above.

