Mathematics Contests
NCS Team Contest | Putnam Contest
There are 2 mathematics contests that interested UW students
can write.
To be eligible for either, a student must be a regularly
enrolled undergraduate who has not yet obtained a degree.
Below is a brief
description of each contest followed by information about preparation and
registration for the contests.
Any students who are interested or wish to
receive more information should
contact Professor Visentin (Office:
6L24, phone:786-9374).
The 13th Annual NCS Team Contest was held November 14, 2009
3 UW teams (Iain Crump, Alex Leithead, Micheal Pawliuk; Dylan Buhr, Matthias
Pielahn; Jean LeMoullec, Teresa May, Alyssa Vergata) competed in 2008.
UW's team of Piotr Biernot, Ryan Peters and Jenna Tichon placed 17th in 2006.
The North Central Section of the
Mathematical
Association of America (which involves math depts. from Minnesota, Manitoba
and the Dakotas)
has recently begun sponsoring a Mathematical Team Competition.
Taking place in mid-November, this contest debuted in 1997 and we competed
in it
for the first time in 1998. A University may enter as many teams of
up to 3 students as it likes.
The students have 3 hours to solve 10 problems which range from
straightforward to hard and they work together in teams to solve the problems.
Our students seemed to really enjoy this aspect of the competition and did very
well. In 2005 UW's team of
John-Paul Harris and Joel
Peters-Fransen placed 7th out of 65 teams.
Of the 64 teams which entered the 2001
competition, the team of Sean Fitzpatrick, Shonda Gosselin
and Tina Rapke finished in 12th place.
The winning team in 2008 was St. Olaf College in Minnesota. Congratulations on your winning effort!
Here are two sample problems from one of the previous contests. The first was one of the easier questions, the second was about average difficulty.
A
sequence begins with a1, a2,
and for n>2 is defined by an = an-1
- an-2.
Find the sum of the first 2004 terms
(in terms of a1 and a2),
and defend your answer.
A card shuffling machine always rearranges cards in the same way relative
to the order in which they are given
to it. The thirteen spades arranged in the order
A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K
are put into the machine, shuffled, and then the shuffled cards are put into the machine and shuffled again. If at this point the order of the cards is
3, K, 10, 2, Q, 9, 4, J, 8, 6, 7, A, 5,
What was the order of the cards after the first shuffle?
The 70th Annual Putnam
Contest will be held Saturday, December 5, 2009
UW's team of Iain Crump, Micheal Pawliuk
and Alex Leithead placed 65th of 545 teams in 2008.
The William
Lowell Putnam Mathematical Competition is a traditional contest for
individual students and has been held annually
for the last 60 or so years. Written during the first week of December, it
is a six hour exam (3 in the morning, 3 in the afternoon)
in which students attempt to solve 12 fairly difficult problems. Each
year, a list of the top 500 students is distributed to colleges and universities
across the continent.
A student who solves 3 or more problems would usually make this list.
Last year Dylan Buhr made this list.
In 2008, Dylan Buhr ranked 473rd and Iain Crump ranked 619th out of 3627 students.
In 2007, Micheal Pawliuk and Jenna Tichon placed 1180th out of 3753 students
In 2005, Joel Peters-Fransen placed 219th out of 3545 students.
In 2004, Joel Peters-Fransen placed 596th and John-Paul Harris placed 1123rd out
of 3733 students.
In 2002, Stephanie Phillips placed 1288th out of 3349 students. In 2001,
Sean Fitzpatrick
placed 555th out of
2954 students.
In 2000, Kevin Doerksen
placed 422nd out of
2818 students and in 1999, Go Suzuki
placed 217th among the 2900 students who wrote.
All are to be commended for their achievements and participation in such a
prestigious challenge!
Here's former student, Go Suzuki being presented with an award by Professor Currie at a UWMSSA meeting.
Considering that at most Universities only the best 5 or 10 math students enter this contest, placing highly in this elite group
is a great accomplishment. There is also a ranking for each school based on the total of the team members' scores, and in 2000
the University of Winnipeg placed 67th among the 434 Universities across North America which competed. Last year the team competition was won by Harvard.
Here are two of the easier(!) problems from a recent contest.
Basketball star Shanille O'Keal's team statistician keeps track of the number,
S(N), of successful free throws she has made in her first N
attempts of the season.
Early in the season, S(N) was less
than 80% of N, but by the end of the season, S(N) was more
than 80% of N.
Was there necessarily a moment in between when S(N)
was exactly 80% of N?
Let n be a fixed positive integer. How many ways are there to write
n as a sum of positive integers,
n = a1 + a2
+ . . . + ak,
with k an arbitrary positive integer and a1
≤ a2
≤ . . . ≤
ak ≤
a1 + 1?
For example, with n = 4, there are four ways: 4, 2 + 2, 1 + 1 + 2,
1 + 1 + 1 + 1.
