Solving Project Euler Problem 6: Sum Square Difference

 Problem

"The sum of the squares of the first ten natural numbers is: 1² + 2² + ... + 10² = 385

The square of the sum of the first ten natural numbers is: (1 + 2 + ... + 10)² = 55² = 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."

 

Solution

1.      Sum of the Squares: To find the sum of the squares of the first n natural numbers, we calculate the square of each number from 1 to n and then add those squares together. Mathematically, this can be expressed as:

Sum of Squares = 1² + 2² + 3² + ... + n²

2.      Square of the Sum: To find the square of the sum of the first n natural numbers, we first calculate the sum of those numbers and then square the result. Mathematically, this can be expressed as:

Square of Sum = (1 + 2 + 3 + ... + n)²

 

The problem asks for the difference between these two quantities, which can be calculated as:

Difference = Square of Sum – Sum of Squares

 

1.      We define a function, sum_square_difference, that takes one argument, n, representing the number of natural numbers we want to consider (in this case, 100).

2.      We initialize sum_of_squares and square_of_sum to zero as our starting points.

3.      Using a for loop that iterates from 1 to n (inclusive), we calculate the sum of the squares of the first n natural numbers and the sum of the first n natural numbers.

4.      After the loop finishes, we calculate the square of the sum by squaring the value of square_of_sum.

5.      Finally, we calculate the difference between the square of the sum and the sum of the squares, which is the result we are looking for.

 

Solving Project Euler Problems provides a great opportunity to practice coding and algorithmic thinking.