Problem #PRU-98016

Problems Discrete Mathematics Combinatorics Integer lattices Integer lattices (other) Set theory and logic Order relations Methods Pigeonhole principle Pigeonhole principle (other)
 10–15  4.0

Problem

We are given 101 rectangles with integer-length sides that do not exceed 100.

Prove that amongst them there will be three rectangles \(A, B, C\), which will fit completely inside one another so that \(A \subset B \subset C\).