Hey guys! Promys alum here from last year.
I’ll be happy to try answer any questions about the program that you may have
Like @vanillapuff and @OMPursuit said, the desired result of the problem set is to incite a passion for the act of problem solving, as this method of finding solutions by inquiry is really what drives the environment of the camp over the six weeks. If you’re having fun - that’s great! And the admissions people also like to know your way of attempting problems you have no idea how to approach.
From what I can remember, skill level had a wide range, from those who knew school level concepts to those of USAMO - even MOP - caliber, but everyone shares a love for the problem sets and problem-solving. As a result, the number of problems you get is less important than the conjectures you create and the patterns you notice; I knew some who answered 5/6 and some who answered 9/10 - that being said, I believe “the more, the better” maxim applies.
And if you’re looking for more specific information, I’d follow vanillapuff’s advice and look on the AoPS thread as well.
Concerning when application results come out, I got mine May 1, so it may be a couple weeks until acceptances are revealed.