Problem

Source: Iranian National Olympiad (3rd Round) 2002

Tags: geometry, combinatorics proposed, combinatorics



In an $m\times n$ table there is a policeman in cell $(1,1)$, and there is a thief in cell $(i,j)$. A move is going from a cell to a neighbor (each cell has at most four neighbors). Thief makes the first move, then the policeman moves and ... For which $(i,j)$ the policeman can catch the thief?