The objective of the puzzle is to break the code used. That is, to replace each letter of the cryptarithm by a numeral so that the resulting mathematical expression is true. Cryptarithms may have several solutions. However, there are elegant ones with only one unique solution.
Cryptarithm is an arithmetic problem in which letters have been substituted for numbers and which is solved by finding all possible pairings of digits with letters that produce a numerically correct answer. Cryptarithm now denotes mathematical problems usually calling for addition, subtraction, multiplication, or division and replacement of the digits by letters of the alphabet or some other symbols. There are three types of cryptarithms ; alphametics, digimetic, skeletal division.
• ALPHAMETICS: If a cryptarithm uses letters in place of digits and these letters form sensible letters or phrases, the puzzle is termed as alphametic.
• DIGIMETIC: A type of cryptarithm in which digits are used to represent other digits
• SKELETAL DIVISION: A long division in which most or all of the digits are replaced by symbols (usually asterisks) to form a cryptarithm.
A cryptarithm is a genre of mathematical puzzle in which the digits are replaced by letters of the alphabet or other symbols.
The invention of Cryptarithmetic has been ascribed to ancient China. This art was originally known as letter arithmetic or verbal arithmetic. In India, during the Middle Ages, were developed the arithmetical restorations or “skeletons” a type of cryptarithms in which most or all of the digits have been replaced by asterisks.
In 1864 the first cryptarithm appeared in the USA, in American Agriculturist.
The word cryptarithmetic (“cryptarithmie” in French) was introduced by M. Vatriquant, writing under the pseudonym Minos, in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics published in French from 1931 to 1939.
A type of alphametic addition puzzle termed “doubly-true” was introduced in 1945 by Alan Wayne. It is made up of “number words” that, when read, also form a valid sum.
In 1955, J. A. H. Hunter coined the word alphametic to designate a cryptarithm whose letters form sensible words or phrases.
The world’s best known alphametic puzzle is undoubtedly SEND + MORE = MONEY. It was created by H. E. Dudeney and first published in the July 1924 issue of Strand Magazine.
Given below are the fundamental rules to solve a cryparithemic problem:-