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www/statics/euler/Euler_Problem-074_description.md

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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:
+
+~~~
+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?