Red, blue, and green children raising their hands
Source: XVIII Tuymaada Mathematical Olympiad (2011)
July 29, 2011
combinatorics unsolvedcombinatorics
Problem Statement
Red, blue, and green children are arranged in a circle. When a teacher asked the red children that have a green neighbor to raise their hands, children raised their hands. When she asked the blue children that have a green neighbor to raise their hands, children raised their hands. Prove that some child that raised her hand had two green neighbors.