# A dangerous game .....

**Discrete Mathematics**Level 5

A pawn, starting on the lower left corner square of a standard \(8\) by \(8\) chessboard, is to be moved one square at a time to the upper right corner square. The only permitted moves are one square up or one square to the right.

Four squares, (other than the starting and finishing squares), chosen at random, are rigged so that if the pawn is moved to one of these squares it vaporizes, never to be seen again. The probability that the pawn reaches the upper right corner square intact is \(\dfrac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. Find \(b - a\).