Category Archives: Problem Solving

Contest Pigeons!

(This is a talk I gave for the Canadian IMO team at their 2014 winter camp at York University on Jan 3, 2014.) The pigeonhole principle is a remarkable combinatorial theorem that looks silly and obvious, but turns out to be quite powerful and useful, especially in the context of contest problem solving. I’m going […]

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Ropes and Dwarfs in a Munich Subway

People in Germany like Math! After my recent trip to Bonn, Germany, I visited my friend Maria in Munich, Germany for a weekend. She was wonderful and showed me all around town. One thing about her that has always impressed me was how into mathematics she is. When I met her in Toronto last year, […]

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The Battery Problem – Math for my Mom

(After writing some posts directed at other mathematicians, here is one for everybody.) I was sifting through some old issues of Crux Mathematicorum last Friday. For those of you who don’t know, this is a wonderful magazine that contains tons of math questions generally like those you would see in a math contest or olympiad, […]

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Secret Santa 3: The Paradox.

Last time I discussed the solution to Sam’s problem: Sam’s Problem. Is it possible for two people to each choose a natural number so that both numbers are exactly 1 apart and neither person knows who has the larger of the two numbers? I established, by induction, that it is impossible to do this. Great. […]

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The Secret Santa Problem (Part 2)

Last time, just in time for Christmas, we looked at the Secret Santa Problem. Basically the problem is to set up a secret santa type gift exchange without using any external aids like random number generators. A similar problem given to me by Sam Coskey is the following: Sam’s Problem. Is it possible for two […]

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The Secret Santa Problem

Happy holidays everyone! As Christmas approaches so do the Christmas related problems. I’m not talking about the long lines at stores or the busy days filled with errands, I’m talking about Christmas math problems. Here is one I learned at my department holiday party from Eric Hart and Jeremy Voltz. This whole post is going […]

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