# Euler 0028

### The Problem:

If you were to build a square starting with 1 in the middle then going right, down, left 2, up 2, right 2, and repeat, all the corner numbers would be diagonals.

On the Project Euler website there is a nice graphic that I'm not putting here.

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

### Considerations and Approach:

This problem is bait. We don't have to generate a 2d structure. Instead we can observe the pattern of skipping.   
1.3.5.7.9...13...17...21...25.....30

We start with one and add 1. Every four times we add, we add 2 to the skipping distance, and we declare our square 2 larger!

<div class="md-output__section has-scroll" id="bkmrk-keep-iterating-throu"></div>### The Code:

<details id="bkmrk-target_under-%3D-1000-"><summary></summary>

```python
max_square = 1001

spiral = 1
square_size = 2
total = 1
while square_size + 1 <= max_square:
    for i in range(4):
        spiral += square_size
        total += spiral
    
    square_size += 2
    
print(total)
```

</details>