Did anyone here take the Putnam exam this weekend (or administer it)?

It had an unusually hard A1 and an unusually easy B1

 

Part B was notably harder than A.

I made way too many dumb mistakes. I could've tripled my score if I had just thought more clearly during the test.

 

Part B was overly difficult IMO. I was also surprised they had a real group theory question (A5)! (Which, IIRC, is an easy exercise in Dummit & Foote.)

 

Huh. Sorry for making a new thread. I made my thread earlier this afternoon and hit submit, but my internet froze. I just now resubmitted my thread, then saw this thread.

 

I have moved this thread to GD because it is asking about the test and NOT the math. The other thread was looking at the MATH so it is still in General Math.

 

I had similar problems, also due to B2. Initially I could only get 1/2 in the upper bound, and not 1/8. But an hour later I realized that there was some vital piece of information in my construction that I wasn't using. Namely, I defined F(x) = [itex]\int_0^x f(t) \, dt[/itex], then because F(1)=F(0)=0, we get (by Rolle's theorem) a c in (0,1) such that F'(c)=0=f(c) (the last equality being the FTC), so now we can use the MVT or a local approximation to proceed from here. What I missed - for a very long time - was that c is an extreme point of F!

After seeing the two-line solution to B5 I'm kicking myself.

 

No opinions on A2?

 

The question doesn't even ask for a proof. A good guesser (or a lucky one, like me) will see the square as the likely solution, write down the area, and move on. Total time: 1 minute, tops!

Going out on a limb, the convex set with maximal area probably has an area of 8.

 

And get 1/10!

 

:rofl: So that's how it works! If they don't ask me for a proof, I wouldn't think to give 'em one!

 

Yes, that's what I meant. So, I'd have scored a 0 on that one, damn!

 

What about for problem B3 for this year? I had a friend who was able to derive a legitimate formula for x(2007), but couldn't prove it. He wrote down his formula (which was correct), and wrote a little bit about how he derived it before time was up.

Do you think he'll get a point?

 

I think if the final answer is correct, but the method is sketchy, you'll usually get 1/10.