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Turkey Junior National Olympiad
2006 Turkey Junior National Olympiad
3
3
Part of
2006 Turkey Junior National Olympiad
Problems
(1)
Turkey Junior Olympiad 2006, Part II - P3
Source:
1/20/2013
In the beginnig, all nine squares of
3
×
3
3\times 3
3
×
3
chessboard contain
0
0
0
. At each step, we choose two squares sharing a common edge, then we add
1
1
1
to them or
−
1
-1
−
1
to them. Show that it is not possible to make all squares
2
2
2
, after a finite number of steps.