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

Last Updated : 16 Feb, 2023

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++

// 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; 
} 

Java

// Java program to check if  
// a number is Magic number. 
import java.io.*; 
public 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. 

Python3

# 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. 

C#

// 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. 

PHP

<?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. 
?> 

Javascript

<script> 
  
// JavaScript program to check if  
// a number is Magic number. 
function isMagic( n) 
   { 
       var 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 
    var n = 1234; 
    if (isMagic(n)) 
    document.write("Magic Number"); 
           
    else
        document.write("Not a magic Number"); 
      
// This code is contributed by shivanisinghss2110 
  
</script> 

Output:

Magic Number

Time Complexity: O(log₁₀n)
Auxiliary Space: O(1), As constant extra space is used.

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++

// 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; 
} 

C

// 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; 
} 

Java

// Java program to check 
// Whether the number is Magic or not. 
import java.io.*; 
public class GFG{ 
      
public static void main(String[] args)  
{ 
      
    // Accepting sample input 
    int x = 1234; 
  
    // Condition to check Magic number 
    if (x % 9 == 1) 
        System.out.printf("Magic Number"); 
    else
        System.out.printf("Not a Magic Number"); 
} 
} 
  
// This code is contributed by Amit Katiyar

Python3

# Python3 program to check 
# Whether the number is Magic or not. 
  
# Accepting sample input 
x = 1234
  
# Condition to check Magic number 
if (x % 9 == 1): 
    print("Magic Number") 
else: 
    print("Not a Magic Number") 
  
# This code is contributed by kirti 

C#

// C# program to check 
// Whether the number is Magic or not. 
using System; 
using System.Collections.Generic; 
  
class GFG{ 
      
public static void Main(String[] args)  
{ 
      
    // Accepting sample input 
    int x = 1234; 
  
    // Condition to check Magic number 
    if (x % 9 == 1) 
        Console.Write("Magic Number"); 
    else
        Console.Write("Not a Magic Number"); 
} 
} 
  
// This code is contributed by Princi Singh

Javascript

<script> 
  
// JavaScript program to check 
// Whether the number is Magic or not. 
  
// Accepting sample input 
var x = 1234; 
  
// Condition to check Magic number 
if (x % 9 == 1) 
    document.write("Magic Number"); 
else
    document.write("Not a Magic Number"); 
  
// This code is contributed by shivanisinghss2110  
  
</script> 

Output:

Magic Number

Time Complexity: O(1)
Auxiliary Space: O(1) As constant extra space is used.

Check if the sum of digits of a number divides it

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

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