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April 25, 2015

Homework Help: grid problem (geometry)

Posted by john on Saturday, June 15, 2013 at 10:38am.

The squares of a 260 chessboard are coloured black and white in the standard alternating pattern. At random, exactly half of the black squares are removed from the board. The expected number of white squares that have no neighbours after this process can be expressed as a/b where a and b are coprime positive integers. What is the value of a+b?

Details and assumptions:

>Note: The black squares are not removed with probability 12. Rather, it is given that exactly 30 black squares are removed.

>A square is a neighbour if it is located directly to the left, right, top or bottom of the initial square. Squares that are connected by exactly 1 vertex are not neighbors.

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