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The knight in 2009 x 2009 board - [UKRMO 2009 Grade 10]

Source:

January 23, 2011
combinatorics proposedcombinatorics

Problem Statement

There is a knight in the left down corner of 2009×20092009 \times 2009 chessboard. The row and the column containing this corner are painted. The knight cannot move into painted cell and after its move new row and column that contains a square with knight become painted. Is it possible to paint all rows and columns of the chessboard?
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