Division 2 and division 1 easy explanations are complete. Go here: http://apps.topcoder.com/wiki/display/tc/SRM+569
I think I have div1 medium figured out, I just need to make sure to understand a couple of thing. Div1 hard is hard as usual, but after rng_58 explanation I think/hope this won't take me as long as last match.
There are forces at works towards compensating the current trend of unsolvable div1 1000s by extending the duration of the matches. I really dislike the idea. A similar change happened to Google's Code Jam and I think that the problem set quality has been on a downwards spiral since then. And the longer matches have been less comfortable to my taste. Instead of increasing the chances to solve problems, problems became longer to solve.
What I do know is that we used to have people solving div1 hard problems in the past. So it is certainly possible to make problem sets that are solvable in the current 75 minutes.