MathDB

Alice and Bob play a game on a complete graph

G

with

2014

vertices. They take moves in turn with Alice beginning. At each move Alice directs one undirected edge of

G

. At each move Bob chooses a positive integer number

m,

1 \le m \le 1000

and after that directs

m

undirected edges of

G

. The game ends when all edges are directed. If there is some directed cycle in

G

Alice wins. Determine whether Alice has a winning strategy.

Problem Statement