IMO 2021 Shortlist C6
A hunter and an invisible rabbit play a game on an infinite square grid. First the hunter fixes acolouringofthecellswith...
Category: Combinatorics
Problem
A hunter and an invisible rabbit play a game on an infinite square grid. First the hunter fixes acolouringofthecellswithfinitelymanycolours. The rabbitthen secretly chooses a cell to start in. Every minute, the rabbit reports the colour of its current cell to the hunter, and then secretly moves to an adjacent cellthat ithas not visited before (two cellsare adjacent if they share a side). The hunter wins if after some finite time either • the rabbit cannot move; or • the hunter can determine the cell in which the rabbit started. Decide whether there exists a winning strategy for the hunter. Shortlisted problems 7