Verbal arithmetic, also known as alphametics, cryptarithmetic, crypt-arithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters. The goal is to identify the value of each letter. The name can be extended to puzzles that use non-alphabetic symbols instead of letters.
The equation is typically a basic operation of arithmetic, such as addition, multiplication, or division. The classic example, published in the July 1924 issue of Strand Magazine by Henry Dudeney, is:
The solution to this puzzle is O = 0, M = 1, Y = 2, E = 5, N = 6, D = 7, R = 8, and S = 9.
Traditionally, each letter should represent a different digit, and (as in ordinary arithmetic notation) the leading digit of a multi-digit number must not be zero. A good puzzle should have a unique solution, and the letters should make up a cute phrase (as in the example above).
Verbal arithmetic can be useful as a motivation and source of exercises in the teaching of algebra.
Read more about Verbal Arithmetic: History, Solving Cryptarithms, Other Information
Famous quotes containing the words verbal and/or arithmetic:
“Language makes it possible for a child to incorporate his parents’ verbal prohibitions, to make them part of himself....We don’t speak of a conscience yet in the child who is just acquiring language, but we can see very clearly how language plays an indispensable role in the formation of conscience. In fact, the moral achievement of man, the whole complex of factors that go into the organization of conscience is very largely based upon language.”
—Selma H. Fraiberg (20th century)
“I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.”
—Gottlob Frege (1848–1925)