Question 12
The diagram given below shows an underground maze in the form of a $4\times4$ square. A snake, initially at position $P$, starts crawling along the path P-Q-R-S in a loop. A mouse, initially at position $A$, has to reach position $B$, moving across the maze. The mouse can only move vertically up or horizontally right. If the snake and the mouse reach the same position at the same time, the snake will eat the mouse; also if the two cross each other along a path, the snake will eat the mouse (the snake and the mouse move at the same speed). Given that the mouse and the snake start moving at the same time, what is the number of safe paths for the mouse to move from $A$ to $B$?
(For example, A-C-D-E-R-G-H-I-B is a safe path for the mouse, since when the mouse reaches $R$, the crawling snake will be at point $P$)
(For example, A-C-D-E-R-G-H-I-B is a safe path for the mouse, since when the mouse reaches $R$, the crawling snake will be at point $P$)