So I got one submission for an answer to my Modern Word Problem from my brother Steve. I’ll excerpt part of it here:
I guess the problem is how to effectively use that $100. Knowing that you are going to perpetually get 1/6 BOGO and thus have to spend $1 more dollar you can find your initial buy-in.
x + (1/6)x + (1/6)^2x + …. + (1/6)^nx = 100 [but of course you want that last term to be a whole number]
He talked through a bit more of the math and different ways that you may solve that equation. His final answer: 38 free songs.
My solution is less thorough but yields similar results. 1/6 of your original 100 gives you 16 more bottles. 1/6 of that gives you 2. You can keep going but you aren’t going to get any more whole bottles. So your total number of bottles is 118 bottles. 1/3 of those would be winners which leaves you with 39.
There is a whole bunch of things that I am ignoring here and I think Steve’s answer is much better. If I were asking this as an interview question (which I have considered doing), I would have accepted either answer.
Steve got the extra credit as well. You have no chance whatsoever of winning an iPod mini. Sorry.