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curriculum/challenges/japanese/10-coding-interview-prep/project-euler/problem-358-cyclic-numbers.md
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---
id: 5900f4d21000cf542c50ffe5
title: 'Problem 358: Cyclic numbers'
title: '問題 358: 巡回数'
challengeType: 5
forumTopicId: 302018
dashedName: problem-358-cyclic-numbers
@ -8,25 +8,25 @@ dashedName: problem-358-cyclic-numbers
# --description--
A cyclic number with $n$ digits has a very interesting property:
$n$ 桁の巡回数は非常に興味深い性質を持っています:
When it is multiplied by 1, 2, 3, 4, ... $n$, all the products have exactly the same digits, in the same order, but rotated in a circular fashion!
1, 2, 3, 4, ... $n$ を乗じると、すべての積に全く同じ数字が使われ、数字を循環させると順序も同じになります！
The smallest cyclic number is the 6-digit number 142857:
最小の巡回数は、6 桁の数 142857 です。
$$\begin{align} & 142857 × 1 = 142857 \\\\ & 142857 × 2 = 285714 \\\\ & 142857 × 3 = 428571 \\\\ & 142857 × 4 = 571428 \\\\ & 142857 × 5 = 714285 \\\\ & 142857 × 6 = 857142 \end{align}$$
The next cyclic number is 0588235294117647 with 16 digits:
次の巡回数は、16 桁の 0588235294117647 です。
$$\begin{align} & 0588235294117647 × 1 = 0588235294117647 \\\\ & 0588235294117647 × 2 = 1176470588235294 \\\\ & 0588235294117647 × 3 = 1764705882352941 \\\\ & \ldots \\\\ & 0588235294117647 × 16 = 9411764705882352 \end{align}$$
Note that for cyclic numbers, leading zeros are important.
なお、巡回数では先行ゼロが重要です。
There is only one cyclic number for which, the eleven leftmost digits are 00000000137 and the five rightmost digits are 56789 (i.e., it has the form $00000000137\ldots56789$ with an unknown number of digits in the middle). Find the sum of all its digits.
左端の 11 桁が 00000000137 で、右端の 5 桁が 56789 (すなわち $00000000137\ldots56789$ の形を取り、中間の数字は不明) の巡回数は 1 つしかありません。 この数のすべての桁の和を求めなさい。
# --hints--
`cyclicNumbers()` should return `3284144505`.
`cyclicNumbers()` は `3284144505` を返す必要があります。
```js
assert.strictEqual(cyclicNumbers(), 3284144505);