# Contests

## Mathematics and Statistics

## NCS Team Contest | Putnam Contest

## There are two yearly 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: 204-786-9374).

## Problem Solving Sessions for Fall 2019

Contact Dr. Terry Visentin for the fall schedule: t.visentin@uwinnipeg.ca

## News: UWinnipeg student ranks highly in prestigious math contest

Two UWinnipeg students took part in the very prestigious William Lowell Putnam Mathematics Competition and did favourably in this very difficult math contest. Third year Honours Math student Adam Borchert did exceptionally well, ranking 555th among the very best math students in North America. Phil Lafrance (4th yr, Honours Math) also distinguished himself by making progress on a difficult problem. Through the years, the Putnam has proved a formative experience for many internationally-known Mathematics researchers.

Students compete as individuals by writing two 3 hour exams, each consisting of 6 very difficult math problems. A total of 4320 students from 577 colleges and universities across North America competed and this year’s contest was especially difficult. Roughly one third of the contestants were unable to earn points on any of the 12 problems, but both of our students did.

UWinnipeg’s Putnam team has been coached by Dr. Terry Visentin of the Department of Mathematics & Statistics. Visentin conducts weekly problem solving seminars to prepare the students for the contest.

“I’m very proud of how our students performed this year,” said Visentin. “All the very best universities in North America enter this competition, so to score this well is a great credit to the hard work of these students and to the preparation they’ve received by the many fine instructors in our department.”

In 2015, the team of Adam Borchert, Jeremy Nicholson and Alex Stephens placed 17^{th} among 82 teams from 29 colleges and universities across Manitoba, Northwestern Ontario, Minnesota, North Dakota and South Dakota. Each team, consisting of up to 3 students, has three hours to attempt to solve 10 rather challenging math problems. To prepare for the contest, students take time away from their normal course work to learn new solving techniques and work on practice problems.

The North Central Section of the Mathematical Association of America sponsors this Team Math 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 always seem to enjoy this aspect of the competition and have performed well over the years.

In 2014, six UWinnipeg students took part. The team of Adam Borchert, Phillip Lafrance and Trevor Thompson placed 30^{th} and the team of Matthew Brown, Serina Camungol and Gaia Moravcik placed 39^{th} out of 90 teams.

In 2013, nine students took part, with the top team of Phillip Lafrance, Jehu Peters and Tim Pressey placing 10th out of 83 teams. That same team had placed 13th in 2012.

In 2011, UW team "Three Math-keteers" (Max Bennett, Blake Madill, Matt Morison) placed 30th in the total of 76 teams that year.

Our best performance came in 2005 when John-Paul Harris and Joel Peters-Fransen placed 7th out of 65 teams. This narrowly surpassed the 8th place performance of Erica Moodie, Jennifer Prokop and Go Suzuki in 1999.

#### Here are two sample problems from previous contests.

(1) 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.

(2) 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 Annual Putnam Contest is held on the first Saturday in December.

The William Lowell Putnam Mathematical Competition is a traditional contest for individual students and has been held annually for the last 75 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.

Read the history behind the prestigious William Lowell Putnam competition .

YEAR |
STUDENT |
RANK/# OF CONTESTANTS |

2014 | Adam Borchert | 555th of 4320 |

2013 | Tim Pressey | 266th of 4113 |

2013 | Yifeng Zang | 597th of 4113 |

2012 | Tim Pressey | 415th of 4277 |

2012 | Yifeng Zang | 713th of 4277 |

2008 | Dylan Buhr | 473rd of 3627 |

2008 | Iain Crump | 619th of 3627 |

2005 | Joel Peters-Fransen | 219th of 3545 |

2004 | Joel Peters-Fransen | 596th of 3733 |

2001 | Sean Fitzpatrick | 555th of 2954 |

2000 | Kevin Doerksen | 422nd of 2818 |

1999 | Go Suzuki | 217th of 2900 |

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 2013 the University of Winnipeg placed 62nd among the 557 Universities across North America which competed.

Last year the team competition was won by MIT.

#### Here are two of the easier(!) problems from a previous contest.

(1) 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*?

(2) 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.