Hooligans cutting circuits (grade 9 version)
Source: All-Russian MO 1999
December 31, 2012
combinatorics
Problem Statement
There are components in a circuit, every two of which were initially joined by a wire. The hooligans Vasya and Petya cut the wires one after another. Vasya, who starts, cuts one wire on his turn, while Petya cuts one or three. The hooligan who cuts the last wire from some component loses. Who has the winning strategy?