Cryptarithms are puzzles in which letters or symbols are substituted for the digits in arithmetic calculations.  Cryptarithms come in three types- alphametic, digimetic and skeletal division.
1)ALPHAMETIC CRYPTARITHMS: If a cryptarithm uses letters in place of digits and these letters form sensible letters or phrases, the puzzle is termed as alphametic.  For e.g. SEND
2)DIGIMETIC CRYPTARITHM:  A cryptarithm which uses digits to represent pther digits.    __1__
                     x   9__
                 __ __ 9 __
         +   __ __ __ 7
             H A P P Y
3) SKELETAL DIVISION: A long division in which most or all of the digits are replaced by symbols (usually asterisks) to form a cryptarithm.