The William Lowell Putnam Mathematical Competition 2006
The photo on the right was taken before the afternoon session
of the 2006 Putnam, thanks to Alex Flury! Most of the Stanford competitors are shown.
The William Lowell Putnam Mathematical Competition will take place on Saturday, December 2, 2006. The Putnam will take place in the Vidalakis room
at the Schwab Residential Center, on Serra Street right by the corner with
Campus Drive East. Here is a map (it's actually the building just below the one in red).
We'll meet at 7:40 am. The first session will be 811 am, and the second
session will be 14 pm. We'll meet again for the second session at 12:50.
The Putnam is a challenging opportunity for you to test your mathematical
mettle. In the 2005 competition, 3545 individuals participated,
representing 500 colleges and universities across Canada and the U.S.
The Stanford team placed seventh,
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 37, 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 Monday Oct. 2,
5:155:45 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 5:156:45.
(Rough schedule: 55:15 beforehand,
people can drop by to discuss ``leftovers'' from the previous week.
5:155:30: short discussion of new technique. 5:306:15: work on problems.
6:156:45: eat pizza, watch ``volunteers'' present solutions and explain
how they thought about the problems.)
Some faculty and graduate students
always turn up with wise words, including hopefully
Mark Lucianovic, Daniel Mathews, Dragos Oprea, Andy Schultz, Henry Segerman,
Kannan Soundararajan, and others.
Practice problems will include some on the
topics discussed, and some others. Handouts will appear here.
 Monday, October 9: general problemsolving strategy, induction,
and the pigeonhole principle. (We start with this every year.)
Problems: ps pdf.
Problem of the week (from Sound): Does there exist a circle
with radius 100 in the plane containing 31415 lattice points (points
of the form (a,b) where a and b are integers)?
 Monday, October 16: generating functions.
Cihan Baran pointed out that the wonderful book
generatingfunctionology by Herbert Wilf is available online
here.
Problems: ps pdf.
Problem of the week (from Sound):
In a hotly contested election year, each Senator has slapped the face of
one other Senator. Can you form a committee of 34 Senators none of whom
has slapped another committee member?
 Monday, October 23: analysis.
Problems: ps pdf.
Problem of the week (from Sound):
Two players A and B play the following game. A thinks of a polynomial
with nonnegative integer coefficients. B must guess the polynomial.
B has two shots: she can pick a number and ask A to return the
polynomial value there, and then she has another such try. Can B win
the game?
 Monday, October 30: Mark Lucianovic explained
number theory.
Problems: ps pdf.
Problem of the week from Sound:
The RitzCarlton has 80 rooms, but a hundred guests. Fortunately for the
hotel at any point of time no more than eighty guests show up. At check
in, the hotel manager craftily gives each guest a number of keys such that
no matter which eighty guests arrive the manager can assign each guest a
room to which he already has a key. (E.g. the manager can do this by
giving each guest all eighty keys.) What is the minimum number of keys
the manager can get away with?

Monday, November 6: invariants.
Problems: ps pdf. (With typo corrected)
Problem of the week from Sound (with very clever political satire
added by Ravi): An indicted senator gives you an
m by n chocolate bar. What is the minimum number of times you must break
it in order to get 1 by 1 squares?

Monday, November 13: algebraic tools and techniques.
Problems: ps pdf.
Problem of the week from Sound: Look at the leading decimal
digit of 2^n. Does 7 appear more frequently or 8?

Monday, November 20: no meeting (Thanksgiving week!).

Monday, November 27: last regular meeting: Putnam problems and strategy.
Problems: ps pdf.
 There will also be a Masterclass for a few experts (everyone is welcome), on Mondays (immediately after the regular seminar, roughly 78 pm).
 Monday, October 9. Problems (Natth's problem now corrected): ps,
pdf.
 Monday, October 16. Problems:
ps,
pdf.
 Monday, October 23. No meeting due to problem shortage.
 Monday, October 30. Problems:
ps,
pdf.
 Monday, November 6.
Problems:
ps,
pdf.
 Monday, November 13.
Problems:
ps,
pdf.

Monday, November 20: no meeting (Thanksgiving!).
 Monday, November 27.
Problems:
ps,
pdf.
 The official Putnam website.
 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 (2day reserve, under
the course ``VAKILSEM''), in Building 380 (fourth floor).
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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