Cryptarithm Contents

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25 March 2016

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The word cryptarithm was first coined by the puzzlist Minos, which is a pseudonym of Simon Vatriquant. In 1955, J. A. H. Hunter introduced the word “alphametic” to designate cryptarithms, such as Dudeney’s, whose letters form meaningful words or phrases.

Cryptarithm is a type of puzzle where words are put together into particular formula such that digits can be substituted for the letters to make the formula true. Another example other than that of Henry Dudeney, i.e. Send + More = Money, is: –

+ BB

The solution for the above cryptarithm is
+ 99
= 100

There are three types of cryptarithms. They are:-
Skeletal Division

A type of cryptarithm in which a set of words is written down in the form of a long addition sum or some other mathematical problem. The object is to replace the letters of the alphabet with digits to make a valid arithmetic sum. There is also a subset of alphametics called ‘doubly-true’ where the words are spelt out numbers which also form a valid sum:


+ Ten
+ Ten
= Sixty
The solution to the above doubly-true alphametic is
2 9 7 8 6
8 5 0
+ 8 5 0
3 1 4 8 6

A type of cryptarithm in which digits are used to represent other digits. An example of a digimetic is :-
+ 20
+ 20 =

The solution to this digimetic is : –
+ 10
+ 10
= 80

Skeletal Division
A long division in which most or all of the digits are replaced by symbols (usually asterisks) to form a cryptarithm. Physicist Richard Feynman sent the following puzzle for his father attached to a letter to his mother in 1939: –

This is an example of skeletal division.
The quotient is thus (….A..):(.A.) = (..A.)
The solution to this division is not as easy as it looks. However, the solution is: – 7289
484 ) 3527876
Richard Feynman and his father traded puzzles like this all the time, so they must have spent a lot of time working on them, and they were both rapid and accurate paper and mental calculators!

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