INTRODUCTION

A Dudeney number is a positive integer for which the sum of its digits is equal to the the cube root of the number itself. The name derives from Henry Dudeney, who noted the existence of these numbers in one of his puzzles, Root Extraction, where a professor in retirement at Colney Hatch postulated this as a general method for root extraction.

For example:
512 = (5+1+2) = 83

19683= (1+9+6+8+3)3 = 273

0 and 1 are Trivial Dudeney numbers and all other Dudeney numbers are Nontrivial Dudeney numbers.

For in-depth Mathematical information regarding the nature of the Dudeney Number, please- Click Here.

JAVA CODE

public class Dudeney
{
public static void main(int n)
{
int x=n;                        //Creating a copy of the number
int sum=0;                  //Variable to calculate sum of digits
while(n!=0)
{
int a=n%10;                //Extracting the Digit
sum=sum+a;             //Calculating the sum of Digits
n=n/10;                      //Reducing the number of Digit by 1 (removing the units Digit)
}
if(x==(sum*sum*sum))                     //Condition of Dudeney Number
System.out.println (“Yes; A Dudeney Number”);
else
System.out.println (“Not a Dudeney Number”);
}
}

LIST OF DUDENEY NUMBERS

0
1
512
4913
5832
17576
19683

FUN FACT

There are only 6 Dudeney numbers. You might not find the validity of this statement. If interested to know the proof of the statement by using techniques like Bounding From Above, Limiting The Search Space, and Brute Force The Remaining Possibilities, please- Click Here.

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