Pepsi is currently running a promotion with the caps of its 20oz bottled sodas. They are giving away free songs on iTunes. So I came up with a word problem. I’ll post the solution tomorrow:

Under each cap you can get one of three things: “Free Song” [FS], “Try Again” [TA], “Buy One Get One Free” [BOGO]. Pepsi (as required by law) gives you the odds of winning. You get a FS 1/3 of the time and BOGO 1/6 of the time.

So the question is, given $100 (and assuming that each bottle costs only $1), how many Free Songs can you win? And what algorithm would you follow to maximize your return?

Extra Credit: How many iPod Mini’s will you have won when you run out of money?