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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-440-gcd-and-tiling.md

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+---
+id: 5900f5241000cf542c510037
+challengeType: 5
+title: 'Problem 440: GCD and Tiling'
+forumTopicId: 302112
+---
+
+## Description
+<section id='description'>
+We want to tile a board of length n and height 1 completely, with either 1 × 2 blocks or 1 × 1 blocks with a single decimal digit on top:
+
+For example, here are some of the ways to tile a board of length n = 8:
+
+Let T(n) be the number of ways to tile a board of length n as described above.
+
+For example, T(1) = 10 and T(2) = 101.
+
+Let S(L) be the triple sum ∑a,b,c gcd(T(ca), T(cb)) for 1 ≤ a, b, c ≤ L.
+For example:
+S(2) = 10444
+S(3) = 1292115238446807016106539989
+S(4) mod 987 898 789 = 670616280.
+
+Find S(2000) mod 987 898 789.
+</section>
+
+## Instructions
+<section id='instructions'>
+
+</section>
+
+## Tests
+<section id='tests'>
+
+```yml
+tests:
+  - text: <code>euler440()</code> should return 970746056.
+    testString: assert.strictEqual(euler440(), 970746056);
+
+```
+
+</section>
+
+## Challenge Seed
+<section id='challengeSeed'>
+
+<div id='js-seed'>
+
+```js
+function euler440() {
+
+  return true;
+}
+
+euler440();
+```
+
+</div>
+
+
+
+</section>
+
+## Solution
+<section id='solution'>
+
+```js
+// solution required
+```
+
+</section>