Cryptarithms

Cryptarithms are essentially a form of code - a substitution cipher. Each of the digits from 0 to 9 is replaced by a separate letter of the alphabet and these letters are then used to represent a simple arithmetic sum. This combination of cryptography and arithmetic gives the name cryptarithmetic. (This was initially crypt-arithmetic, a name invented by Maurice Vatriquant in 1931 - the hyphen is usually dropped today).

The objective of the solver is simple: find out which digits are represented by each number, subject to the constraint that the arithmetic must work. There is also an unwritten rule that the first digit of any number in the sum cannot be a leading zero.

In theory a cryptarithm could simply be a jumble of letters. However that would be inelegant. Thus most published cryptarithms are designed so that the letters form real English words. In the best cryptarithms the words themselves make sense taken together. Perhaps the most common example of this is SEND + MORE = MONEY. This particular cryptarithm puzzle was invented by H.E. Dudeney and publish in 1924 in Strand Magazine.

Where the letters of a cryptarithm form real words and phrases it is known as an alphametic puzzle. The term alphametic was invented by J.A.H. Hunter in 1955. Such puzzles are also known as verbal arithmetic. Alphametics are, of course, not restricted to English. In particular German seems well suited to their creation.

Solving cryptarithms is a combination of deduction, trial & error and mathematical intuition. In the SEND MORE MONEY puzzle, for example, we can immediately say that "M = 1" because of the leading M in MONEY.

Cryptarithms can today be solved by brute force - you can buy computer software that will generate and solve cryptarithms extremely quickly. But where's the fun in that?

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Cryptarithms Cryptarithms are essentially a form of code - a substitution cipher. Each of the digits from 0 to 9 is replaced by a separate letter of the alphabet and these letters are then used to represent a simple arithmetic sum. This combination of cryptography and arithmetic gives the name cryptarithmetic. (This was initially crypt-arithmetic, a name invented by Maurice Vatriquant in 1931 - the hyphen is usually dropped today). The objective of the solver is simple: find out which digits are represented by each number, subject to the constraint that the arithmetic must work. There is also an unwritten rule that the first digit of any number in the sum cannot be a leading zero. In theory a cryptarithm could simply be a jumble of letters. However that would be inelegant. Thus most published cryptarithms are designed so that the letters form real English words. In the best cryptarithms the words themselves make sense taken together. Perhaps the most common example of this is SEND + MORE = MONEY. This particular cryptarithm puzzle was invented by H.E. Dudeney and publish in 1924 in Strand Magazine. Where the letters of a cryptarithm form real words and phrases it is known as an alphametic puzzle. The term alphametic was invented by J.A.H. Hunter in 1955. Such puzzles are also known as verbal arithmetic. Alphametics are, of course, not restricted to English. In particular German seems well suited to their creation. Solving cryptarithms is a combination of deduction, trial & error and mathematical intuition. In the SEND MORE MONEY puzzle, for example, we can immediately say that "M = 1" because of the leading M in MONEY. Cryptarithms can today be solved by brute force - you can buy computer software that will generate and solve cryptarithms extremely quickly. But where's the fun in that?	Galapemy Store Games Puzzles Geometric Jigsaw Logic Number Cryptarithms Word Toys
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