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Introduction to Shalosh B. Ekhad's Computer-Generated Alphametics

By Doron Zeilberger

A Mathematician is Born

The highlight of my summer vacation, when I was a kid, was the yearly trip to "Doda Gitti veDod Hans" (Aunt Gitti and Uncle Hans). Starting when I was nine years old, my younger (by a year and a half) brother Gil and I traveled alone by train from Kiryat Motzkin (North of Haifa) to Jerusalem. There we enjoyed the company of our cousins Matti and Ada (whom we looked up to since they were already fourteen and sixteen year old). Aunt Gitti was a great baker (in fact she still is!), very musical (she still plays the piano at 90) and of course, very nice (she still is!). Uncle Hans Weiss (1902-1983) was very interesting and wise. In addition to having a brilliant legal mind (he was a Judge in Germany before Hitler forced him (and everybody else) out, and in Israel was a high-ranking official in the Legal Department of the Treasury Department), he loved literature, and surprisingly, Astronomy. He was a member of the Israel Amateur Astronomy Society, and I avidly read the newsletter that he received, later joined the society myself, and decided to become an astronomer when I grew up. But this never came to pass, because Hans, even more surprisingly for a lawyer, also loved math. It was him who first told me about Fermat's Last Theorem, and laughed when I immediately tried to prove it, saying that there is no rush. But what really got me hooked on math, back when I was eleven, and most probably made me drop astronomy and transfer to math, was the `cryptarithms' that he showed me how to do, essentially using logic, trial-and-error, and backtracking.

Now that Aunt Gitti is turning ninety (on Jan. 6, 2003), I was reminded of my debt of gratitude to both Hans and Gitti. I wrote a Maple package called OtiotUmisparim ("Letters and Numbers", the name of the weekly puzzle in the Israeli daily Yedi'ot Akharonot, currently edited by Yossi Harshoshanim), that automatically generates alphametics, that is cryptarithms consisting entirely of words in the input vocabulary. This webbook only contains a small sample. You can generate many yourself (provide that you have Maple on your computer), and if you enter your own vocabulary (that should have at least two hundred words to be effective), you can target it for any (natural) language or topic.

In order to use OtiotUmisparim , just download it, and follow the on-line instructions. Have fun!

Happy 90th Birthday, Doda Gitti!

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