Question 72
An invisible hare occupies one of $N$ vertices of a graph $G$. Several hunters try to kill the hare. Each minute all of them simultaneously shoot: each hunter shoots to a single vertex, they choose the target vertices cooperatively. If the hare was in the target vertex during a shoot, the hunting is finished. Otherwise the hare can jump to one of the neighbouring vertices or stay in its vertex.
The hunters know an algorithm that allows to kill the hare by at most $N!$ shoots. Prove that then there exists an algorithm that allows to kill the hare by at most $2^N$ shoots.
The hunters know an algorithm that allows to kill the hare by at most $N!$ shoots. Prove that then there exists an algorithm that allows to kill the hare by at most $2^N$ shoots.