## Problem of the Day #125: Dr. Kim’s Solar Cells
*July 22, 2011*

*Posted by Sreenath in : potd , trackback*

Izzy is standing at one corner of a 20 ft by 20 ft classroom. She begins walking towards the midpoint of one of the opposite walls. When she reaches a wall, she will bounce off in the opposite direction at the same angle at which she hit the wall. If she is ever within 3 feet of one or more solar cells, she will trip towards it, destroying the solar cell(s). Dr. Kim would like to place his solar cells so they will not be destroyed during Izzy’s rampage. The area of the region in which Dr. Kim can safely deploy his solar cells can be expressed in the form $\frac{a-b\sqrt{c}}{d}$, where $a$, $b$, and $d$ are relatively prime positive integers and $c$ is not divisible by the square of any prime. Compute $a+b+c+d$.

## Comments»

In my defense, I only broke three cells and injured four people.

infinite reflections or no?

yes

what happens if she hits a corner?

she bounces off both walls

then how is the answer possibly not 0 then

Dr. Kim never loses