There is a book
The Liar's Paradox and The Towers of Hanoi: The Ten
greatest Math Puzzles of all Time
Thats just two problems; however,
the book does have 8 more puzzles.
I list them below.
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.
To ask if these are great math puzzles, you have to define great
Influential? Interesting Mathematically? Interesting Historically?
Important? Intrinsic math value?
Intellectually challenging? Other adjectives beginning with I?
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.
: 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
: A non-math person can understand the
question and think about it, and hopefully have fun with it.
They all qualify.
Posted By GASARCH to Computational Complexity
at 2/08/2008 10:53:00 AM