[lacker]

A similar problem that I like.

A "lattice point" on the plane is a point where both coordinates are integers, like (3, 4) or (-2, -1). Prove that for any five lattice points, there will be two of them that if you connect them with a line segment, there's another lattice point between them on that line.

[chias]

If you want to avoid "scary" math words, you could frame this as picking any 5 'corners' on a sheet of squared paper (of any arbitrary size)

[bobbylarrybobby]

Wow, very cool problem. Took me a second, very satisfying to land on the solution.

[stephan411]

Nice, thank you. I wouldn't have believed it.

[tantalor]

Worth mentioning that the "another lattice point on that line" is not necessarily one of the five.

[stephan411]

But it seems to be a special point too