Have Some Sums to Solve: The Compleat Alphametics Book

Alphametics, an arithmetic problem where the digits are replaced by letters, are an area of mathematics that anyone can enjoy. Solving them generally takes only simple algebra and a degree of persistence. To create a truly interesting problem, the letters should form a catchy phrase, for example the title of this book is an addition alphametic  HAVE + SOME + SUMS + TO = SOLVE I regularly use alphametic problems when teaching basic programming, as most can be solved using a computer program containing several nested loops. Steven Kahan is one of the world's leading experts on these problems, having been the editor of the alphametics column in Journal of Recreational Mathematics for many years. His knowledge of the field and collection of problems makes for an excellent combination of material that will keep you interested as you try to solve them. This collection not only explains the nature of the problems, but the standard techniques used to solve them. These techniques are an excellent introduction to some of the basic principles of arithmetic and I use them to explain some of the consequences of positional notation in basic algebra classes. Most students find such problems fun and I have used some of the simpler alphametics as exam questions. Detailed solutions to all of the problems are included in case you do get stuck. This is a book that is fun to read and some of the material can be used for educational purposes. I highly recommend that you examine it with either of those interests in mind.

The title is is a sum: HAVE + SOME + SUMS + TO = SOLVE. Every letter stands for a number. Solving the puzzle is to find the correct substitution for each letter by a digit. The book discusses such puzzles. Every second page has a puzzle. Introduction gives history of evolution of such a form of puzzle. The book is constructed in four sections. A good preface introduces the concept of alphametic puzzle, with the puzzle ( SEND + MORE = MONEY). The solution approach is discussed. Section two is collection of such puzzles. Each puzzle has some interesting titbit. Each puzzle is provided with a sheet for writing solution. Section three gives clues and directions for each puzzle. Section four gives the solution. The book discussion is restricted to alphametics. For example the puzzle on prime : A + LARGER + PRIME + WILL = APPEAR, discusses about the concept of primes and points out ( 2 ** 19937) -1 is a prime with 6002 digits. In association with another puzzle, there are interesting discussion on magic squares and a magic square. STEVEN + SUSAN = ALWAYS.