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A183032
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Seconds (rounded down) at which the minute hand overlaps with hour hand on the analog clock.
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4
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0, 27, 54, 21, 49, 16, 43, 10, 38, 5, 32
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OFFSET
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0,2
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COMMENTS
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At which a.m. times h:m:s (with fractions of seconds) does the minute hand overlap with the hour hand on an analog clock? This is problem 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version).
a(n) gives the full second for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand overlaps the hour hand on an analog clock, provided the minute is A178181(n), and the fraction of the second is A183033(n)/11.
For the same problem on an analog quartz clock (discrete seconds) the best approximation with rounded seconds is given in A181874.
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REFERENCES
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Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.
Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover, 1959.
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LINKS
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FORMULA
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a(n) = floor(300*n/11) (mod 60), n=0..10.
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EXAMPLE
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The eleven overlap times are:
00:00:00 plus 0/11 s, 01:05:27 plus 3/11 s;
02:10:54 plus 6/11 s, 03:16:21 plus 9/11 s,
04:21:49 plus 1/11 s, 05:27:16 plus 4/11 s,
06:32:43 plus 7/11 s, 07:38:10 plus 10/11 s,
08:43:38 plus 2/11 s, 09:49:05 plus 5/11 s,
10:54:32 plus 8/11 s.
The next time would be 12:00:00.
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MATHEMATICA
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Table[ Floor@ Mod[300/11 n, 60], {n, 0, 10}]
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CROSSREFS
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KEYWORD
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nonn,fini,full,easy
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AUTHOR
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STATUS
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approved
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