# Project Euler: #6 - Sum square difference

### **Problem**

The sum of the squares of the first ten natural numbers is,

$$1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 + 8^2 + 9^2 + 10^2 = 385$$

The square of the sum of the first ten natural numbers is,

$$(1+2+3+4+5+6+7+8+9+10)^2 = 55^2 = 3025$$

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is

$$3025 − 385 = 2640$$

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

---

### **Problem Description**

Well, the problem itself is self-explanatory.

The example given is for first `10` natural numbers. We need to find the difference between the Sum of Squares & Squares of the Sum of first `100` natural numbers.

i.e. `1 to 100`.

---

### **Approach**

This is a detailed approach.

Two functions are involved. One function is to calculate the square of each number from `1` to `100` and add those squares.

Another function is to add the numbers from `1` to `100` and square their sum.

Finally, find the difference between both.

Very simple, Right?

---

### **Solution**

```javascript
const sumOfSqrNums = (start, end) => {
    let sumOfSqrs = 0;

    if (start > end) {
        console.log(`${start} > ${end}! Enter a valid Start & End.`);
    } else {
        for (let i = start; i <= end; i++) {
            sumOfSqrs += Math.pow(i, 2);
        }
    }
    return sumOfSqrs;
}

const sqrOfSumNums = (start, end) => {
    let sumOfNums = 0;

    if (start > end) {
        console.log(`${start} > ${end}! Enter a valid Start & End.`);
    } else {
        for (let i = start; i <= end; i++) {
            sumOfNums += i;
        }
    }
    return Math.pow(sumOfNums, 2);
}

let difference = sqrOfSumNums(1, 100) - sumOfSqrNums(1, 100);
console.log(difference);
```

You can find my solution on GitHub [**06**](https://github.com/sansk/project-euler-solutions-javascript/tree/main/06)

This particular solution was executed with a better complexity in Hacker rank. But there are still much better solutions to this. If you have another or a better solution, please leave it in the comments below.

For the other Project Euler Solutions, please follow the series [**Project Euler Solutions in JS.**](https://theintrovertcoder.hashnode.dev/series/project-euler)

Thank you!