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

• Difficulty Level : Easy
• Last Updated : 14 Jul, 2021

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.#includeusing 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 codeint 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.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 coden = 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

 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


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++

 // C++ program to check// Whether the number is Magic or not.#include 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  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.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 inputx = 1234 # Condition to check Magic numberif (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


Output:
Magic Number

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