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

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f5241000cf542c510037	Problem 440: GCD and Tiling	5	302112	problem-440-gcd-and-tiling

--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 \sum_{a, b, c} gcd(T(c^a), T(c^b)) for 1 ≤ a, b, c ≤ L.

For example:

$$\begin{align} & S(2) = 10\,444 \\ & S(3) = 1\,292\,115\,238\,446\,807\,016\,106\,539\,989 \\ & S(4)\bmod 987\,898\,789 = 670\,616\,280. \end{align}$$

Find S(2000)\bmod 987\\,898\\,789.

--hints--

gcdAndTiling() should return 970746056.

assert.strictEqual(gcdAndTiling(), 970746056);

--seed--

--seed-contents--

function gcdAndTiling() {

  return true;
}

gcdAndTiling();

--solutions--

// solution required