- The Riddle of The Sphinx. Is this even a math puzzle? They say that it is since it involves making analogies.
- The Alcuin River Crossing Puzzle. Trying to cross a river with a Wolf, Goat, and Head of Cabbage. Very old problem in what is now graph theory. This problem did not start graph theory, but could have.
- Fibonacci's Rabbit Problem. Possibly the first recurrence.
- Euler's Koningsberg Bridge Problem. This problem started graph theory.
- The Four color problem. This generated alot of math of interest. They claim `the solution changed math as we know it'
- Towers of Hanoi. A nice exercise (my wife coded it up when she took CS 1, I've taught it in Discrete Math), but not that big a deal.
- Lloyd's get-off-the-earth puzzle. This is similar to Rubits cube in spirit. I never heard of it before this book.
- Liar's paradox. Classic and very old. Could be the first serious study of self reference.
- Magic Squares. C'mon, not that important!
- Cretan Layrinth (Mazes). Very old, but again, not that important.
Great: Influential? Interesting Mathematically? Interesting Historically? Important? Intrinsic math value? Intellectually challenging? Other adjectives beginning with I? If great means influential then some of the above qualify: Fib Rabbits, Euler Bridge, Four-color, Liar's paradox. Others may also qualify- I would need to know more about the history of math to tell.
Math: I can't define it but I know it when I see it. Riddle of the Sphinx I would say no. The rest are reaonable to call math.
Puzzle: A non-math person can understand the question and think about it, and hopefully have fun with it. They all qualify.