HMMT November 2019 U35

You are trying to cross a 400 foot wide river. You can jump at most 4 feet, but you have many stones you can throw into the river. You will stop throwing stones and cross the river once you have placed enough stones to be able to do so. You can throw straight, but you can't judge distance very well, so each stone ends up being placed uniformly at random along the width of the river. Estimate the expected number $N$ of stones you must throw before you can get across the river. An estimate of $E$ will earn $\left\lfloor 20 \min \left(\frac{N}{E}, \frac{E}{N}\right)^{3}\right\rfloor$ points.