Check Magic Number in C

What You’ll Learn

Magic numbers (in this tutorial) collapse by repeated decimal digit sums until one digit remains — and that digit must be 1. This page covers the definition, digital-root intuition, a live preview, algorithm steps, worked C examples, edge cases, and complexity.

📝 Problem & Approach

Given a positive integer n, decide whether it is magic under the repeated digit-sum rule; optionally list every magic value in a closed interval.

/* n = 19
 * 19 → 1+9 = 10
 * 10 → 1+0 = 1   → magic
 *
 * n = 18
 * 18 → 1+8 = 9   → not magic
 */

Inputs & Outputs

Minimal workflow

function digit_sum(n):   // n >= 0
    s ← 0
    while n > 0:
        s ← s + (n mod 10)
        n ← floor(n / 10)
    return s

function is_magic(n):   // assume n > 0
    while n > 9:
        n ← digit_sum(n)
    return (n = 1)

Method comparison

🔮 Live Preview

Enter a positive integer to watch the same digit-sum chain as the C code.

Press “Run check” to see the digit-sum steps.

Examples Gallery

Two complete C programs — classify a single value, and list magic numbers in [1, 50]. Click View Output to reveal sample console results.

#include <stdio.h>

/* Returns 1 if num is a magic number (repeated digit sum ends at 1), else 0 */
int is_magic_number(int num) {
    while (num > 9) {
        int sum = 0;

        while (num > 0) {
            sum += num % 10;
            num /= 10;
        }

        num = sum;
    }

    return num == 1;
}

int main(void) {
    int number = 19;

    if (is_magic_number(number)) {
        printf("%d is a Magic Number.\n", number);
    } else {
        printf("%d is not a Magic Number.\n", number);
    }

    return 0;
}

19 is a Magic Number.

#include <stdio.h>

int is_magic_number(int num) {
    while (num > 9) {
        int sum = 0;
        while (num > 0) {
            sum += num % 10;
            num /= 10;
        }
        num = sum;
    }
    return num == 1;
}

int main(void) {
    printf("Magic Numbers in the range 1 to 50:\n");

    for (int i = 1; i <= 50; ++i) {
        if (is_magic_number(i)) {
            printf("%d ", i);
        }
    }

    printf("\n");
    return 0;
}

Magic Numbers in the range 1 to 50:
1 10 19 28 37 46

🔎 Worked Walkthrough — n = 19

Trace each digit-sum pass until a single digit remains.

By contrast, 18 → 9 stops at 9, so it is not magic.

🔄 Sample Values

Known results for common interview inputs.

🎯 Practice Problems

Try these variations to lock in the pattern.

Notes

⏱️ Time and Space Complexity

💡 Best Practices