# King and Rook

**Discrete Mathematics**Level 3

**NOT**in check (that is, the Rook is not attacking the Black King), can be expressed as \(\frac{m}{n}\), in which \(m\) and \(n\) are coprime positive integers, find \(n-m\).

**Details and Assumptions:** e.g. If the Rook is on \(f2\), the \(f1\), \(f3\), \(f4\), \(f5\), \(f6\), \(f7\), \(f8\), \(g2\), \(h2\), \(e2\), \(d2\), \(c2\), \(b2\) and \(a2\) squares are under attack.

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