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Did anyone here take the Putnam exam this weekend (or administer it)? What did you think?

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Did anyone here take the Putnam exam this weekend (or administer it)? What did you think?

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It had an unusually hard A1 and an unusually easy B1

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

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morphism

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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.)

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It's ok. By the way, semi-official solutions are http://www.unl.edu/amc/a-activities/a7-problems/putnamindex.shtml" [Broken]. I say "semi-official" because they're not official, they're done by Kiran Kedlaya and his compatriots, but everyone regards them like they would official solutions.

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Integral

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- #9

morphism

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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.

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Gokul43201

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No opinions on A2?

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Gokul43201

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

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morphism

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And get 1/10!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!

- #14

Gokul43201

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:rofl: So that's how it works! If they don't ask me for a proof, I wouldn't think to give 'em one!And get 1/10!

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What do you mean by maximal? Do you mean maximal without going to the other side of the hyperbolas? Because the original question just asked for the set to hit all four branches of the hyperbolas, and you can make arbitrarily large convex sets with that property. But if you mean the set has to be contained within the hyperbolas, then you might be right. (Then it's easy to see that the set may contain at most one point on each branch of the hyperbola.) That problem seems harder to me.

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Gokul43201

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Yes, that's what I meant. So, I'd have scored a 0 on that one, damn!Probably 0 for that problem as the answer isn't particularly hard to guess.

What do you mean by maximal? Do you mean maximal without going to the other side of the hyperbolas?

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Do you think he'll get a point?

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morphism

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