Magic Number in Java with Program & Explanation | Interview Program

Magic Number in Java with Program & Explanation

Q: Is 55 a Magic Number?

No. 5 + 5 = 10 → 1 + 0 = 1... wait, that IS 1. So 55 is actually a Magic Number. Correction: 55 → 5+5=10 → 1+0=1, so 55 IS a Magic Number.

Welcome, Java learners! 🎯 In this post, you'll learn how to write a Magic Number program in Java — one of the most popular coding interview questions for beginners and freshers.

We'll cover the definition, the algorithm, a complete working Java program with line-by-line explanation, and the expected output.

What is a Magic Number?

A Magic Number is a number whose digits are repeatedly summed until a single digit is obtained. If that single digit equals 1, the original number is called a Magic Number.

Example — is 199 a Magic Number?

199 → 1 + 9 + 9 = 19
19 → 1 + 9 = 10
10 → 1 + 0 = 1 ✅

Since the final single digit is 1, 199 is a Magic Number.

Other Magic Numbers: 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100…

Algorithm to Find Magic Number

Read the number num.
Store a copy in tt for printing later.
While s > 9:
- Set num = s and s = 0.
- While num > 0:
  - Extract last digit: d = num % 10.
  - Add to sum: s = s + d.
  - Remove last digit: num = num / 10.
If s == 1 → print "Magic Number".
Else → print "Not a Magic Number".

Complete Java Program

Here is the complete, runnable Java program:

public class First {

    /*
     * A number is said to be a Magic number if the sum of its digits is
     * calculated till a single digit is obtained by recursively adding the sum
     * of its digits. If the single digit comes to be 1 then the number is a
     * magic number.
     *
     * Example: 199 is a magic number as 1+9+9=19 but 19 is not a single digit
     * number so 1+9=10 and then 1+0=1 which is a single digit number and also 1.
     * Hence it is a magic number.
     */
    void magicNumber(int num) {
        int d, s;
        int tt = num;
        s = num;

        // Repeat until a single digit is obtained
        while (s > 9) {
            num = s;
            s = 0;

            // Sum the digits of num
            while (num > 0) {
                d = num % 10;
                s = s + d;
                num = num / 10;
            }
        }

        if (s == 1)
            System.out.println("magic number :- " + tt);
        else
            System.out.println("not a magic number :- " + tt);
    }

    public static void main(String[] args) {
        new First().magicNumber(55);
    }
}

Line-by-Line Explanation

void magicNumber(int num) — the method that checks if a number is magic.
int tt = num; — stores the original number for the final print.
s = num; — initializes the sum with the original number.
while (s > 9) — outer loop runs while the sum is still a multi-digit number.
num = s; s = 0; — resets num to the current sum, and resets s for the inner loop.
while (num > 0) — inner loop iterates through all digits.
d = num % 10; — extracts the last digit.
s = s + d; — adds digit to the sum.
num = num / 10; — removes the last digit.
if (s == 1) — checks if the final single digit is 1.

Output

For input 55:

55 → 5 + 5 = 10 → 1 + 0 = 1 ✅
magic number :- 55

Try these test cases:

199 → 1+9+9 = 19 → 1+9 = 10 → 1+0 = 1 → Magic Number ✅
100 → 1+0+0 = 1 → Magic Number ✅
123 → 1+2+3 = 6 → Not a Magic Number ❌
999 → 9+9+9 = 27 → 2+7 = 9 → Not a Magic Number ❌

Frequently Asked Questions

What is a Magic Number in Java?

A Magic Number is a number whose digits are repeatedly summed until a single digit is obtained. If that single digit equals 1, the original number is called a Magic Number.

How do you find a Magic Number in Java?

Use nested loops: the outer loop keeps the number greater than 9, and the inner loop sums the digits using modulo (%) and integer division (/). After the loop ends, check if the final single digit is 1.

Is 55 a Magic Number?

Yes. 5 + 5 = 10 → 1 + 0 = 1, so 55 is a Magic Number.

Which numbers are Magic Numbers?

Magic Numbers are those whose recursive digit sum equals 1. Examples: 1, 10, 19, 28, 37, 46, 55, 64, 73, 82, 91, 100, 109, 118…

Is Magic Number the same as Happy Number?

No. A Happy Number involves squaring digits repeatedly until you reach 1. A Magic Number uses simple digit summation. They are different concepts.

Conclusion

In this post, you learned how to write a Magic Number program in Java with complete source code and line-by-line explanation. The key idea is to keep summing digits until a single digit remains, then check if it equals 1.

This is a classic interview question — practice it until you can write it without looking at the solution. Once you're comfortable, try variations like:

Finding all Magic Numbers between 1 and 100
Finding the nth Magic Number
Magic Number using recursion

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