chore(i18n,learn): processed translations (#44851)

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

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+---
+id: 5900f5241000cf542c510037
+title: 'Problem 440: GCD and Tiling'
+challengeType: 5
+forumTopicId: 302112
+dashedName: 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:
+
+<img class="img-responsive center-block" alt="ten blocks 1x1 with single decimal digit on top, and 1x2 block" src="https://cdn.freecodecamp.org/curriculum/project-euler/gcd-and-tiling-1.png" style="background-color: white; padding: 10px;" />
+
+For example, here are some of the ways to tile a board of length $n = 8$:
+
+<img class="img-responsive center-block" alt="examples of ways to tile a board of length n = 8" src="https://cdn.freecodecamp.org/curriculum/project-euler/gcd-and-tiling-2.png" style="background-color: white; padding: 10px;" />
+
+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`.
+
+```js
+assert.strictEqual(gcdAndTiling(), 970746056);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function gcdAndTiling() {
+
+  return true;
+}
+
+gcdAndTiling();
+```
+
+# --solutions--
+
+```js
+// solution required
+```