Combinatorics · Pigeonhole principle · Packing · Discrete geometry
A park has the shape of a square with side \(1\) km. Inside it grow \(4567\) trees, each of diameter at most \(50\) cm, and each tree lies entirely within the park.
Prove that the park contains a \(10\) m \(\times\) \(20\) m space in which there is no tree, not even a part of one.
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian Municipal Competition 2017, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source