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id	title	challengeType	forumTopicId	dashedName
5900f3b61000cf542c50fec9	Problem 74: Digit factorial chains	5	302187	problem-74-digit-factorial-chains

--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,

69 → 363600 → 1454 → 169 → 363601 (→ 1454)
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?

--hints--

digitFactorialChains() should return a number.

assert(typeof digitFactorialChains() === 'number');

digitFactorialChains() should return 402.

assert.strictEqual(digitFactorialChains(), 402);

--seed--

--seed-contents--

function digitFactorialChains() {

  return true;
}

digitFactorialChains();

--solutions--

// solution required

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