A probability problem by A Former Brilliant Member

Probability Level pending

The cells of a 7 × 7 7\times 7 square are colored with two colors. Find the minimum number of rectangles with vertices of the same color and with sides parallel to the sides of the square.

Note: This is a original problem. Actually the original one was a proof based but I just made it different but it still holds the same meaning.


The answer is 21.

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