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?

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".

Posted by David on 2004-11-22 01:04:47