HMMT November 2018 U36

An $n \times m$ maze is an $n \times m$ grid in which each cell is one of two things: a wall, or a blank. A maze is solvable if there exists a sequence of adjacent blank cells from the top left cell to the bottom right cell going through no walls. (In particular, the top left and bottom right cells must both be blank.) Let $N$ be the number of solvable $5 \times 5$ mazes. Estimate $N$. An estimate of $E>0$ earns $\left\lfloor 20 \min \left(\frac{N}{E}, \frac{E}{N}\right)^{2}\right\rfloor$ points.