## Will cryptarithmetic survive innovation?

In the beginning there were only cryptarithms (most of them multiplications, divisions and square roots) which were solved by humans (with paper, pencil and eraser) using the sheer power of logic, and they got exhilarated every time they broke a code!... Those buffs considered cryptarithms the most fascinating genre of mathematical recreations.

The "Hunter effect"

Then, in 1955, J. H. Hunter introduced the alphametics, puzzles where the words make sense. The positive effect is that the puzzles became more attractive and elegant. The negative one is that only the additions survived, and all other kinds of more complex operations (multiplications, divisions, square roots) were practically ousted from the cryptarithmetic kingdom.

Why that happened? Because it is very difficult - almost impossible - to create one of those problems completely alphametic. When having fun with cryptarithms, I myself prefer the multiplications and divisions, which have got more color and zest and require different math reasoning to be solved. For me additions are too simple and monotonous, so I regret profoundly the loss of those instigating old divisions and multiplications.

And the worst part of the story, as far as alphametics dominated the landscape and became a fade, is that the loss will be forever irreversible, as it stems from mathematical restrictions: it is almost technically impossible to compose "alphametic" divisions and multiplications while restricted to using only 10 letters of the alphabet, processing multiple operands makes difficult to extract and combine English words that make sense.

Jim Mayfield, at the University of Maryland Baltimore County, very smartly almost bypassed those restrictions. He devised an amazing computer program that creates a cryptarithmetic puzzle every time you log in. These are long division cryptarithms where the digits are "masked" with words from the English vernacular repertory. The result is that you get semi-alphametic divisions, where some words are valid English but don´t make much sense, as far as they are selected without semantic meaning.

Inspired on Mayfield´s semi-alphametic works, I decided to popularize the multiplication and division cryptarithms I had been composing along the last decades. You can see them at My Cryptarithms. I did this as a tentative of reviving those traditional puzzles seldom available anymore.

Computers and the Internet

In the old times very few people managed to compose a substantial number of cryptarithms. It demanded real hard work, expertise, and lots of guessing and trial-and-error. By then, puzzlemakers couldn´t create a problem that exceeded their own mathematical knowledge. And when publishing those puzzles the authors even used to screen out the very hard puzzles, thus avoiding put their readers to flight. Alphametics were then very scarce, and if you succeeded in gathering 40 puzzles you had enough material to edit a book.

With modern computer resources now available everywhere, by using computer generators and solvers, everyone can have fun making their own alphametics by the dozens. The negative effect of this revolution occurs whenever one of these weekend alphametic puzzlemakers decides to publish his works on the Web: long lists containing hundreds of puzzles but - this is the point - most of those creations are not soluble by hand, by human creatures, and only the damn computers that created them can solve them thanks to very powerful mathematical algorithms!

The consequence is that newcomers to cryptarithmetic get discouraged and scared when coming across these terrifying lists of insoluble puzzles, getting an uncomfortable feeling of inferiority and dumbness! By doing so, those constructors are spoiling and destroying the future of cryptarithmetic as a popular form of recreational mathematics!

What is the use of displaying long lists of puzzles only soluble by computers? As Martin Gardner said, what satisfaction can one get from solving a problem by giving it to a computer that will crack it in a matter of milliseconds? The whole enjoyment in solving a cryptarithm is to do so by hand.

So here is a piece of advice to the modern alphametic constructor: if you care for the future of cryptarithmetic, please screen all your puzzles before publicizing them. Display only the ones that are elegant and that you have previously solved by hand. Try also, like the old masters did, to grade the lists of puzzles in order of difficulty. By doing this, you are giving a chance for the new generation of beginners get acquainted with alphametics, fall in love with them (as you did!), so maintaining alive and growing the wonderment and adoration all we devote to this noble art.

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Copyright © 2001 by Jorge A C B Soares.
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Last updated: July 20, 2003.

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