Problem

Source:

Tags: combinatorics



A boy and a girl were sitting on a long bench. Then twenty more children one after another came to sit on the bench, each taking a place between already sitting children. Let us call a girl brave if she sat down between two boys, and let us call a boy brave if he sat down between two girls. It happened, that in the end all girls and boys were sitting in the alternating order. Is it possible to uniquely determine the number of brave children?