King Arthur is placing a+b+c knights around a table.
a knights are dressed in red, b knights are dressed in brown, and c 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 a+21,b+21, and c+21 combinatoricsColoringtable