# King and Bishop

**Discrete Mathematics**Level 3

Dimitri places a Black King and a White Bishop on an empty chessboard. If the probability that Dimitri places the King and the Bishop on the chessboard such that the King is **NOT** in check (that is, the Bishop is not attacking the Black King), can be expressed as \(\dfrac{m}{n}\), in which \(m\) and \(n\) are coprime positive integers, find \(m+n\).

As an explicit example, if the Bishop is on \(f2\), the \(g1\), \(e1\), \(g3\), \(h4\), \(e3\), \(d4\), \(c5\), \(b6\) and \(a7\) squares are under attack.

Dimitri can place the Bishop either on a white or black square.

The King and the Bishop cannot be placed in the same square.

###### This is the third problem of the set Look after the King!

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