49 lines
975 B
Markdown
49 lines
975 B
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 ∑ sg(i) for 1 ≤ i ≤ 20 is 156.
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What is ∑ sg(i) for 1 ≤ i ≤ 150?
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# --hints--
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`euler254()` should return 8184523820510.
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```js
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assert.strictEqual(euler254(), 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 euler254() {
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return true;
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}
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euler254();
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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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