# King and Pawn

Dimitri places a Black King and a White Pawn on an empty chessboard. He cannot place the Pawn on the first or eighth row ($$1$$ or $$8$$). If the probability that Dimitri places the King and the Pawn on the chessboard such that the King is $$NOT$$ in check (that is, the Pawn is not attacking the Black King), can be expressed as $$\dfrac{m}{n}$$, in which $$m$$ and $$n$$ are coprime positive integers, find $$n-m$$.

As an explicit example, if the Pawn is on $$f2$$, the $$g3$$ and $$e3$$ squares are under attack, then the White Pawn attacks only the $$2$$ (at most) squares immediately forwardly and diagonally.

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

×