# A collection of nice problems

#### Nic McPhee

University of Minnesota, Morris

This is a collection of problems I've gathered from various sources. I've tried to choose problems that are conceptually simple to understand. Thus the statement of most of the problems should be understandable to anyone with basic high school math. The difficulty of the solutions varies quite a bit, however, ranging from simple "Ah-ha"s to problems requiring either non-trivial effort or non-trivial mathematics. I've made no effort to indicate difficulty, both because difficulty is so relative, and because I think all the problems are fun and interesting, and therefore deserve thinking about even if the thinking doesn't necessarily lead to a solution.

The problems have been numbered (in a largely arbitrary fashion), and grouped 10 to a page to make finding a specific problem a little easier. This isn't the greatest organization scheme, but it works; feel free to suggest alternatives.

[Problems 0-9]
[Problems 10-19]

I've not credited sources for specific problems because the sources often provide the solution as well, and I will use these for homework and exam questions at various times. If you're interested in the source for a specific problem, feel free to send me some mail. I will say, however, that many of these problems came from these excellent sources:

- Problem-solving through problems by Loren C. Larson, Springer-Verlag.
- A problem seminar by Donald J. Newman, Springer-Verlag.
- Most any book by Raymond Smullyan.
- A logical approach to discrete math by David Gries and Schneider, Springer-Verlag.
- An unpublished set of problems collected by Jan van de Snepscheut.

If you know of a particularly good collection of similar problems, feel free to send me e-mail.

End of **A collection of nice problems**

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mcphee@cda.morris.umn.edu

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Saturday, September 27, 1997.
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