Brains + Teamwork = $

Brains + Teamwork = $ McGill University

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McGill Reporter
September 12, 2002 - Volume 35 Number 01
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Brains + Teamwork = $

It's a step or two above determining where a train leaving from Montreal travelling at 97 km/h will meet a train from Toronto travelling at 83 km/h. Last spring, in the Society of Industrial and Applied Mathe-matics newsletter, a call for brave mathematicians was sent out by Nick Trefethen, a renowned professor of numerical analysis at Oxford. Called the "100 Digits, 100 Dollar" challenge, the ten problems allowed contestants to earn up to ten points for each correct digit in each problem. One hundred dollars was promised to the team that could get all of them correct. Ninety-four teams from around the world answered the call, but only 20 of these were successfully able to answer each question to ten decimals - including McGill's team.

"We're an active bunch up here, and when a challenge like this goes out we will answer it," said professor Nilima Nigam, who helped organize McGill's team from the department of mathematics and statistics. The team included professor Martin Gander, post doctoral fellow Paul Tupper, graduate student Sebastien Loisel and undergraduate student Felix Kwok.

Nigam said the team worked on the problems on and off for five weeks, each spending roughly thirty hours of their leisure time on the would-be stumpers. Every member took on a couple of different problems, with some overlap of responsibility in order to ensure the correct answers were reached.

Mathematics professor Georg Shmidt followed the competition and said that success in the challenge required "a desktop computer and ingenuity" - unlike the professor from MIT who hit the problems with a supercomputer and got nowhere.

"The questions were very eclectic - you really had to know a lot of different things," he said.

Another team with McGill connections was also successful - McGill alum Stan Wagon worked with former physiology staff member Danny Kaplan. Both are now at Macalester College in the States.

Think you can answer one? A flea starts at (0,0) on the infinite 2D integer lattice and executes a biased random walk: at each step it hops north or south with probability 1/4, east with probability 1/4 + e, and west with probability 1/4 - e. The probability that the flea returns to (0,0) sometime during its wanderings is 1/2. What is e?

Solution

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