c18554dd44
* fix: clean-up Project Euler 341-360 * fix: improve wording Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
66 lines
1.5 KiB
Markdown
66 lines
1.5 KiB
Markdown
---
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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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$$\begin{align}
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& 142857 × 1 = 142857 \\\\
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& 142857 × 2 = 285714 \\\\
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& 142857 × 3 = 428571 \\\\
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& 142857 × 4 = 571428 \\\\
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& 142857 × 5 = 714285 \\\\
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& 142857 × 6 = 857142
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\end{align}$$
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The next cyclic number is 0588235294117647 with 16 digits:
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$$\begin{align}
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& 0588235294117647 × 1 = 0588235294117647 \\\\
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& 0588235294117647 × 2 = 1176470588235294 \\\\
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& 0588235294117647 × 3 = 1764705882352941 \\\\
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& \ldots \\\\
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& 0588235294117647 × 16 = 9411764705882352
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\end{align}$$
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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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