Chapter 2, Problem 5PP

In cryptarithmetic puzzles, mathematical equations are written using letters. Each letter can be a digit from 0 to 9, but no two letters can be the same. Here is a sample problem:

$\text{SEND}+\text{MORE}=\text{MONEY}$

A solution to the puzzle is $S=9,R=8,O=0,M=1,Y=2,E=5,N=6,D=7.$

Write a program that finds solutions to the following cryptarithmetic puzzle:

$\text{TOO}\text{+}\text{TOO}\text{+}\text{TOO}\text{+}\text{TOO}\text{=}\text{GOOD}$

The simplest technique is to use a nested loop for each unique letter (in this case T, O, G, D). The loops would systematically assign the digits from $0-9$ to each letter. For example, it might first try $\text{T}=0,\text{O}=0,\text{G}=0,\text{D}=0,$ then $\text{T}=0,\text{O}=0,\text{G}=0,\text{D}=1,$ then $\text{T}=0,\text{O}=0,\text{G}=0,\text{D}=2,$ etc. up to $\text{T}=9,\text{O}=9,\text{G}=9,\text{D}=9.$ In the loop body, test that each variable is unique and that the equation is satisfied. Output the values for the letters that satisfy the equation.