MathDB
HMMT Feb 2023 Team p5

Source:

February 20, 2023

Problem Statement

Let SS be the set of all points in the plane whose coordinates are positive integers less than or equal to 100100 (so SS has 1002100^2 elements), and let LL be the set of all lines ℓ\ell such that ℓ\ell passes through at least two points in SS. Find, with proof, the largest integer N≥2N \geq 2 for which it is possible to choose NN distinct lines in LL such that every two of the chosen lines are parallel.
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