This (I think) unsolved problem (that I mentioned recently) is so close to the present topic that I'm curious if anything at all is known about it (or if math-fun folks can solve it with their combined brainpower. QUESTION: Given a unit square in the plane, does there exist a point having its 4 distances to the vertices all rationals? (Or clearing denominators, the equivalent question as mentioned earlier: Q2: Does there exist an integer n such that given a square of side n in the plane, there is a point having its 4 distances to the vertices all integers? ) also, i'd like to understand why mike reid's statement << it is possible to have arbitrarily many points in the plane, no three collinear, such that all distances between them are integers, and no two such distances are equal.

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is true. ------------------------------------------------------------------- And what about the higher-dimensional analogues: Q3: What is the maximum number of points in R^n, no hyperplane (i.e., n-1 dimensional plane) containing n+1 of them, such that all interpoint distances are integers? ? --Dan