suppose you have four points in a 5-dimensional space:
Then for your AnyPoint(x0,y0,z0,w0,v0)
for i= 1 to 5
If Distance <> 1 then EXIT: NO SUCH NUMBER POSSIBLE.
''AnyPoint() is at distance 1 from all other points.
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.
Just wondering, but how are you using more than three dimensions to define your points.