1.4 KiB
1.4 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f48d1000cf542c50ffa0 | 5 | Problem 289: Eulerian Cycles | 301940 |
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 }
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.
Instructions
Tests
tests:
- text: <code>euler289()</code> should return 6567944538.
testString: assert.strictEqual(euler289(), 6567944538);
Challenge Seed
function euler289() {
// Good luck!
return true;
}
euler289();
Solution
// solution required