## Tuesday, March 18, 2008

### Overdue Spring Break Post

You don't realize just how much you need a break until you get one. Mine wasn't too eventful, I just went back home and decided to relax a little (honestly it was more like a lot). Even though I didn't do all that much it was still enjoyable.

Firstly I heard back from the REUs that I had applied to last month. I got an offer from one of the REUs and will be working on one of the more interesting problems in my opinion. Here is the description of the project that is provided on their website:

In the mid 1990's an electronic puzzle called "Light's Out'' became popular. The puzzle consists of a grid of lights, and at the start, some of these lights are on. Pressing one of the lights will toggle it and the four lights adjacent to it on and off. (Diagonal neighbors are not affected.) To win, one must switch off all of the lights. This puzzle can be reformulated in terms of graph theory with vertices representing lights and edges representing adjacency. One can then study graph theoretic properties of the puzzle, as well as optimal winning strategies and "always winnable'' graphs.

This project will deal with adding a probabilistic element to the puzzle. One question relates to the expected number of moves required to win under a strategy of randomly pressing vertices on a winnable graph. Another avenue of research would involve assigning probabilities to various edges, so that lights are only toggled on or off with a certain probability when any vertex is pressed. The study of these questions may lead to other interesting variations on this theme.

This program runs from June 2nd to July 25th and is in Holland, Michigan which is only about two hours away from Chicago.

In addition to this great news I got to hang out with some friends. Don't think I will need to play Guitar Hero for at least another 2 months. Also went and saw Definitely Maybe with Ann, the movie was fantastic until the ending where it all sort of fell apart. I suppose they couldn't have thought of a better ending. The next movie I want to see is 21, this is kind of a big deal since I normally don't set out to see specific movies.

#### 1 comment:

Ann said...

haha. yay guitar hero! lol.
and i still don't understand that ending with her real mom and all..
i hopes you have an awesome time at your REU.