69 lines
1.7 KiB
Markdown
69 lines
1.7 KiB
Markdown
---
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id: 5900f40c1000cf542c50ff1e
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title: 'Problem 159: Digital root sums of factorisations'
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challengeType: 5
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forumTopicId: 301790
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dashedName: problem-159-digital-root-sums-of-factorisations
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---
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# --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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$$\begin{align}
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& 24 = 2 \times 2 \times 2 \times 3\\\\
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& 24 = 2 \times 3 \times 4 \\\\
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& 24 = 2 \times 2 \times 6 \\\\
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& 24 = 4 \times 6 \\\\
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& 24 = 3 \times 8 \\\\
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& 24 = 2 \times 12 \\\\
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& 24 = 24
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\end{align}$$
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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, and repeating that process until a number arrives at less than 10. 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. The chart below demonstrates all of the DRS values for 24.
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| Factorisation | Digital Root Sum |
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|---------------|------------------|
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| 2x2x2x3 | 9 |
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| 2x3x4 | 9 |
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| 2x2x6 | 10 |
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| 4x6 | 10 |
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| 3x8 | 11 |
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| 2x12 | 5 |
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| 24 | 6 |
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The maximum Digital Root Sum of 24 is 11. The function $mdrs(n)$ gives the maximum Digital Root Sum of $n$. So $mdrs(24) = 11$.
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Find $\sum{mdrs(n)}$ for $1 < n < 1,000,000$.
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# --hints--
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`euler159()` should return `14489159`.
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```js
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assert.strictEqual(euler159(), 14489159);
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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 euler159() {
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return true;
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}
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euler159();
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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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