How many ways can four points be arranged in a plane so that the six distances between pairs of points take on only two different values?

(In reply to What are the defining characteristics of "different arrangements"? by David)

>>I can't be certain what is meant by the question. What
>>would consitute a different arrangement? Or, expressing my
>>puzzlement by means of an apparently different question:
>>If we had two suggested exampls of arrangments, what
>>features would any comparison between them have to have in
>>order for them to be said to be a different arrangement
>>or "way"? On some interpretation of the meaning (as
>>illustrated by a comment so far), the answer could be "an
>>infinite number".

In a puzzle like this, the best way to consider it is to start by placing the first two points at random. This fixes two points, one edge (or possibly one diagonal) and one of the lengths. Then construct the other points according to the restraints in the puzzle, discounting rotations and reflections.

Posted by TomM on 2004-11-22 01:28:28