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.
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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.
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)
Wow, very cool problem. Took me a second, very satisfying to land on the solution.
Nice, thank you. I wouldn't have believed it.
Worth mentioning that the "another lattice point on that line" is not necessarily one of the five.
But it seems to be a special point too