Verbal arithmetic

The classic example, published in the July 1924 issue of Strand Magazine by Henry Dudeney,[1] is:

An 1864 example in The American Agriculturist[2] disproves the popular notion that it was invented by Sam Loyd.

The name "cryptarithm" was coined by puzzlist Minos (pseudonym of Simon Vatriquant) in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics, and was translated as "cryptarithmetic" by Maurice Kraitchik in 1942.

Solving a cryptarithm by hand usually involves a mix of deductions and exhaustive tests of possibilities.

For instance the following sequence of deductions solves Dudeney's SEND+MORE = MONEY puzzle above (columns are numbered from right to left):

In computer science, cryptarithms provide good examples to illustrate the brute force method, and algorithms that generate all permutations of m choices from n possibilities.

For example, the Dudeney puzzle above can be solved by testing all assignments of eight values among the digits 0 to 9 to the eight letters S,E,N,D,M,O,R,Y, giving 1,814,400 possibilities.