## Project Euler 173: Using up to one million tiles find many different "hollow" square laminae can be formed.

#### Problem Description

We shall define a square lamina to be a square outline with a square "hole" so that the shape possesses vertical and horizontal symmetry. For example, using exactly thirty-two square tiles we can form two different square laminae:

With one-hundred tiles, and not necessarily using all of the tiles at one time, it is possible to form forty-one different square laminae.

Using up to one million tiles how many different square laminae can be formed?

#### Analysis

Ran a brute force for the first 10,000 tiles and found the series. So the next step is to form a generating function to calculate the answer, but, alas, this is unlikely to ever happen.

#### Project Euler 173 Solution

Runs < 0.001 seconds in Python.

```
import math
tiles = 1000000 // 4
L = int(math.sqrt(tiles)) + 1
print "Project Euler 173 Solution =", sum(tiles/i-i for i in range(1, L))
```

#### Comments

- See also, Project Euler 173 Solution:

*Project Euler 173 Solution last updated June 20, 2014*

## Discussion

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