66 lines
1.6 KiB
Markdown
66 lines
1.6 KiB
Markdown
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---
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id: 5900f3b61000cf542c50fec9
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title: 'Problem 74: Digit factorial chains'
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challengeType: 5
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forumTopicId: 302187
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dashedName: problem-74-digit-factorial-chains
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---
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# --description--
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The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
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<div style='margin-left: 4em;'>1! + 4! + 5! = 1 + 24 + 120 = 145</div>
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Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:
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<div style='margin-left: 4em;'>
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169 → 363601 → 1454 → 169<br>
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871 → 45361 → 871<br>
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872 → 45362 → 872<br>
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</div>
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It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
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<div style='margin-left: 4em;'>
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69 → 363600 → 1454 → 169 → 363601 (→ 1454)<br>
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78 → 45360 → 871 → 45361 (→ 871)<br>
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540 → 145 (→ 145)<br>
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</div>
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Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.
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How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
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# --hints--
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`digitFactorialChains()` should return a number.
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```js
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assert(typeof digitFactorialChains() === 'number');
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```
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`digitFactorialChains()` should return 402.
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```js
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assert.strictEqual(digitFactorialChains(), 402);
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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 digitFactorialChains() {
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return true;
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}
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digitFactorialChains();
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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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