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Sep 26 at 2:35 vote accept Will.Octagon.Gibson
Sep 25 at 1:08 comment added HarryH This is supposed to be an answer. The question stated: "A 24-hour digital clock occasionally shows times that are palindromes such as 0:34:30, 21:33:12, and 1:20:21, if we ignore the colons. What is the smallest interval between two such times?" "two such times", that means 'on the display', not 'between two nearest possible moments that you look at the display'. And to add pedantry to injury: comments to other answers should be posted in the comment sections of those answers.
Sep 24 at 19:46 comment added Don Hatch @Brian wrote "Were I to present this puzzle to others, I'd probably rot13(gjrnx gur jbeqvat gb znxr gur pbeerpgarff bs guvf nafjre zber qrsvavgvir)" Pshaw! This played out exactly how it should have. (1) People understood the question as intended and found the intended answer, then (2) Nuclear Hoagie thought outside of the box and found an even better answer, then (3) you thought even further outside the box (in your subsequent observation Rot13(Vs lbh qb abg pbafvqre NN:OO:PP.100 naq NN.OO:PP.200 gb or qvfgvapg gvzrf...)) and found one even better (well, maybe) than that.
Sep 24 at 14:12 comment added Nuclear Hoagie @Brian Yes, there are an infinite amount of distinct times occurring for each clock reading. Why wouldn't you consider now and 0.1s from now to be different times even if they occur during the same second? Doing so doesn't help you find any closer palindromes, though - the clock can only read seconds. There are no palindromes separated by 0.1s, the fractional seconds aren't part of the display (but that doesn't mean we can only read the clock at whole-second times).
Sep 23 at 21:26 comment added Brian Rot13(Vs lbh qb abg pbafvqre NN:OO:PP.100 naq NN.OO:PP.200 gb or qvfgvapg gvzrf, gura lbhe nafjre srryf n ovg zrffl. Vs lbh qb pbafvqre gubfr gb or qvfgvapg gvzrf, gura nethnoyl bar pna qb fvtavsvpnagyl orggre guna lbhe nafjre (r.t., zl rknzcyr vf 100zf).)
Sep 23 at 21:03 comment added Nuclear Hoagie @Brian I agree the wording could be slightly more explicit. But I would find it odd that one could look at the clock for less time than "the smallest interval between two palindromic times", and still see two different palindromic times.
Sep 23 at 19:31 comment added Brian +1 for a brilliant solution, though it's correctness is debatable. rot13(Gur dhrfgvba nfxf gur "vagreiny orgjrra gjb fhpu gvzrf." Lbh vagrecerggrq guvf nf, "ubj zhpu gvzr cnffrq sebz NN:OO:PP gb QQ:RR:SS?" Ubjrire, n zber qverpg vagrecergngvba jbhyq or "jung vf gur qvssrerapr orgjrra NN:OO:PP naq QQ:RR:SS." Gur ynggre vf vaqrcraqrag bs npghny gvzr naq guhf vf rknpgyl gjb frpbaqf). Personally, I think this solution is more fun. Were I to present this puzzle to others, I'd probably rot13(gjrnx gur jbeqvat gb znxr gur pbeerpgarff bs guvf nafjre zber qrsvavgvir).
Sep 23 at 17:32 history edited Nuclear Hoagie CC BY-SA 4.0
added 99 characters in body
Sep 23 at 17:20 history answered Nuclear Hoagie CC BY-SA 4.0