80 lines
2.3 KiB
Markdown
80 lines
2.3 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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forumTopicId: 302173
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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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|Type of Number|Formula|Sequence|
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|--- |--- |--- |
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|Triangle|P<sub>3</sub>,<var><sub>n</sub></var>=<var>n</var>(<var>n</var>+1)/2|1, 3, 6, 10, 15, ...|
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|Square|P<sub>4</sub>,<var><sub>n</sub></var>=<var>n</var><sup>2</sup>|1, 4, 9, 16, 25, ...|
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|Pentagonal|P<sub>5</sub>,<var><sub>n</sub></var>=<var>n</var>(3<var>n</var>−1)/2|1, 5, 12, 22, 35, ...|
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|Hexagonal|P<sub>6</sub>,<var><sub>n</sub></var>=<var>n</var>(2<var>n</var>−1)|1, 6, 15, 28, 45, ...|
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|Heptagonal|P<sub>7</sub>,<var><sub>n</sub></var>=<var>n</var>(5<var>n</var>−3)/2|1, 7, 18, 34, 55, ...|
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|Octagonal|P<sub>8</sub>,<var><sub>n</sub></var>=<var>n</var>(3<var>n</var>−2)|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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<ol>
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<li>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).</li>
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<li>Each polygonal type: triangle (P<sub>3,127</sub> = 8128), square (P<sub>4,91</sub> = 8281), and pentagonal (P<sub>5,44</sub> = 2882), is represented by a different number in the set.</li>
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<li>This is the only set of 4-digit numbers with this property.</li>
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</ol>
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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>cyclicalFigurateNums()</code> should return a number.
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testString: assert(typeof cyclicalFigurateNums() === 'number');
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- text: <code>cyclicalFigurateNums()</code> should return 28684.
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testString: assert.strictEqual(cyclicalFigurateNums(), 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 cyclicalFigurateNums() {
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return true;
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}
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cyclicalFigurateNums();
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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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