Question

Find all three-digit numbers with non-zero first digit that are equal to the sum of the cubes of their digits.(FORTON)

Answer 1

Ans: There is only 4 three-digit number that is equal to the sum of the cubes of their digits.

Numbers are:

153, 370, 371, and 407

Procedure:

The three-digit numbers with a non-zero first digit are from 100 to 999.

To find all the three-digit numbers with non-zero first digit that are equal to the sum of the cubes of their digits, we can run a loop from 100 to 999 and check each number whether the number satisfies the property or not.

Here an algorithm to find the numbers:

For example, the code is written in JAVA. (Any language can be used with the same algorithm)

Code:

import java.io.*;
import java.util.*;

public class UniqueNumbers{

   public static void main(String[] args){
      
       for(int i=100;i<=999;i++){               //For loop from 100 to 999

           int number = i;

           int digit1 = i%10;                   //Will give the unit digit of the number
           int digit2 = (i/10)%10;               //Will give the second digit of the number
           int digit3 = i/100;                   //will give the third digit of the number

           //To find the sum of cubes of digit

           int sum = (int)Math.pow(digit1,3) + (int)Math.pow(digit2,3) + (int)Math.pow(digit3,3);

           if(sum == number){

               System.out.println(number+" ");
           }
       }
       System.out.println("");
   }
}

Outputs :

153

370

371

407

Screenshot of full working code along with output: