The strategy to get out of the circle
Source: Tournament of Towns 2007 - Fall - Junior A-Level - P3
September 3, 2011
combinatorics unsolvedcombinatorics
Problem Statement
Michael is at the centre of a circle of radius metres. Each minute, he will announce the direction in which he will be moving. Catherine can leave it as is, or change it to the opposite direction. Then Michael moves exactly metre in the direction determined by Catherine. Does Michael have a strategy which guarantees that he can get out of the circle, even though Catherine will try to stop him?