SENDing MORE MONEY in any base
Abstract
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.