# King And Knight

**Discrete Mathematics**Level 4

Dimitri places a Black King and a White Knight on 2 distinct squares in an empty chessboard. If the probability that Dimitri places the King and the Knight on the chessboard such that the King is **not** in check (that is, the Knight is not attacking the Black King), can be expressed as \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).

As an explicit example, if the Knight is on \(\text{f2}\), the \(\text{h3}\), \(\text{d3}\), \(\text{d1}\), \(\text{h1}\), \(\text{g4}\) and \(\text{e4}\) squares are under attack.

###### This problem is the second of the set Look after the King!.

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