Question

Enya is standing in the centre square of a 9 x 9 grid. She travels outward one square at a time, moving diagonally or along a row or column. How many different paths can Enya follow to the perimeter? Answer is 320. Please be able to provide a grid explanation thank you :)

Answer 1

\[4\cdot 3\cdot 3\cdot 3+4\cdot(4\cdot3\cdot3+1\cdot(4\cdot 3+1\cdot 5))\]
\[=108+4\cdot(36+17)=108+4\cdot53=108+212=320\]