Unfortunately there isn't any shortcut for solving problems the best way is practice, I gave you a link to MIT openware , I believe you will find there any thing you need(video lecture, lecture notes, problems...). But learning isn't enough you need to practice . After you learn a topic just solve a lot of problems for this topic, you will find it as the best way or learning.
By the way, how does the regional competition works?(open question for calculation or closed for intuition)
And good luck.