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and change all the challenges to new `md` format.
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Oliver Eyton-Williams
2020-11-27 19:02:05 +01:00
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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-289-eulerian-cycles.md
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@ -1,50 +1,35 @@
---
id: 5900f48d1000cf542c50ffa0
challengeType: 5
title: 'Problem 289: Eulerian Cycles'
challengeType: 5
forumTopicId: 301940
---
## Description
<section id='description'>
Let C(x,y) be a circle passing through the points (x, y), (x, y+1), (x+1, y) and (x+1, y+1).
# --description--
For positive integers m and n, let E(m,n) be a configuration which consists of the m·n circles:
{ C(x,y): 0 ≤ x < m, 0 ≤ y < n, x and y are integers }
Let C(x,y) be a circle passing through the points (x, y), (x, y+1), (x+1, y) and (x+1, y+1).
An Eulerian cycle on E(m,n) is a closed path that passes through each arc exactly once.
Many such paths are possible on E(m,n), but we are only interested in those which are not self-crossing:
A non-crossing path just touches itself at lattice points, but it never crosses itself.
For positive integers m and n, let E(m,n) be a configuration which consists of the m·n circles: { C(x,y): 0 ≤ x &lt; m, 0 ≤ y &lt; n, x and y are integers }
An Eulerian cycle on E(m,n) is a closed path that passes through each arc exactly once. Many such paths are possible on E(m,n), but we are only interested in those which are not self-crossing: A non-crossing path just touches itself at lattice points, but it never crosses itself.
The image below shows E(3,3) and an example of an Eulerian non-crossing path.
Let L(m,n) be the number of Eulerian non-crossing paths on E(m,n).
For example, L(1,2) = 2, L(2,2) = 37 and L(3,3) = 104290.
Let L(m,n) be the number of Eulerian non-crossing paths on E(m,n). For example, L(1,2) = 2, L(2,2) = 37 and L(3,3) = 104290.
Find L(6,10) mod 1010.
</section>
## Instructions
<section id='instructions'>
# --hints--
</section>
## Tests
<section id='tests'>
```yml
tests:
- text: <code>euler289()</code> should return 6567944538.
testString: assert.strictEqual(euler289(), 6567944538);
`euler289()` should return 6567944538.
```js
assert.strictEqual(euler289(), 6567944538);
```
</section>
# --seed--
## Challenge Seed
<section id='challengeSeed'>
<div id='js-seed'>
## --seed-contents--
```js
function euler289() {
@ -55,17 +40,8 @@ function euler289() {
euler289();
```
</div>
</section>
## Solution
<section id='solution'>
# --solutions--
```js
// solution required
```
</section>