Cryptarithms — interesting verbal arithmetic

Today we’ve learned about cryptarithms (a.k.a verbal arithmetic) from the problem 2C of the homework Set 1 Olympiad 2.

Verbal arithmetic, also known as alphametics, cryptarithmetic, crypt-arithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters. The goal is to identify the value of each letter. The name can be extended to puzzles that use non-alphabetic symbols instead of letters. (Wikipedia)

Find all the numbers represented by S, E, N, D, M, O, R, N, and Y in the following arithmetic problem.

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

Rules are 1) each letter represents a different digit and 2) the leading digit of a multi-digit number is not zero, i.e., S and M above must not be zero.

You may find more problems at http://www.cryptarithms.com/ or just google “cryptarithms,” then you’ll find a lot of interesting problems.