49 lines
1.0 KiB
Markdown
49 lines
1.0 KiB
Markdown
---
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id: 5900f46b1000cf542c50ff7d
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title: 'Problem 254: Sums of Digit Factorials'
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challengeType: 5
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forumTopicId: 301902
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dashedName: problem-254-sums-of-digit-factorials
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---
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# --description--
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Define $f(n)$ as the sum of the factorials of the digits of $n$. For example, $f(342) = 3! + 4! + 2! = 32$.
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Define $sf(n)$ as the sum of the digits of $f(n)$. So $sf(342) = 3 + 2 = 5$.
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Define $g(i)$ to be the smallest positive integer $n$ such that $sf(n) = i$. Though $sf(342)$ is 5, $sf(25)$ is also 5, and it can be verified that $g(5)$ is 25.
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Define $sg(i)$ as the sum of the digits of $g(i)$. So $sg(5) = 2 + 5 = 7$.
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Further, it can be verified that $g(20)$ is 267 and $\sum sg(i)$ for $1 ≤ i ≤ 20$ is 156.
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What is $\sum sg(i)$ for $1 ≤ i ≤ 150$?
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# --hints--
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`sumsOfDigitFactorials()` should return `8184523820510`.
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```js
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assert.strictEqual(sumsOfDigitFactorials(), 8184523820510);
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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 sumsOfDigitFactorials() {
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return true;
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}
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sumsOfDigitFactorials();
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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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