Question
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:
SEND + MORE = 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 a solution to the cryptarithmetic puzzle of the following:
TOO + TOO + TOO + TOO = GOOD
VideoNote Solution to Programming Project 3.9 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 to 9 to each letter. For example, it might first try T = 0, O = 0, G = 0, D = 0, then T = 0, O = 0, G = 0, D = 1, then T = 0, O = 0, G = 0, D = 2, etc., up to T = 9, O = 9, G = 9, 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.
Answer
Program:
// CryptarithmeticPuzzle.java
public class CryptarithmeticPuzzle
{
public static void main(String[] args)
{
for (int T = 0; T <= 9; T++)
{
for (int O = 0; O <= 9; O++)
{
for (int G = 0; G <= 9; G++)
{
for (int D = 0; D <= 9; D++)
{
if (T != O && T != D && T != G && G != O && G != D && D != O)
{
int too = (100 * T) + (10 * O) + O;
int good = (1000 * G) + (100 * O) + (10 * O) + D;
if (4 * too == good)
{
System.out.println("TOO + TOO + TOO + TOO = "
+ (4 * too));
System.out.println("GOOD = " + good);
System.out.println("Therefore, T = " + T
+ ", O = " + O + ", G = " + G
+ ", and D = " + D);
System.out.println();
}
}
}
}
}
}
}
}
Output:
TOO + TOO + TOO + TOO = 664
GOOD = 664
Therefore, T = 1, O = 6, G = 0, and D = 4
TOO + TOO + TOO + TOO = 1996
GOOD = 1996
Therefore, T = 4, O = 9, G = 1, and D = 6