Ten greatest Math Puzzles of All time- NOT

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.

1. The Riddle of The Sphinx. Is this even a math puzzle? They say that it is since it involves making analogies.
2. 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.
3. Fibonacci's Rabbit Problem. Possibly the first recurrence.
4. Euler's Koningsberg Bridge Problem. This problem started graph theory.
5. The Four color problem. This generated alot of math of interest. They claim `the solution changed math as we know it'
6. 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.
7. Lloyd's get-off-the-earth puzzle. This is similar to Rubits cube in spirit. I never heard of it before this book.
8. Liar's paradox. Classic and very old. Could be the first serious study of self reference.
9. Magic Squares. C'mon, not that important!
10. Cretan Layrinth (Mazes). Very old, but again, not that important.

To ask if these are great math puzzles, you have to define great, math, and puzzle.
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.