---
id: 5900f5021000cf542c510014
challengeType: 5
title: 'Problem 405: A rectangular tiling'
---
## Description
We wish to tile a rectangle whose length is twice its width.
Let T(0) be the tiling consisting of a single rectangle.
For n > 0, let T(n) be obtained from T(n-1) by replacing all tiles in the following manner:
The following animation demonstrates the tilings T(n) for n from 0 to 5:
Let f(n) be the number of points where four tiles meet in T(n).
For example, f(1) = 0, f(4) = 82 and f(109) mod 177 = 126897180.
Find f(10k) for k = 1018, give your answer modulo 177.
## Instructions
## Tests
```yml
tests:
- text: euler405() should return 237696125.
testString: assert.strictEqual(euler405(), 237696125, 'euler405() should return 237696125.');
```
## Challenge Seed
```js
function euler405() {
// Good luck!
return true;
}
euler405();
```