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Magic Number in Java

Last Updated on July 11, 2023 by Mayank Dham

In this article, we embark on a journey to uncover the world of Magic Numbers in the context of Java programming. We delve into what Magic Numbers are, their distinctive properties, and the various ways they manifest in Java applications. By exploring algorithms, patterns, and Java programming techniques, we aim to shed light on the magic behind these enigmatic numerical entities.

Throughout the article, we will examine the characteristics of Magic Numbers, discover their prevalence in mathematical puzzles and games, and explore their applications in programming scenarios. We will also delve into techniques for identifying and utilizing Magic Numbers efficiently in Java.

What is Magic Number in Java?

If the sum of a number’s digits can be calculated down to a single digit repeatedly by adding the sum of the digits after each addition, the number is said to be a magic number. The number is a magic number if the single digit equals 1.

While the concept of Magic Numbers is not limited to Java and can be found in other programming languages, it is important to note that their usage is generally discouraged. Magic Numbers can make the code less readable, less maintainable, and more prone to errors. It is considered a best practice to avoid hard-coding numeric values directly in the code and instead use constants or variables with descriptive names to improve code readability and maintainability.

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

Brute Force Approach To Find Magic Number in Java

  1. Read the input number num.
  2. Initialize a variable current as 0 to represent the current number being checked.
    • Start a loop to iterate through all numbers from 1 to num.
    • Set current as the current number being checked.
    • Initialize a variable sum as 0 to store the sum of the digits.
      • Start an inner loop to calculate the sum of the digits of current.
      • Extract the last digit of current using the modulus operator % and add it to sum.
      • Reduce the value of current by dividing it by 10 using the integer division operator //.
      • Repeat until current becomes 0.
        -Check if sum is equal to num.
      • If they are equal, num is a Magic Number.
      • Print or store the value of num accordingly.
  3. End the loop.
  4. Output the Magic Numbers found during the loop.

Code Implementation

class PrepBytes
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");
        System.out.println("Not a magic Number");


Magic Number

Time Complexity: O(log10n) will be the time complexity for magic number in Java.
Auxiliary Space: O(1) will be the space complexity for magic number in Java, As constant extra space is used.

Efficient Approach To Find the Magic Number in Java

  • Read the input number x.
  • Check the condition x % 9 == 1 to determine if the number is a Magic Number.
  • The condition checks if the remainder of x divided by 9 is equal to 1.
  • If the condition is true, print "Magic Number".
  • If the condition is false, print "Not a Magic Number".

Code Implementation

class PrepBytes{
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");
        System.out.printf("Not a Magic Number");


Magic Number

Time Complexity: O(1) will be the time complexity for finding the magic number in Java.
Auxiliary Space: O(1) As constant extra space is used.

In this article, we explored the concept of Magic Numbers in Java and learned how to identify them. Magic Numbers, defined as numbers that satisfy specific conditions or exhibit special properties, can add an intriguing dimension to our understanding of numeric patterns and programming challenges.

We discussed both a brute force approach and an efficient approach to finding Magic Numbers in Java. The brute force approach involved iterating through numbers and calculating the sum of their digits, while the efficient approach optimized the process by selectively checking potential Magic Numbers.

By delving into the logic and implementation of Magic Number identification, we gained insights into the importance of code readability, maintainability, and avoiding hard-coded values. We emphasized the significance of using constants or variables with meaningful names instead of directly embedding numeric values in code.

FAQ Related To Magic Number in Java

Q: Can Magic Numbers be negative or zero?
A: The concept of Magic Numbers typically applies to positive integers. Negative numbers and zero are not commonly considered Magic Numbers.

Q: Are Magic Numbers only applicable to Java?
A: No, Magic Numbers are not limited to Java. The concept exists in programming and mathematics in general, and various programming languages can incorporate Magic Numbers.

Q: Should we always avoid Magic Numbers in code?
A: It is generally recommended to avoid using Magic Numbers directly in code. Instead, prefer using constants or variables with descriptive names to improve code readability, maintainability, and prevent hard-coding.

Q: Can Magic Numbers be optimized further?
A: The efficiency of Magic Number identification can be improved by employing advanced algorithms or mathematical techniques specific to the problem domain. However, the specific optimization depends on the context and requirements.

Q: Are Magic Numbers limited to specific mathematical properties?
A: Magic Numbers can encompass various mathematical properties, depending on the specific problem or condition being explored. They can include properties like divisibility, patterns, or relationships with other numbers.

Q: Are there any other types of special numbers similar to Magic Numbers?
A: Yes, there are several categories of special numbers, such as Prime Numbers, Perfect Numbers, Armstrong Numbers, and more. Each type has its unique properties and patterns, offering further avenues for exploration.

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