Colour small squares on the standard squared paper in two colors A, B. Name two small squares with common side as "neighbor". Let every colored set be "path connected": for any two small squares of the color A(resp. B) there is a sequence of color A(resp. B) neighbor squares from one to another. Prove that must there exists square $3\times 3$ which has 6 squares of same color. (Added: I can't prove it)