Maths Olympiad Prep

Track / Stage 4 / 204 of 340 #944 of 2444

Problem 944

AMC 12 late, AIME early
Combinatorics Difficulty 4.8 Prove it Belarus — Selection and Training Session · Belarus

A rectangle RR with odd integer side lengths is divided into small rectangles with integer side lengths.
Prove that there is at least one rectangle among the small rectangles whose distances from the four sides of RR are either all odd or all even.

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Next problem →

Official solution

1. See IMO-2017 Shortlist, Problem C1.

Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.