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Co-authored-by: Oliver Eyton-Williams <ojeytonwilliams@gmail.com> Co-authored-by: Kristofer Koishigawa <scissorsneedfoodtoo@gmail.com> Co-authored-by: Beau Carnes <beaucarnes@gmail.com>
1.8 KiB
1.8 KiB
id, challengeType, isHidden, title, forumTopicId
| id | challengeType | isHidden | title | forumTopicId |
|---|---|---|---|---|
| 5900f3b61000cf542c50fec9 | 5 | false | Problem 74: Digit factorial chains | 302187 |
Description
The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:
1! + 4! + 5! = 1 + 24 + 120 = 145
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:
169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872
It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
871 → 45361 → 871
872 → 45362 → 872
69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)
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.
How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?
Instructions
Tests
tests:
- text: <code>digitFactorialChains()</code> should return a number.
testString: assert(typeof digitFactorialChains() === 'number');
- text: <code>digitFactorialChains()</code> should return 402.
testString: assert.strictEqual(digitFactorialChains(), 402);
Challenge Seed
function digitFactorialChains() {
// Good luck!
return true;
}
digitFactorialChains();
Solution
// solution required