Famous alphametic A puzzle in which the digits in a correct mathematical expression, suc...

Famous alphametic A puzzle in which the digits in a correct mathematical expression, such as a sum, are replaced by letters is called cryptarithm; if, in addition, the puzzle’s words make sense, it is said to be an alphametic. The most well-known alphametic was published by the renowned British puzzlist Henry E. Dudeney (1857–1930):

Brute Force and Exhaustive Search

Two conditions are assumed: first, the correspondence between letters and decimal digits is one-to-one, i.e., each letter represents one digit only and different letters represent different digits. Second, the digit zero does not appear as the left-most digit in any of the numbers. To solve an alphametic means to find which digit each letter represents. Note that a solution’s uniqueness cannot be assumed and has to be verified by the solver.

a. Write a program for solving cryptarithms by exhaustive search. Assume that a given cryptarithm is a sum of two words.

b. Solve Dudeney’s puzzle the way it was expected to be solved when it was first published in 1924.