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A183033 Minute with hour hand overlap problem on analog clock. Fractions of seconds.

%I A183033 #23 Mar 15 2015 10:36:09
%S A183033 0,3,6,9,1,4,7,10,2,5,8
%N A183033 Minute with hour hand overlap problem on analog clock. Fractions of seconds.
%C A183033 At which a.m. times h:m:s (with fractions of seconds) does the minute hand overlap the hour hand on an analog clock? This is problem 43 of the referenced Loyd/Gardner book, which also gives the solution (pp. 41-42, solution pp. 180-181 in the German version).
%D A183033 Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.
%D A183033 Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover, 1959.
%F A183033 a(n)/11 gives the fraction of the 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 full second is A183032(n). See the eleven times given in EXAMPLE.
%F A183033 a(n) = floor((300*n)/11) (mod 12), n=0..10. (See the Mathematica code given by _Robert G. Wilson v_, and also the solution in Loyd's book with (27 + 3/11)s = 300/11 s.)
%e A183033 The eleven overlap times are:
%e A183033 00:00:00 plus  0/11 s,
%e A183033 01:05:27 plus  3/11 s,
%e A183033 02:10:54 plus  6/11 s,
%e A183033 03:16:21 plus  9/11 s,
%e A183033 04:21:49 plus  1/11 s,
%e A183033 05:27:16 plus  4/11 s,
%e A183033 06:32:43 plus  7/11 s,
%e A183033 07:38:10 plus 10/11 s,
%e A183033 08:43:38 plus  2/11 s,
%e A183033 09:49:05 plus  5/11 s,
%e A183033 10:54:32 plus  8/11 s.
%e A183033 The next time would be 12:00:00.
%t A183033 Table[ Mod[ Floor[300/11 n], 12], {n, 0, 10}]
%K A183033 nonn,fini,full,easy
%O A183033 0,2
%A A183033 _Wolfdieter Lang_, Dec 20 2010