MathDB

On a

2\times 40

chessboard colored black and white in the standard alternating pattern,

20

rooks are placed randomly on the black squares. The expected number of white squares with only rooks as neighbors can be expressed as

a/b

, where

a

and

b

are coprime positive integers. What is

a + b

? (Two squares are said to be neighbors if they share an edge.)

Problem Statement