Question 6
Sophie is at $(0,0)$ on a coordinate grid and would like to get to $(3,3)$. If Sophie is at $(x,y)$, in a single step she can move to one of $(x + 1, y)$, $(x, y + 1)$, $(x - 1, y + 1)$, or $(x + 1, y - 1)$. She cannot revisit any points along her path, and neither her $x$-coordinate nor her $y$-coordinate can ever be less than $0$ or greater than $3$. Compute the number of ways for Sophie to reach $(3,3)$.