Gwen Stacy and Spiderman are separated on a \( 3 \) by \( 3 \) grid at lattice points inside \( (0, 0) \), \( (3, 3) \), \( (0,3) \), and \( (3,0) \). Spiderman is at \( (3, 3) \), and Gwen is at \( (0, 0) \). Spiderman must get to Gwen. Unfortunately, Electro is at \( (1,1) \), and Spiderman can either avoid Electro, or if he gets to Electro, he has a \( \frac{2}{3} \) chance of passing easily and safely, and \( \frac{1}{9} \) chance of barely passing, but if this happens, he gets thrown back to \( (2, 2) \). Gwen cannot move at all, and Spiderman can only move left or down \( 1 \) unit at a time (with equal probability).
The probability that Spiderman gets to Gwen is \( \frac{a}{b} \) where \( a \) and \( b \) are coprime and positive integers. Find \( a+b \).
by
David Lee
