I got 4 solutions for A1, but couldn't throw out the 2 extraneous ones in time.
B1 was a lot easier than it seems.
B3 was insane; I didn't get it. One of my genius friends saw the solution, but couldn't prove it, or put it in closed form. After getting home, I rearranged his solution into closed form, and now that I have access to mathematica, I was able to show that he was right.
Now that the fun's over, I need to get back to graduate apps/hating life.