Question 7
Louis moves around on the lattice points according to the following rules: From point $(x, y)$ he may move to any of the points $(y, x)$, $(3x, -4y)$, $(-2x, 5y)$, $(x+1, y+6)$ and $(x-7, y)$. Show that if he starts at $(0,1)$ he can never get to $(0,0)$.