Problem 6

from project_euler import get_problem_description

get_problem_description(6)

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

$$1^2 + 2^2 + ... + 10^2 = 385.$$

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

$$(1 + 2 + ... + 10)^2 = 55^2 = 3025.$$

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.

def sum_of_squares(numbers):
    return sum((num**2 for num in numbers))


def square_of_sum(numbers):
    return sum(numbers) ** 2


numbers = range(11)
assert sum_of_squares(numbers) == 385

assert square_of_sum(numbers) == 3025

numbers = range(101)
square_of_sum(numbers) - sum_of_squares(numbers)

25164150