This book is part of a series of books each containing mathematical problems, some easy and some challenging. They are presented in thirteen sets, Book 0 to Book 12: each containing 101 problems and each set becoming progressively more challenging.
Some of the problems need only common sense and clear reasoning to solve. Others require some results and techniques you will need to discover by searching through other resources. All problems, I hope, will provide enjoyment.
These problems are dedicated to students who rejoice in wrestling with and finally overcoming, a problem in which a solution, to begin with, is not apparent. They are also dedicated to teachers who encourage their students to rise beyond the security offered by prefabricated exercises and experience the creative vitality of mathematics.
A short list of ‘answers only’ is provided with each set of problems, complete solutions are available elsewhere. I would encourage people to battle with a problem for an extended period until rewarded with a resounding victory or defeat. Only in the latter case should you seek help from the solution. The solutions are not definitive although they may suggest possibilities for exploring similar situations. There will certainly be other solutions and more elegant ones. You are encouraged to seek them.
While I hope that many of these challenges may be new to you, I make no claim for the originality of any of these problems. I acknowledge my debt to the original creators of these problems, recognising how hard it is to make up a problem which is ingenious, interesting and solvable without being trivial, tedious or impossible.
I hope that this collection of problems will be considered useful. Good luck!
“The mind is at best when at play” (J.L. Synge). Approach these problems as mathematical play.
MASA wish to thanks V. Frost, C. Swan and P. Carter for their contributions in the production of the series of 101 Mathematical Challenge Books.