Project Euler

Problem

This problem comes from Project Euler 28

Problem

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

It can be verified that the sum of the numbers on the diagonals is 101.

What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

Solution

Let’s notice a few things:

• In the first “ring,” the numbers 3, 5, 7, and 9 go up by two
• In the second “ring,” the numbers 13, 17, 21, and 25 go up by four

We can see that every “corner” increases by $2 \times \text{ring}$ . Therefore, we can calculate the total by calculating each corner and adding that to the total.

Code

# Project Euler: Problem 28
# Number Spiral Diagonals

total = 1  # "ring" 0
corner = 1 # "corner" of "ring" 0

for ring in range(1, 501):
    for _ in range(0, 4):
        corner += 2*ring    # 3, 5, 7, 9, 13...
        total += corner     # 1, 4, 9, 16, 25... 
print(total)