Putnam Exam

[totoismomo]

@Trunk

I took it twice.

I got a zero the first time.

The second time I took it, I and several other students had done a volunteer study session once a week for a semester with a professor. We did problems with each other, on the board, had discussions; we prepped as much as we could. We focussed only on areas that we might excel, knowing that our best chance of scoring was nailing one where we “specialized”.

Test came. I found a question that was right up my alley. I put together what I thought was a reasonable proof, and after our discussions after the test, others thought that I had maybe nailed it (and by nailing it, I mean, getting a 10).

I got a 1. I think everyone else got 0’s.

Yes, I’m a bit baffled by people who say they could have done better if they had studied. It seems like the kind of thing that is impossible to study for, other than learning “global strategies” like how to apply the pigeonhole principle like iamthewalrus(:3= suggested (incidentally, something my adviser emphasized, too).

For those interested in the Putnam’s level of difficult, here’s an example off of this year’s test:

Define x[sub]0[/sub] = 1,
and let x[sub]n[/sub] = 3*x[sub]n-1[/sub] + floor[sqrt[5]*x[sub]n-1[/sub]]
(ex: x[sub]1[/sub] = 5, x[sub]2[/sub]=26, and so on)

Find an expression for x[sub]2007[/sub] in closed form.

I played with this one for an hour, and got nowhere. Never dealt with the floor function in an analytic way before. My best guess now, after looking on the web a little, is to use the fourier expansion for the floor function somehow.

[Snarky_Kong]

@iamthewalrus(:3=

The test is given in 2 3-hour sections, with 6 questions each. The strategy for any person of less than truly incredible ability is to pick a single question in each section and solve it really well. Picking the right question is critical. Year 2 I spent all of the first section trying to solve a problem about the maximum length of a section of parabola inscribed in a unit circle, integrating along the curve, and not only did I not get the right answer, to this day I don’t quite understand where I went wrong. That was just beyond my calculus abilities at the time (and I haven’t taken further calc classes since, so I’d guess it remains beyond them).

Isn’t this going to approach 4? A very steep parabola along a diameter.

[Trunk]

@Snarky_Kong

Isn’t this going to approach 4? A very steep parabola along a diameter.

Prove it!