a red knights, b brown, c orange , King Arthur places around table
Source: Norwegian Mathematical Olympiad 2015 - Abel Competition p2a
September 3, 2019
combinatoricsColoringtable
Problem Statement
King Arthur is placing knights around a table.
knights are dressed in red, knights are dressed in brown, and knights are dressed in orange.
Arthur wishes to arrange the knights so that no knight is seated next to someone dressed in the same colour as himself. Show that this is possible if, and only if, there exists a triangle whose sides have lengths , and