Editing Verbal arithmetic (section)

{{short description|Puzzle of reconstructing equations that have been enciphered into words}}
'''Verbal arithmetic''', also known as '''alphametics''',  '''cryptarithmetic''', '''cryptarithm''' or '''word addition''', is a type of [[mathematical game]] consisting of a mathematical [[equation]] among unknown [[number]]s, whose [[numerical digit|digit]]s are represented by [[Letter (alphabet)|letter]]s of the alphabet.  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 (mathematics)|division]].  The classic example, published in the July 1924 issue of ''[[The Strand Magazine]]'' by [[Henry Dudeney]],<ref>[[Henry Dudeney|H. E. Dudeney]], in ''[[Strand Magazine]]'' vol. 68 (July 1924), pp. 97 and 214. https://babel.hathitrust.org/cgi/pt?id=mdp.39015055410669&seq=109</ref> is:

<math>\begin{matrix}
     &   & \text{S} & \text{E} & \text{N} & \text{D} \\
   + &   & \text{M} & \text{O} & \text{R} & \text{E} \\
 \hline
   = & \text{M} & \text{O} & \text{N} & \text{E} & \text{Y} \\
\end{matrix}</math>

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 an ordinary arithmetic notation) the leading digit of a multi-digit number must not be zero.  A good puzzle should have one unique solution, and the letters should make up a phrase (as in the example above).

Verbal arithmetic can be useful as a motivation and source of exercises in the [[education|teaching]] of [[elementary algebra]].