I think you are approaching the problems with the same old paradigm that we used for reading. Before Photoreading, I would try to master or learn everything as I read, forcing what I could in through the concious mind. That's not effective. You need to go over the material many times, each time learning more as you go.
Same is true with problems. Stop thinking u have to solve them the first time through. Think of it as you would a video game, you play through once, and as you get better, you return to the same levels to try them again. Use this multiple pass through method on the problems. Try a set of problems, then use the answer key for the ones you cannot get. Do NOT get stuck. A day later, work through the problems again, then again, and again, until they become second nature. If multiple passes helps in reading, wouldn't multiple attempts at solving the same problems also strengthen your ability? I think so.
Don't get stuck. Use the answers key. Keep working through the problems - even the ones you can answer - multiple times. I'm just a newbie here, but I hope this helps.
P.S. Do this in conjunction with what AlexK recommended.
