27 lines
875 B
Markdown
27 lines
875 B
Markdown
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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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~~~
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1! + 4! + 5! = 1 + 24 + 120 = 145
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~~~
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Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169;
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it turns out that there are only three such loops that exist:
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~~~
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169 -> 363601 -> 1454 -> 169
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871 -> 45361 -> 871
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872 -> 45362 -> 872
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~~~
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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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~~~
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69 -> 363600 -> 1454 -> 169 -> 363601 (-> 1454)
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78 -> 45360 -> 871 -> 45361 (-> 871)
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540 -> 145 (-> 145)
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~~~
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Starting with 69 produces a chain of five non-repeating terms,
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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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