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Message: [QUOTE="Hans Fugal, post: 4525280"] What you have described here is the halting problem. Good luck with that. And what stops it from being a 1x10^50 length period, or any arbitrary length? And what the quiz neglected to mention is that there is an easy test for unhappy number, which the mathworld page enumerates: Iterating this sum-of-squared-digits map always eventually reaches one of the 10 numbers 0, 1, 4, 16, 20, 37, 42, 58, 89, or 145 (Sloane's A039943; Porges 1945). So if you hit one of those unhappy numbers you know you're in an unhappy loop. [/QUOTE]