Loops, functions, and mathematical logic form the backbone of programming. Whether you are preparing for coding interviews or brushing up on fundamentals, these classic problems strengthen your problem-solving skills and help you write efficient JavaScript code.

In this blog, we’ll cover popular loop-based and math-based problems along with explanations and solutions.

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✅ 1. Sum of All Natural Numbers from 1 to n

A natural number series grows linearly, and the simplest approach is using a loop.

function sumOfNaturalNumber(num){
    let sum = 0;
    for(let i = 1; i <= num; i++){
        sum = sum + i;
    }
    return sum;
}

console.log(sumOfNaturalNumber(5));  // 15
console.log(sumOfNaturalNumber(10)); // 55
console.log(sumOfNaturalNumber(8));  // 36

📌 Concept: Looping + accumulator pattern
📌 Alternative formula: n * (n + 1) / 2

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✅ 2. Sum of Digits of a Number

Extract the last digit using % 10 and remove digits using Math.floor(num / 10).

function sumOfDigits(num){
    let sum = 0;
    while(num > 0){
        sum += num % 10;
        num = Math.floor(num / 10);
    }
    return sum;
}

console.log(sumOfDigits(1287)); // 18

📌 Useful for: Digital sums, numeric algorithm problems.

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✅ 3. Count the Number of Digits in a Number

function countDigits(num){
    num = Math.abs(num);
    let count = 0;
    do {
        count++;
        num = Math.floor(num / 10);
    } while (num > 0);
    return count;
}

console.log(countDigits(121));            // 3
console.log(countDigits(-1211413131));     // 10

📌 Why do this? Helps in modular arithmetic and numeric pattern detection.

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✅ 4. Check if a Number is Palindrome

A palindrome number remains the same when reversed.

let isPalindrome = function(x) {
    let copyNum = x, reverseNum = 0;

    while(copyNum > 0){
        const lastDigit = copyNum % 10;
        reverseNum = reverseNum * 10 + lastDigit;
        copyNum = Math.floor(copyNum / 10);
    }

    return x === reverseNum;
};

console.log(isPalindrome(121));  // true
console.log(isPalindrome(1234)); // false

📌 Used in: LeetCode, HackerRank and coding interviews.

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✅ 5. Find nth Fibonacci Number

The Fibonacci sequence follows:
0, 1, 1, 2, 3, 5, 8...

let fib = function(n) {
    if(n < 2){
        return n;
    }

    let prev = 0, curr = 1, next;
    for(let i = 2; i <= n; i++){
        next = prev + curr;
        prev = curr;
        curr = next;
    }
    return next;
};

console.log(fib(5));  // 5
console.log(fib(10)); // 55

📌 Efficient iterative solution.
📌 No recursion needed.

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✅ 6. Missing Number in an Array

Given an array of numbers from 0 to n, find which one is missing.

let missingNumber = function(nums) {
    let sum = 0;
    for(let i = 0; i < nums.length; i++){
        sum += nums[i];
    }
    return nums.length * (nums.length + 1) / 2 - sum;
};

⭐ One-Line Solution

let missingNumber = (nums) => 
    nums.length*(nums.length+1)/2 - nums.reduce((acc, num) => num + acc);

console.log(missingNumber([3,0,1])); // 2
console.log(missingNumber([9,6,4,2,3,5,7,0,1])); // 8

📌 Uses math formula + reduce.

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📝 Practice Questions (Try Yourself)

✔ Count Odd Numbers in an Interval Range
✔ Fizz Buzz
✔ Power of Two
✔ Find Square Root of a Number

🔥 These problems are great to sharpen your fundamentals before moving to advanced DSA topics!

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🎯 Final Thoughts

Practicing loops, math logic, and functions in JavaScript builds a strong foundation that prepares you for real-world coding challenges and technical interviews. Keep solving, keep learning, and your logical thinking will grow rapidly.