Hello!

I'm trying to solve this problem:

Having k points in an n-dimentional space, I want to find a new point, any point P that is at distance 1 from each of them, or find out if it is impossible.
So, the system of equations would be

for each i = 1..k
Sum, for j = 1..n of (Xij - Pj) ^2 = 1

but Xij are constants, so

for each i = 1..k
Ci + (Sum, for j = 1..n of Pj ^2 - 2XijPj) = 1

With Ci = Sum, for j=1..n of Xij^2

Is there an easy, computational way of calculating this?

Sorry for my not-standard notation, I'm new to the forum.