53 lines
1.5 KiB
Markdown
53 lines
1.5 KiB
Markdown
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---
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id: 5900f4d21000cf542c50ffe5
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title: 'Problem 358: Cyclic numbers'
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challengeType: 5
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forumTopicId: 302018
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dashedName: problem-358-cyclic-numbers
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---
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# --description--
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A cyclic number with $n$ digits has a very interesting property:
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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!
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The smallest cyclic number is the 6-digit number 142857:
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$$\begin{align} & 142857 × 1 = 142857 \\\\ & 142857 × 2 = 285714 \\\\ & 142857 × 3 = 428571 \\\\ & 142857 × 4 = 571428 \\\\ & 142857 × 5 = 714285 \\\\ & 142857 × 6 = 857142 \end{align}$$
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The next cyclic number is 0588235294117647 with 16 digits:
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$$\begin{align} & 0588235294117647 × 1 = 0588235294117647 \\\\ & 0588235294117647 × 2 = 1176470588235294 \\\\ & 0588235294117647 × 3 = 1764705882352941 \\\\ & \ldots \\\\ & 0588235294117647 × 16 = 9411764705882352 \end{align}$$
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Note that for cyclic numbers, leading zeros are important.
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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.
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# --hints--
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`cyclicNumbers()` should return `3284144505`.
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```js
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assert.strictEqual(cyclicNumbers(), 3284144505);
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```
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# --seed--
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## --seed-contents--
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```js
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function cyclicNumbers() {
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return true;
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}
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cyclicNumbers();
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```
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# --solutions--
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```js
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// solution required
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```
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