SENDing MORE MONEY in any base
One of the most significant conceptual jumps involved in algebra is the use of letters (and other symbols) to represent numbers. One way to get students used to this notion is via puzzles. This paper describes a generalization of one such puzzle, based on a terse telegraph message from impoverished college student to parents — “SEND MORE MONEY” — and well-known in some mathematical circles (a December 2001 web search turned up over two dozen hits). In this type of puzzle, which has been termed alphametics, each word is associated to a number with as many digits as there are letters, and each letter is associated with a distinct digit, 0 through 9. A puzzle solution identifies which digit corresponds to each of the letters.