Armadillo and Badger are playing a game. Armadillo chooses a nonempty tree (a simple acyclic graph) and places apples at some of its vertices (there may be several apples on a single vertex). First, Badger picks a vertex v0 and eats all its apples. Next, Armadillo and Badger take turns alternatingly, with Armadillo starting. On the i-th turn the animal whose turn it is picks a vertex vi adjacent to vi−1 that hasn't been picked before and eats all its apples. The game ends when there is no such vertex vi.Armadillo's goal is to have eaten more apples than Badger once the game ends. Can she fulfill her wish? olympic revengecombinatoricsgraph theory