“It is an arithmetic problem which is represented i n letters. It involves the decoding of digit represented by a character. It is in the form of some arithmetic equation where digits are distinctly represented by some characters. The problem requires finding of the digit represented by each character.

Assign a decimal digit to each of the letters in such a way that the answer to the problem is correct. If the same letter occurs more than once, it must be assigned the same digit each time. No two different letters may be assigned the same digit”.


Cryptarithmatic problem is an interesting constraint satisfaction problem for which different algorithms have been developed. Cryptarithm is a mathematical puzzle in which digits are replaced by letters of the alphabet or other symbols. Cryptarithmatic is the science and art of creating and solving cryptarithms.

The different constraints of defining a cryptarithmatic problem are as follows.

  • Each letter or symbol represented only one and a unique digit throughout the
  • When the digits replace letters or symbols, the resultant arithmetical operation must be correct. The above two constraints lead to some other restrictions in the

For example:

Consider that, the base of the number is 10. Then there must be at most 10 unique symbols or letters in the problem. Otherwise, it would not possible to assign a unique digit to unique letter or symbol in the problem. To be semantically meaningful, a number must not begin with a 0.

So, the letters at the beginning of each number should not correspond to 0. Also one can solve the problem by a simple blind search. But a rule based searching technique can provide the solution in minimum time.