Not many, just 5 dimensions

Discrete Mathematics Level 2

Find least possible value of \(n\), such that we can always choose 2 points out of \(n\) points in 5-dimensional space (wherever they may be marked), such that there's at least one more lattice point on the segment joining them.

Details and assumptions:-

  • In the 5D space, every point can be represented as coordinates \((a,b,c,d,e)\), where \(a,b,c,d,e,f \in \mathbb{R}\)
  • Lattice points are points that have integer coordinates.

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