## Problem of the Day #125: Dr. Kim’s Solar CellsJuly 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 $a+b+c+d$.

1. Izzy - July 22, 2011

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

2. phenomist - July 22, 2011

infinite reflections or no?

3. Sreenath - July 22, 2011

yes

4. Eugene - July 22, 2011

what happens if she hits a corner?

5. Sreenath - July 22, 2011

she bounces off both walls

6. phenomist - July 22, 2011

then how is the answer possibly not 0 then

7. Sreenath - July 22, 2011

Dr. Kim never loses