# I'm in the space!

There are $$n$$ distinct lattice points marked in the 3D space.

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

Details and assumptions:-

$$\bullet$$ In the 3D space, every point can be represented as coordinates $$(x,y,z)$$, where $$x,y,z \in \mathbb{R}$$

$$\bullet$$ Lattice points are points that have integer coordinates.

Easier version 2D

Harder version 5D

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