This webpage ~~is currently being~~ will someday be reorganized.

Problem sets for 2018.

The putnam exam is an annual mathematics exam originating from Harvard, aimed at undergraduate students in North America. It is written on the first Saturday in December, in two three hour papers. It's all long-answer, no multiple choice.

If you like playing with fun math problems, then this might just be your thing.

If you are interested in being part of our putnam team at University of Ottawa, then send Mike Newman an email (mnewman at you-know-where).

If you're trying to track me down, you find me here: schedule, office and email.

In the meantime, here is a problem (that I shamelessly stole from the Putnam website itself).

Players 1, 2, 3, …, n are seated around a table and each has a single penny. Player 1 passes a penny to Player 2, who then passes two pennies to Player 3. Player 3 then passes one penny to Player 4, who passes two pennies to Player 5, and so on, players alternately passing one penny or two to the next player who still has some pennies. A player who runs out of pennies drops out of the game and leaves the table. Find an infinite set of numbers n for which some player ends up with all n pennies. |

Here's an old one that I shamelesssly stole from somewhere that I can no longer remember.

Find all rational numbers a and b such
that a.
^{b}=b^{a} |

Here's another that I will attribute to Claude Shannon (if you know the reference or just know better than please tell me).

A message is to be transmitted over some imperfect medium, so it may be that some
of it is corrupted. Consider the message to be a (large) number. It is to be
written in base
If we choose
What value of
Note that the amount of information in a |

The general idea is to work on solving problems, share our insights, solutions, and stumbling blocks. I'll suggest some things to work on for a given week, but you can also bring your own problems (solved or not!). Presenting solutions is highly encouraged. It's a time-honoured truth that nothing crystallizes your own thinking like explaining it to someone else. It really is a win-win.

A few links for now, mostly to other peoples' collections of problems. Thank you to all of those people.

- Mathematics problem archive of Christopher Small at the University of Waterloo.
- The putnam training page of Miguel Lerma at Northwestern University. See especially the easy putnam problems, the putnam training problems 2011, and the previous selection and training tests.
- An archive of old Putnam tests. Needless to say you are encouraged to download the problems as opposed to the solutions.
- An MIT open course on problem solving. See especially the assignments.
- An old website for the New Zealand Math Olympiad.