Problem
of the
Week
PROBLEM 167
The following problem was suggested by Jens Vob, Hamburg, Germany.  Muchas gracias Jens.

(a) For the 3 ´ 7 grid on the left, is there a way to color the crossing points with two colors in such a way that no rectangle with equally colored corner points (and sides being parallel to the grid lines) exists? Explain why or why not. 
(b) Same question for a 4 ´ 6 grid.  
(c) And once more for a 5 ´ 5 grid.

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ã2003 Alberto L. Delgado