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Policeman and thief

Source: Iranian National Olympiad (3rd Round) 2002

October 2, 2006
geometrycombinatorics proposedcombinatorics

Problem Statement

In an m×nm\times n table there is a policeman in cell (1,1)(1,1), and there is a thief in cell (i,j)(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)(i,j) the policeman can catch the thief?
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