41 lines
1.2 KiB
Markdown
41 lines
1.2 KiB
Markdown
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---
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id: 5900f3ea1000cf542c50fefd
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title: 'Problem 126: Cuboid layers'
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challengeType: 5
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forumTopicId: 301753
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dashedName: problem-126-cuboid-layers
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---
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# --description--
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The minimum number of cubes to cover every visible face on a cuboid measuring 3 x 2 x 1 is twenty-two.
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If we then add a second layer to this solid it would require forty-six cubes to cover every visible face, the third layer would require seventy-eight cubes, and the fourth layer would require one-hundred and eighteen cubes to cover every visible face. However, the first layer on a cuboid measuring 5 x 1 x 1 also requires twenty-two cubes; similarly the first layer on cuboids measuring 5 x 3 x 1, 7 x 2 x 1, and 11 x 1 x 1 all contain forty-six cubes. We shall define C(n) to represent the number of cuboids that contain n cubes in one of its layers. So C(22) = 2, C(46) = 4, C(78) = 5, and C(118) = 8. It turns out that 154 is the least value of n for which C(n) = 10. Find the least value of n for which C(n) = 1000.
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# --hints--
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`euler126()` should return 18522.
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```js
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assert.strictEqual(euler126(), 18522);
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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 euler126() {
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return true;
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}
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euler126();
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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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