Problems for Mathematicians, Young and Old

PREFACE
I wrote this book for fun, and I hope you will read it the same way.
It was fun indeed-the book almost wrote itself. It consists of some of the many problems that I started saving and treasuring a long time ago.
Problems came up in conversations with friends, and in correspondence, and in books, and in lectures. I enjoyed them, thought about them, tried
to solve them, tried to change them, and tried to think of new ones, and then I tried to organize and write down the ones I was fondest of-and
this book is the result.

Problems, hints, solutions
The problems come complete with their statements, hints, and solutions.
The statements are not intended to be the most general ones known to humanity-their purpose is to stimulate thought, not abolish it. If you
can think of extensions and improvements of the results asked for, you have done what I hoped you would do.
The hints are intended to be just that-suggestions intended to get you to look in a possibly profitable direction. A hint might, for instance, be a question. That doesn't mean that you have to know the answer to the question before you can solve the problem-but, possibly, the question might offer more food for thought than the original statement of the problem does.
As for the solutions, they are sometimes "wrong", or partially wrong -and then soon corrected. Don't give up if you see something wrong-
keep going and try to set things right. The solutions make no pretense of being the best, the shortest, the most elegant, or even complete. Some
of the solutions are chatty discussions, and some are hardly more than slightly extended hints that say just enough to point you in the right
direction. In either case the purpose of a "solution" is to have you solve the problem-and to enjoy doing so…