The William Lowell Putnam Mathematical Competition 2004
The William Lowell Putnam Mathematical Competition will take place on Saturday, December 4, 2004. The Putnam will take place in the Vidalakis room
at the Schwab Residental Center, on Serra Street right by the corner with
Campus Drive East. Here is a map.
The problems and solutions are below.
It is a challenging opportunity for you to test your mathematical
mettle. In the 2003 competition, 3615 individuals participated,
representing 479 colleges and universities across Canada and the U.S.
The Stanford team placed eleventh,
and many individuals did very well. (I have a text file of results
that I can forward to anyone interested.)
The measure I look to is the number of competitors on the list of top
performers sent out with the results; we had 31, making us one of the
top three.
The competition emphasizes ingenuity rather than knowledge, so freshmen
are not at much of a disadvantage compared to seniors. Interest in or
experience with problem solving is a plus. Not just math majors
have done well; many recent winners have come from nearby disciplines,
including physics, computer science, and engineering.
Completely solving even one of the twelve problems is a
significant achievement, and in almost all years would place you well
above the median. (Keep in mind that the particpants are selfselected
from among the best in the continent.)
Links:

The introductory poster.
 The introductory meeting will take place Tues., Oct. 5,
5:306 pm,
in 380383N (in the corner of the third floor of the math department.
Here is the introductory handout.
 Meetings: We will have informal dinnertime problem solving practice
sessions this quarter, on Mondays from 6 to 7:30.
Practice problems will include some on the
topics discussed, and some others. Handouts will appear here.
 Monday, October 18: general problemsolving strategy, induction,
and the pigeonhole principle. (I start with this every year.)
Website of the week: The BanachTarski paradox, at the wonderful "Fun Math Facts" website at Harvey Mudd College.
Here are the problems: (ps,
pdf)
 Monday, October 25: Alok Aggarwal (number theory / modular arithmetic).
The problem of the week is a devious checker puzzle from Henry Segerman;
it's the first problem on the masterclass sheet below.
Problems: (ps,
pdf)
 Monday, November 1: Lenny Ng (generating functions or recursions).
Last week, Alok did a beautiful card trick, with his amazingly psychic
assistant.
The website of the week is a beautiful explanation of
what makes the card trick work, by Michael Kleber.
Problems: (ps,
pdf)
 Monday, November 8: Vin da Silva: "there's no such thing
as democracy" (Arrow's Theorem etc.).
The website of the week is related: the Slate article
that came out this past week, Game Theory for Swingers:
What states should the candidates visit before Election Day?,
by Jordan Ellenberg (a professor at Princeton that some of you have met).
Problems: (ps,
pdf)
 Monday, November 15: Ben Brubaker (counting).
Two websites of the week: (1)
a Wired magazine article about how the titfortat
prisoner's dilemma strategy was dethroned by clever conspiring.
(2)
Last week, we had a Colonel Blotto tournament (see the last problem on
last week's problem sheet for the rules); Omkar and Roger won, with
Jim just behind.
Here is some information about an
earlier "Colonel Blotto" tournament, with some discussion of strategies
that did well.
Problems: (ps,
pdf)
 Monday, November 22: Henry Segerman (the mathematics of juggling).
[Henry couldn't make it because he was sick.]
Website of the week:
interview with Manjul Bhargava of Princeton on Fibonacci numbers, music,
and many other things (related to Lenny Ng's talk from Nov. 1).
Problems: (ps,
pdf)
 Monday, November 29: Let's try this again: Henry Segerman (the mathematics of juggling).
We then tried an exercise on brainstorming:
looking the last two year's Putnams, and trying to figure out
ideas on how to get started on the problems.
Website of the week: a breakthrough in number theory
a fast primality test
(article by terrific author Sara Robinson).
Problems: 2002 competition and solutions,
2003 competition and solutions.
 There will also be a Masterclass for a few experts (everyone is welcome). It will take place Mondays 7:458:45.

Here are the 2004 Putnam
problems
and solutions.
You'll notice the slick solution to B4 by our very own Andy Lutomirski.
 The official Putnam website.

We'll have one last meeting on Monday, January 31, 68:30 pm, to go
over the solutions to the Putnam. Solutions will be presented by
Shaowei, Bob, John, Ben, Alok, myself, and anyone else interested.
 Recommended reading:
 I really like Loren Larson's "Problem Solving Through
Problems"  definitely worth
owning. It's great preparation for the Putnam.
 It is also great help (more than you would think) trying many old problems.
I'd especially recommend the collection of recent Putnams
"The
William Lowell Putnam Mathematical Competition 19852000: Problems,
Solutions, and Commentary", by Kiran Kedlaya, Bjorn Poonen, and myself.
 There are more good problems in the previous Putnam book,
"The William Lowell Putnam Mathematical Competition Problems and Solutions: 19651984", by Alexanderson, Klosinski, and Larson (look especially at those
in the 1980's).
All of these books are in the math library (possibly on reserve), in Building 380.
Also, on the web you can find
 a compilation of old Putnam problems and solutions on the web, collected
by Kiran Kedlaya;
 to find solutions to older Putnams, you can read
the official solutions in the American Mathematical Monthly, which
you can see electronically
(from any Stanford computer)
here.
At that page, 'Search this journal' for "William Lowell Putnam"
in the title.
 Some more links are available through this good
UCSD site,
by Patrick Fitzsimmons.
 Last year's Stanford Putnam website.
Want more? Additional suggestions for others? Please
let me know.
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