# King and Queen

**Discrete Mathematics**Level 3

**NOT**in check (that is, the Queen 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 Queen is on \(f2\), the \(f1\), \(f3\), \(f4\), \(f5\), \(f6\), \(f7\), \(f8\), \(g2\), \(h2\), \(e2\), \(d2\), \(c2\), \(b2\), \(e1\), \(g1\), \(g3\), \(h4\), \(e3\), \(d4\), \(c5\), \(b6\), \(a7\) and \(a2\) squares are under attack.

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