79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
91 lines
1.7 KiB
Markdown
91 lines
1.7 KiB
Markdown
---
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id: 5900f3a91000cf542c50febc
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challengeType: 5
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title: 'Problem 61: Cyclical figurate numbers'
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---
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## Description
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<section id='description'>
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Triangle, square, pentagonal, hexagonal, heptagonal, and octagonal numbers are all figurate (polygonal) numbers and are generated by the following formulae:
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Triangle
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P3,n=n(n+1)/2
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1, 3, 6, 10, 15, ...
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Square
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P4,n=n2
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1, 4, 9, 16, 25, ...
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Pentagonal
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P5,n=n(3n−1)/2
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1, 5, 12, 22, 35, ...
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Hexagonal
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P6,n=n(2n−1)
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1, 6, 15, 28, 45, ...
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Heptagonal
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P7,n=n(5n−3)/2
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1, 7, 18, 34, 55, ...
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Octagonal
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P8,n=n(3n−2)
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1, 8, 21, 40, 65, ...
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The ordered set of three 4-digit numbers: 8128, 2882, 8281, has three interesting properties.
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The set is cyclic, in that the last two digits of each number is the first two digits of the next number (including the last number with the first).
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Each polygonal type: triangle (P3,127=8128), square (P4,91=8281), and pentagonal (P5,44=2882), is represented by a different number in the set.
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This is the only set of 4-digit numbers with this property.
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Find the sum of the only ordered set of six cyclic 4-digit numbers for which each polygonal type: triangle, square, pentagonal, hexagonal, heptagonal, and octagonal, is represented by a different number in the set.
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler61()</code> should return 28684.
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testString: assert.strictEqual(euler61(), 28684, '<code>euler61()</code> should return 28684.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler61() {
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// Good luck!
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return true;
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}
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euler61();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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