AMM Problem 12474 Solution

In this article, I provide the solution to AMM Problem 12474. You may be wondering why I posted so many articles all at once today. I just finished exams, and was missing some nice math problems. So, I sat down, opened AMM and just picked some interesting ones. These are the most typeable ones I solved!
This problem is based on probability. It feels like something you'd get in a quantitative finance interview because it's one of those "find a good strategy to do this thing with high confidence". But its likely to be harder than what one would expect in such an interview. (It's an AMM problem, it's not supposed to be solved in much more than 1 hour under stress anyway).
You need knowledge of Hoeffding's inequality to solve this problem (or at least it makes it easier). This is another reason it may be harder than a quant interview questions due to needing more background than basic probability theory.
Also, the "cleverness" for this problem seems to lie in the proof of the strategy, rather just the strategy itself. Again, this might make it harder that what you should do for a quant interview prep and make it more research/math style.
Nevertheless, it feels similar enough to a quant interview problem that I would recommend this to anyone preparing for a quant interview who wants a good challenge.
I would recommend trying to solve it yourself before reading on. The problem took me ~20 mins to fully prove and ~1 hour to type out. But also Hoeffding was fresh in my memory.

The proof can be found clicking here

I hope you enjoyed reading the article

Any feedback is greatly appreciated!