Good Source(s) of Old Math Puzzlers for Students

Question

I am looking for good tried and true (mathematics, science, logic) problems to present to high school math students from time to time for entertainment, as well as for the purpose of trying to sharpen their critical reasoning skills.

Tractable problems with unexpected outcomes, such as the "Rope Around the Earth Problem", is what I have in mind.

Are there any sources that anyone knows of (perhaps archived on the Internet) that contain plenty of "puzzlers" that talented students are apt to find interesting? Many thanks.

Answer 1

I really like the book "Mathematical Puzzles: A Connoisseur's Collection" by Peter Winkler (Link to google books)

To paraphrase the author, the problems in the book satisfy the following properties:

• Amusement: should be fun to solve
• Universality: should suggest some general mathematical truth
• Elegance: easy to state, perhaps with an element of surprise
• Difficulty: the solution must not be obvious
• Solvability: must possess at least one solution that is elementary

Answer 2

For reasons mentioned here, I recommend Tatham's Puzzles and Manufactoria. Tatham's puzzles are automatically generated, so they can be played over and over again, and many people who like logical puzzles will definitely like them. Unfortunately, they do not have "unexpected outcomes", but I hope you find them a good puzzle source!

I want to say that many typical puzzle collections (even those claimed to be logic puzzles) do not actually rely on logic, but on pattern matching, which is not logic. Hence if your goal is to sharpen logical reasoning, then these puzzles are pointless. I have not read Peter Winkler's books mentioned in panini's answer, but it is a good sign that the author says that the problems "should suggest some general mathematical truth". Just to give an example of what is not logical, completing a sequence is not logical, and arguably most such puzzles are wrong from an information-theoretic viewpoint.