Putnam! Year 4
Dec. 6th, 2008 06:07 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
sniffnoy(EDIT 1:10 AM: Added some more summarization.)
Obviously, I will be as vague as required till solutions can be posted. (Which is 21:00 EST Sunday, right?)
A1: You call this a Putnam problem? Are you kidding me?
A2: Also easy.
A3: I had a nice solution for this that I'm surprised nobody else used. I mean, it's the same in essentials as what most other people did, but it allowed me to sweep lots of bookkeeping under the rug. (Actually, I realized afterward, there was a slight error, of the bookkeeping sort... but it's very minor, just a slight technical distinction.)
A4: Tried some computation, it got nasty, left it alone. Though I'm pretty certain my computations were wrong. Such a nice solution I saw afterward, though! Also, apparently I forget basic [subject].
A5: I should have gotten this one, but a failure to make an obvious identification led me down a path I couldn't finish. The solution I turned in was not only incomplete, but only worked in a special case.
A6: Nothing.
B1: Pretty easy.
B2: All the time I spent working on this problem, I spent trying to remember or reconstruct [formula]. I knew basically what it looked like, so I could rederive it, right? Turns out no. When I got home, I immediately looked up the formula. Turned out I had remembered it right, but was miscalculating (in a pretty dumb way, too) when attempting to rederive it! Although, after doing a bit, it seems that formula may not be so helpful (in fact, I'm not certain it actually applies, and suspect it doesn't). Nobody else did it that way.
B3: Nothing.
B4: I got myself so confused doing this. Spoke to someone afterward who got it, he said he used [theorem]. But I was sure [theorem] couldn't possibly apply in this case! I don't know if he used [theorem] proper or just something based off the proof of it, but I'm pretty sure I was wrong about it not applying in that case - both because I realized afterward I had gotten mixed up about what it said, and also because in the one example I tried it definitely did apply. ...wow, I just did it, and it was actually pretty simple once I sorted that out. Damn. Although there was one other obvious thing I should have thought of doing that I didn't, but I'm not sure it would have helped when I was convinced [theorem] didn't apply.
B5: This one I got pretty nicely.
B6: Well, obviously we only need to [do something], but where to go from there?
So, 5 problems, and maybe a point for A5. Of which 3 were pretty universally easy, and I really should have gotten B4 and possibly A5 and not wasted so much time on B2, so, yeah, not actually so good, but not horrible, I guess.
So how'd the rest of the team do? The team was me, Calvin, and Alex Zorn[0]. Calvin beasted the first half, getting A1-A5 and giving a sketch for A6, though it's unknown whether it actually works. Alex, on the other hand, only got A1 and A2. For the second half, Calvin got B1 (which he used an overcomplicated solution for), B2, and B6 (using a trick I'm going to have to start remembering at some point); he didn't get B3, and I don't know whether he got B4 or B5. I don't know at all how Alex did on the second half, as he didn't stick around.
-Harry
[0]Alex is a first year, and yes, he is related to Max Zorn; in fact, he's his great-grandson. I mentioned him earlier when the summer before last, when I was at REU and he was at YSP.
Obviously, I will be as vague as required till solutions can be posted. (Which is 21:00 EST Sunday, right?)
A1: You call this a Putnam problem? Are you kidding me?
A2: Also easy.
A3: I had a nice solution for this that I'm surprised nobody else used. I mean, it's the same in essentials as what most other people did, but it allowed me to sweep lots of bookkeeping under the rug. (Actually, I realized afterward, there was a slight error, of the bookkeeping sort... but it's very minor, just a slight technical distinction.)
A4: Tried some computation, it got nasty, left it alone. Though I'm pretty certain my computations were wrong. Such a nice solution I saw afterward, though! Also, apparently I forget basic [subject].
A5: I should have gotten this one, but a failure to make an obvious identification led me down a path I couldn't finish. The solution I turned in was not only incomplete, but only worked in a special case.
A6: Nothing.
B1: Pretty easy.
B2: All the time I spent working on this problem, I spent trying to remember or reconstruct [formula]. I knew basically what it looked like, so I could rederive it, right? Turns out no. When I got home, I immediately looked up the formula. Turned out I had remembered it right, but was miscalculating (in a pretty dumb way, too) when attempting to rederive it! Although, after doing a bit, it seems that formula may not be so helpful (in fact, I'm not certain it actually applies, and suspect it doesn't). Nobody else did it that way.
B3: Nothing.
B4: I got myself so confused doing this. Spoke to someone afterward who got it, he said he used [theorem]. But I was sure [theorem] couldn't possibly apply in this case! I don't know if he used [theorem] proper or just something based off the proof of it, but I'm pretty sure I was wrong about it not applying in that case - both because I realized afterward I had gotten mixed up about what it said, and also because in the one example I tried it definitely did apply. ...wow, I just did it, and it was actually pretty simple once I sorted that out. Damn. Although there was one other obvious thing I should have thought of doing that I didn't, but I'm not sure it would have helped when I was convinced [theorem] didn't apply.
B5: This one I got pretty nicely.
B6: Well, obviously we only need to [do something], but where to go from there?
So, 5 problems, and maybe a point for A5. Of which 3 were pretty universally easy, and I really should have gotten B4 and possibly A5 and not wasted so much time on B2, so, yeah, not actually so good, but not horrible, I guess.
So how'd the rest of the team do? The team was me, Calvin, and Alex Zorn[0]. Calvin beasted the first half, getting A1-A5 and giving a sketch for A6, though it's unknown whether it actually works. Alex, on the other hand, only got A1 and A2. For the second half, Calvin got B1 (which he used an overcomplicated solution for), B2, and B6 (using a trick I'm going to have to start remembering at some point); he didn't get B3, and I don't know whether he got B4 or B5. I don't know at all how Alex did on the second half, as he didn't stick around.
-Harry
[0]Alex is a first year, and yes, he is related to Max Zorn; in fact, he's his great-grandson. I mentioned him earlier when the summer before last, when I was at REU and he was at YSP.
