79d9012432
* fix(curriculum): tests quotes * fix(curriculum): fill seed-teardown * fix(curriculum): fix tests and remove unneeded seed-teardown
81 lines
1.5 KiB
Markdown
81 lines
1.5 KiB
Markdown
---
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id: 5900f40c1000cf542c50ff1e
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challengeType: 5
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title: 'Problem 159: Digital root sums of factorisations'
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---
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## Description
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<section id='description'>
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A composite number can be factored many different ways.
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For instance, not including multiplication by one, 24 can be factored in 7 distinct ways:
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24 = 2x2x2x3
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24 = 2x3x4
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24 = 2x2x6
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24 = 4x6
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24 = 3x8
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24 = 2x12
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24 = 24
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Recall that the digital root of a number, in base 10, is found by adding together the digits of that number,
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and repeating that process until a number is arrived at that is less than 10.
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Thus the digital root of 467 is 8.
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We shall call a Digital Root Sum (DRS) the sum of the digital roots of the individual factors of our number.
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The chart below demonstrates all of the DRS values for 24.
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FactorisationDigital Root Sum2x2x2x3
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92x3x4
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92x2x6
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104x6
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103x8
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112x12
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524
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6The maximum Digital Root Sum of 24 is 11.
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The function mdrs(n) gives the maximum Digital Root Sum of n. So mdrs(24)=11.
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Find ∑mdrs(n) for 1 < n < 1,000,000.
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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>euler159()</code> should return 14489159.
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testString: assert.strictEqual(euler159(), 14489159, '<code>euler159()</code> should return 14489159.');
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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 euler159() {
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// Good luck!
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return true;
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}
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euler159();
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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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