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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-289-eulerian-cycles.md

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+---
+id: 5900f48d1000cf542c50ffa0
+challengeType: 5
+title: 'Problem 289: Eulerian Cycles'
+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).
+
+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 }
+
+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.
+
+Find L(6,10) mod 1010.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>euler289()</code> should return 6567944538.
+    testString: assert.strictEqual(euler289(), 6567944538);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function euler289() {
+
+  return true;
+}
+
+euler289();
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+```js
+// solution required
+```
+
+</section>