MathDB

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

v_0

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

v_i

adjacent to

v_{i-1}

that hasn't been picked before and eats all its apples. The game ends when there is no such vertex

v_i

.
Armadillo's goal is to have eaten more apples than Badger once the game ends. Can she fulfill her wish?

Problem Statement