Quote:
Originally Posted by aidan 
If your number of points, exceeds the number of dimensions in your n-dimensional space, and NONE of the points are coincident with any other point then you will have an impossible condition to meet.
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If you are given three points in a plane, then it is possible(not is all cases) to find a point that is equidistant from all of them(the centre of the circle with three points on the circumference)..........it seems contradiction with your statement.