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---
id: 5900f48d1000cf542c50ffa0
title: 'Problem 289: Eulerian Cycles'
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challengeType: 5
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forumTopicId: 301940
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dashedName: problem-289-eulerian-cycles
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---
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# --description--
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Let $C(x,y)$ be a circle passing through the points ($x$, $y$), ($x$, $y + 1$), ($x + 1$, $y$) and ($x + 1$, $y + 1$).
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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 }
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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.
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The image below shows $E(3,3)$ and an example of an Eulerian non-crossing path.
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< img class = "img-responsive center-block" alt = "Eulerian cycle E(3, 3) and Eulerian non-crossing path" src = "https://cdn.freecodecamp.org/curriculum/project-euler/eulerian-cycles.gif" style = "background-color: white; padding: 10px;" >
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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 $L(6,10)\bmod {10}^{10}$.
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# --hints--
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`eulerianCycles()` should return `6567944538` .
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```js
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assert.strictEqual(eulerianCycles(), 6567944538);
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```
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# --seed--
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## --seed-contents--
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```js
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function eulerianCycles() {
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return true;
}
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eulerianCycles();
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```
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# --solutions--
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```js
// solution required
```