# mbraak's solution

## to Difference Of Squares in the Clojure Track

Published at Jan 30 2019 · 0 comments
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)² = 55² = 3025.

The sum of the squares of the first ten natural numbers is 1² + 2² + ... + 10² = 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.

## Source

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

## Submitting Incomplete Solutions

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

### difference_of_squares_test.clj

``````(ns difference-of-squares-test
(:require [clojure.test :refer [deftest is]]
[difference-of-squares :as dos]))

(deftest square-of-sum-to-5
(is (= 225 (dos/square-of-sum 5))))

(deftest sum-of-squares-to-5
(is (= 55 (dos/sum-of-squares 5))))

(deftest difference-of-squares-to-5
(is (= 170 (dos/difference 5))))

(deftest square-of-sum-to-10
(is (= 3025 (dos/square-of-sum 10))))

(deftest sum-of-squares-to-10
(is (= 385 (dos/sum-of-squares 10))))

(deftest difference-of-squares-to-10
(is (= 2640 (dos/difference 10))))

(deftest square-of-sum-to-100
(is (= 25502500 (dos/square-of-sum 100))))

(deftest sum-of-squares-to-100
(is (= 338350 (dos/sum-of-squares 100))))

(deftest difference-of-squares-to-100
(is (= 25164150 (dos/difference 100))))``````
``````(ns difference-of-squares)

(defn sum-of-squares [n]
(quot
(*
n
(inc n)
(inc (* 2 n))
)
6
)
)

(defn square-of-sum [n]
(let
[
sum
(quot
(* n (inc n))
2)
]
(* sum sum)
)
)

(defn difference [n]
(-
(square-of-sum n)
(sum-of-squares n)
)
)``````

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