Check if a number is magic (Recursive sum of digits is 1)

A number is said to be a magic number, if the sum of its digits are calculated till a single digit recursively by adding the sum of the digits after every addition. If the single digit comes out to be 1,then the number is a magic number.
For example-
Number= 50113
=> 5+0+1+1+3=10
=> 1+0=1
This is a Magic Number
For example-
Number= 1234
=> 1+2+3+4=10
=> 1+0=1
This is a Magic Number

Examples :

 
Input : 1234
Output : Magic Number

Input  : 12345
Output : Not a magic Number

The approach used brute force. The function keeps adding digits until a single digit sum is reached. To understand how i am calculating the sum upto a single digit view this page- Finding sum of digits of a number until sum becomes single digit

C++

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// CPP program to check if a number is Magic
// number.
#include<iostream>
using namespace std;
  
bool isMagic(int n)
{
    int sum = 0;
      
    // Note that the loop continues
    // if n is 0 and sum is non-zero.
    // It stops when n becomes 0 and
    // sum becomes single digit.
    while (n > 0 || sum > 9)
    {
        if (n == 0)
        {
            n = sum;
            sum = 0;
        }
        sum += n % 10;
        n /= 10;
    }
      
    // Return true if sum becomes 1.
    return (sum == 1);
}
   
// Driver code
int main()
{
    int n = 1234;
    if (isMagic(n))
        cout << "Magic Number";
    else
        cout << "Not a magic Number";
    return 0;
}

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Java

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// Java program to check if 
// a number is Magic number.
class GFG
{
   public static boolean isMagic(int n)
   {
       int sum = 0;
       
       // Note that the loop continues 
       // if n is 0 and sum is non-zero.
       // It stops when n becomes 0 and
       // sum becomes single digit.
       while (n > 0 || sum > 9)
       {
           if (n == 0)
           {
               n = sum;
               sum = 0;
           }
           sum += n % 10;
           n /= 10;
       }
       
       // Return true if sum becomes 1.
       return (sum == 1);
   }
    
   // Driver code
   public static void main(String args[])
    {
     int n = 1234;
     if (isMagic(n))
        System.out.println("Magic Number");
           
     else
        System.out.println("Not a magic Number");
    }
}
  
// This code is contributed by Anshika Goyal.

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Python3

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# Python3 program to check 
# if a number is Magic
# number.
  
def isMagic(n):
    sum = 0;
      
    # Note that the loop 
    # continues if n is 0 
    # and sum is non-zero.
    # It stops when n becomes 
    # 0 and sum becomes single
    # digit.
    while (n > 0 or sum > 9):
        if (n == 0):
            n = sum;
            sum = 0;
        sum = sum + n % 10;
        n = int(n / 10);
          
    # Return true if
    # sum becomes 1.
    return True if (sum == 1) else False;
  
# Driver code
n = 1234;
if (isMagic(n)):
    print("Magic Number");
else:
    print("Not a magic Number");
      
# This code is contributed 
# by mits.

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C#

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// C# program to check if 
// a number is Magic number.
using System;
  
class GFG
{
    public static bool isMagic(int n)
    {
        int sum = 0;
          
        // Note that the loop continues 
        // if n is 0 and sum is non-zero.
        // It stops when n becomes 0 and
        // sum becomes single digit.
        while (n > 0 || sum > 9)
        {
            if (n == 0)
            {
                n = sum;
                sum = 0;
            }
            sum += n % 10;
            n /= 10;
        }
          
        // Return true if sum becomes 1.
        return (sum == 1);
    }
      
    // Driver code
    public static void Main()
    {
        int n = 1234;
        if (isMagic(n))
            Console.WriteLine("Magic Number");
              
        else
            Console.WriteLine("Not a magic Number");
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP program to check if 
// a number is Magic number.
function isMagic($n)
{
    $sum = 0;
      
    // Note that the loop 
    // continues if n is 0
    // and sum is non-zero. 
    // It stops when n becomes 
    // 0 and sum becomes single 
    // digit.
    while ($n > 0 || $sum > 9)
    {
        if ($n == 0)
        {
            $n = $sum;
            $sum = 0;
        }
        $sum += $n % 10;
        $n /= 10;
    }
      
    // Return true if
    // sum becomes 1.
    return ($sum == 1);
}
  
// Driver code
$n = 1234;
if (isMagic($n))
    echo"Magic Number";
else
    echo "Not a magic Number";
  
// This code is contributed 
// by nitin mittal.
?>

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Output:



Magic Number

Output :

Magic Number

Efficient Approach(Shortcut): There is also a shortcut method to verify Magic Number. The function will determine if the remainder on dividing the input by 9 is 1 or not. If it is 1, then the number is a magic number. The divisibility rule of 9 says that a number is divisible by 9 if the sum of its digits are also divisible by 9. Therefore, if a number is divisible by 9, then, recursively, all the digit sums are also divisible by 9. The final digit sum is always 9. An increase of 1 in the original number will increase the ultimate value by 1, making it 10 and the ultimate sum will be 1, thus verifying that it is a magic number.

C

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// C program to check
// Whether the number is Magic or not.
#include <stdio.h>
  
int main() {
      
    // Accepting sample input
    int x = 1234;
      
    // Condition to check Magic number
    if(x%9==1)
        printf("Magic Number");
    else
        printf("Not a Magic Number");       
  
    return 0;
}

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Output:

Magic Number

C++

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// C++ program to check
// Whether the number is Magic or not.
#include <iostream>
using namespace std;
  
int main() {
    // Accepting sample input
    int x = 1234;
      
    // Condition to check Magic number
    if(x%9==1)
        cout << ("Magic Number");
    else
        cout << ("Not a Magic Number");       
  
    return 0;
}

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Output:

Magic Number

Java

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// Java program to check
// Whether the number is Magic or not.
public class Magic {
  
    // Driver Method
    public static void main(String args[])
    {
        // Accepting sample input
        int x = 1234;
  
        // Condition to check Magic number
        if (x % 9 == 1)
            System.out.println("Magic Number");
        else
            System.out.println("Not a Magic Number");
    }
}
// Contributed by Ronit Gupta

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Output:

Magic Number

Python

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# Python3 program to check
# Whether the number is Magic or not.
x = 1234
  
# Condition to check Magic number
if(x%9==1):
    print("Magic Number")
else:
    print("Not a Magic Number")

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Output:

Magic Number

This article is contributed by Ayush Saxena. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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