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* fix: clean-up Project Euler 121-140 * fix: corrections from review Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> * fix: missing backticks Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Sem Bauke <46919888+Sembauke@users.noreply.github.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
55 lines
1.6 KiB
Markdown
55 lines
1.6 KiB
Markdown
---
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id: 5900f3ec1000cf542c50feff
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title: 'Problem 128: Hexagonal tile differences'
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challengeType: 5
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forumTopicId: 301755
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dashedName: problem-128-hexagonal-tile-differences
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---
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# --description--
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A hexagonal tile with number 1 is surrounded by a ring of six hexagonal tiles, starting at "12 o'clock" and numbering the tiles 2 to 7 in an anti-clockwise direction.
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New rings are added in the same fashion, with the next rings being numbered 8 to 19, 20 to 37, 38 to 61, and so on. The diagram below shows the first three rings.
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<img class="img-responsive center-block" alt="three first rings of arranged hexagonal tiles with numbers 1 to 37, and with highlighted tiles 8 and 17" src="https://cdn.freecodecamp.org/curriculum/project-euler/hexagonal-tile-differences.png" style="background-color: white; padding: 10px;">
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By finding the difference between tile $n$ and each of its six neighbours we shall define $PD(n)$ to be the number of those differences which are prime.
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For example, working clockwise around tile 8 the differences are 12, 29, 11, 6, 1, and 13. So $PD(8) = 3$.
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In the same way, the differences around tile 17 are 1, 17, 16, 1, 11, and 10, hence $PD(17) = 2$.
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It can be shown that the maximum value of $PD(n)$ is $3$.
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If all of the tiles for which $PD(n) = 3$ are listed in ascending order to form a sequence, the 10th tile would be 271.
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Find the 2000th tile in this sequence.
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# --hints--
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`hexagonalTile()` should return `14516824220`.
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```js
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assert.strictEqual(hexagonalTile(), 14516824220);
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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 hexagonalTile() {
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return true;
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}
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hexagonalTile();
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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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