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Published at Jul 15 2020
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Instructions

Test suite

Solution

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

The square of the sum of the first ten natural numbers is (1 + 2 + ... + 10)Â² = 55Â² = 3025.

The sum of the squares of the first ten natural numbers is 1Â² + 2Â² + ... + 10Â² = 385.

Hence the difference between the square of the sum of the first ten natural numbers and the sum of the squares of the first ten natural numbers is 3025 - 385 = 2640.

You are not expected to discover an efficient solution to this yourself from first principles; research is allowed, indeed, encouraged. Finding the best algorithm for the problem is a key skill in software engineering.

Go through the setup instructions for TypeScript to install the necessary dependencies:

https://exercism.io/tracks/typescript/installation

Install assignment dependencies:

```
$ yarn install
```

Execute the tests with:

```
$ yarn test
```

In the test suites all tests but the first have been skipped.

Once you get a test passing, you can enable the next one by changing `xit`

to
`it`

.

Problem 6 at Project Euler http://projecteuler.net/problem=6

It's possible to submit an incomplete solution so you can see how others have completed the exercise.

```
import Squares from './difference-of-squares'
describe('Squares', () => {
describe('up to 5', () => {
const squares = new Squares(5)
it('gets the square of sum', () => {
expect(squares.squareOfSum).toBe(225)
})
xit('gets the sum of squares', () => {
expect(squares.sumOfSquares).toBe(55)
})
xit('gets the difference', () => {
expect(squares.difference).toBe(170)
})
})
describe('up to 10', () => {
const squares = new Squares(10)
xit('gets the square of sum', () => {
expect(squares.squareOfSum).toBe(3025)
})
xit('gets the sum of squares', () => {
expect(squares.sumOfSquares).toBe(385)
})
xit('gets the difference', () => {
expect(squares.difference).toBe(2640)
})
})
describe('up to 100', () => {
const squares = new Squares(100)
xit('gets the square of sum', () => {
expect(squares.squareOfSum).toBe(25502500)
})
xit('gets the sum of squares', () => {
expect(squares.sumOfSquares).toBe(338350)
})
xit('gets the difference', () => {
expect(squares.difference).toBe(25164150)
})
})
})
```

```
class Squares {
private size: number
constructor(size: number) {
this.size = size
}
get squareOfSum(): number {
const squareOfSum = Math.pow(this.calculateSquareOfSum(this.size), 2)
return squareOfSum
}
calculateSquareOfSum(size: number): number {
if (size === 0) {
return size
}
return size + this.calculateSquareOfSum(size - 1)
}
get sumOfSquares(): number {
const sumOfSquares = this.calculateSumOfSquares(this.size)
return sumOfSquares
}
calculateSumOfSquares(size: number): number {
if (size === 0) {
return size
}
return Math.pow(size, 2) + this.calculateSumOfSquares(size - 1)
}
get difference(): number {
return this.squareOfSum - this.sumOfSquares
}
}
export default Squares
```

A huge amount can be learned from reading other peopleâ€™s code. This is why we wanted to give exercism users the option of making their solutions public.

Here are some questions to help you reflect on this solution and learn the most from it.

- What compromises have been made?
- Are there new concepts here that you could read more about to improve your understanding?

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