Cryptarithm: Addition and Digits

Cryptarithmetic, also known as alphametics, , crypt-arithmetic, Verbal arithmetic , cryptarithm or word addition, 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. The equation is typically a basic operation of arithmetic, such as addition, multiplication, or division.
For example:
9567 + 1085 = 10652 can be represented like this: abcd + efgb = efcbh
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.
History
The invention of Cryptarithmetic has been ascribed to ancient China. This art was originally known as letter arithmetic or verbal arithmetic. In India, during the Middle Ages, were developed the arithmetical restorations or "skeletons" a type of cryptarithms in which most or all of the digits have been replaced by asterisks.
In 1864 the first cryptarithm appeared in the USA, in American Agriculturist.
The word