Re: 2006 Putnam problems
- From: "Jules" <julianrosen@xxxxxxxxx>
- Date: 5 Dec 2006 06:24:02 -0800
Jules wrote:
steiner@xxxxxxxxxxxxx wrote:
Hi, all!
Would someone please be kind enough to post this year's Putnam
problems? Thanks!
Regards,
Ray Steiner
I am wondering if anybody has solutions to any of the Putnam questions
that they would like to discuss. I was unable to take the Putnam this
year (the GRE subject test was on the same day), but I have been
looking over some of the problems. I was surprised by some of the
later problems on the test, specifically A4 and B5. Both had very
short solutions, which is usually only the case for the first couple of
problems in each section. I haven't yet attempted A1 or B1, but at
first glance, they both look to be more difficult than A4 or B5.
And what about B5? The question basically asks for a function f that
maximizes the integral from 0 to 1 of (f(x) * x ^ 2 - x * (f(x)) ^ 2).
It is clearly sufficient to maximize (f(x) * x ^ 2 - x * (f(x)) ^ 2)
for each x. By a simple computation, (f(x) * x ^ 2 - x * (f(x)) ^ 2)
is maximal when f(x) = x / 2.
.
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