Question

Study question is to find the digit root of a already provided number. The teacher provides us with the number 2638. In order to find the digit root you have to add each digit separately 2 + 6 + 3 + 8 = 19. Then you take the result 19 and add those two digits together 1 + 9 = 10. Do the same thing again 1 + 0 = 1. The digit root is 1.

My first step was to use the variable total to add up the number 2638 to find the total of 19. Then I tried to use the second while loop to separate the two digits by using the %

I have to try and solve the problem by using basic integer arithmetic (+, -, *, /).
1.Is it necessary and or possible to solve the problem using nested while loops?
2.Is my math correct?
3. As I wrote it here it does not run in Eclipse. Am I using the while loops correctly?

import acm.program.*;


public class Ch4Q7 extends ConsoleProgram {
   public void run(){
      println("This program attempts to find the digit root of your number: ");

      int n = readInt("Please enter your number: "); 

      int total = 0;

      int root = total;


      while (n > 0 ){
        total = total + (n %10);
    n = (n / 10);

    }   

   while ( total > 0 ){
     root = total; 
     total = ((total % 10) + total / 10); 
    }


     println("your root should be " + root);
}

}

Answer 1

I think it does run, but just a bit too much 🙂

total = ((total % 10) + total / 10); 

can’t converge to 0. Also, your program as it is will only handle very specific cases. As others pointed out, this can be solved recursively, but also with just a double loop. A succession of loops like you tried won’t work.

Try this (on input vars are the same as in your program, it’s really a plugin replacement for your two loops):

    do {
        while (n > 0) {
            total = total + (n % 10);
            n = (n / 10);
        }
        n = total;
        total = 0;
    } while (n > 9);  // need at least 1 more loop

After this loop n will contain the root number.