Published at Jul 13 2018
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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)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.

Execute the tests with:

```
$ elixir difference_of_squares_test.exs
```

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

Once you get a test passing, you can unskip the next one by
commenting out the relevant `@tag :pending`

with a `#`

symbol.

For example:

```
# @tag :pending
test "shouting" do
assert Bob.hey("WATCH OUT!") == "Whoa, chill out!"
end
```

Or, you can enable all the tests by commenting out the
`ExUnit.configure`

line in the test suite.

```
# ExUnit.configure exclude: :pending, trace: true
```

For more detailed information about the Elixir track, please see the help page.

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.

```
if !System.get_env("EXERCISM_TEST_EXAMPLES") do
Code.load_file("difference_of_squares.exs", __DIR__)
end
ExUnit.start()
ExUnit.configure(exclude: :pending, trace: true)
defmodule DifferenceOfSquaresTest do
use ExUnit.Case
# @tag :pending
test "square of sums to 5" do
assert Squares.square_of_sums(5) == 225
end
@tag :pending
test "sum of squares to 5" do
assert Squares.sum_of_squares(5) == 55
end
@tag :pending
test "difference of sums to 5" do
assert Squares.difference(5) == 170
end
@tag :pending
test "square of sums to 10" do
assert Squares.square_of_sums(10) == 3025
end
@tag :pending
test "sum of squares to 10" do
assert Squares.sum_of_squares(10) == 385
end
@tag :pending
test "difference of sums to 10" do
assert Squares.difference(10) == 2640
end
@tag :pending
test "square of sums to 100" do
assert Squares.square_of_sums(100) == 25_502_500
end
@tag :pending
test "sum of squares to 100" do
assert Squares.sum_of_squares(100) == 338_350
end
@tag :pending
test "difference of sums to 100" do
assert Squares.difference(100) == 25_164_150
end
end
```

```
defmodule Squares do
@moduledoc """
Calculate sum of squares, square of sums, difference between two sums from 1 to a given end number.
"""
@doc """
Calculate sum of squares from 1 to a given end number.
"""
@spec sum_of_squares(pos_integer) :: pos_integer
def sum_of_squares(number) do
# from https://en.wikipedia.org/wiki/Square_pyramidal_number
(2 * :math.pow(number, 3) + 3 * number * number + number) / 6
end
@doc """
Calculate square of sums from 1 to a given end number.
"""
@spec square_of_sums(pos_integer) :: pos_integer
def square_of_sums(number) do
# n*(n+1)/2 is standard formula for sum(1..n)
:math.pow((number * (number + 1) / 2), 2)
end
@doc """
Calculate difference between sum of squares and square of sums from 1 to a given end number.
"""
@spec difference(pos_integer) :: pos_integer
def difference(number) do
square_of_sums(number) - sum_of_squares(number)
end
end
```

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