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Cryptarithm

A cryptarithm is a type of mathematical puzzle in which most or all of the digits in a mathematical expression, such as a sum, are substituted by letters or other symbols.  In a typical puzzle, there is a one-to-one correspondence between the numbers and the letters or symbols replacing them.  That is, the same digit is always represented by the same letter or symbol.  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 was originally called crypt-arithmetic, a word used by M. Vatriquant ( pseudonym Minos), in the May 1931 issue of Sphinx, a Belgian magazine of recreational mathematics published in French.  Later, this word has been shortened to cryptarithm.  In 1955, J. A. H. Hunter introduced the word alphametic to designate a cryptarithm whose letters form meaningful words or phrases.

One of the best known cryptarithm is

 S E N D + M O R E ______________________ M O N E Y

first published in the July 1924 issue of Strand Magazine.  This puzzle was made by the famous puzzlist H. E. Dudeney.  This puzzle is also called an alphametic because the the letters in the puzzle form a sensible phrase SEND MORE MONEY.  This puzzle has the solution of

 9 5 6 7 + 1 0 8 5 ______________________ 1 0 6 5 2

This alphametic or cryptarithm is popular not only because the letters in the puzzle form a very popular phrase, but it has also a unique solution.

Solve some of our cryptarithms involving the following words:

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