I'd like to work on this (be paid to substantially improve my http://www.gwern.net/Mnemosyne ? Where's the downside?), but you ask hard questions which would require a lot of research to be done to my satisfaction and during which I could be scooped. I'm not sure a race is the best way to run this.
Why do you care if it is done to your satisfaction when the prize is awarded based on other's satisfaction with it?
This is an expected value problem. Decide how much a unit of your time is worth, how much time you are willing to invest and then (the hard part) estimate your likelihood for success.
So, if you value your time at $10/hr, are willing to invest 10 hours and estimate you will win the $155 X% of the time then we get this equation:
P(winning)$amount won - P(losing)$amount not won = initial investment
x$155 - (1-x)$0 = $10/hr * 10 hours
solve for x
x ...
EDIT: I am canceling this contest because I feel that the structure of the incentives were poorly thought out (see gwern's comments). I will be posting a new better structured contest in the near future (now posted). If you feel this is unfair or otherwise feel slighted, please contact me at my username at gmail.com.
I'm interested in making projects happen on Less Wrong. In order to find out what works and to inspire others to try things too, I'm sponsoring the following small project:
I hereby offer a prize to the first person to submit a good summary of the evidence on Spaced Repetition to the main page. The winner will get the prize, currently: $265 + 40 to charity (see comments)
The summary should address at least the following questions: