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A178181 Minute with hour hand overlap problem on analog clock.

%I A178181 #26 Sep 23 2021 05:22:54
%S A178181 0,5,10,16,21,27,32,38,43,49,54
%N A178181 Minute with hour hand overlap problem on analog clock.
%C A178181 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 quoted Loyd/Gardner book (pp. 41-42, solution pp. 180-1 in the German version).
%D A178181 Sam Loyd, Mathematische Raetsel und Spiele, ausgewaehlt und herausgegeben von Martin Gardner, Dumont, Koeln, 1978, 3. Auflage 1997.
%D A178181 Sam Loyd, Mathematical puzzles, selected and edited by Martin Gardner, Dover Publications, NY, 1959.
%F A178181 a(n) gives the full minute 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 second is A183032(n) + A183033(n)/11.
%F A178181 a(n)= floor((720/11)*n) (mod 60), n=0..10. See the solution in Loyd's book with (65+5/11)m = 720/11 m.
%F A178181   Note that 60/11 m = (5+5/11)m.
%F A178181 See the eleven times given in EXAMPLE.
%F A178181 a(n) = a(n-1)+a(n-2)-a(n-3) for n=4..10. - _Colin Barker_, Aug 19 2014
%F A178181 a(n) = (-3-(-1)^n+22*n)/4 for n=1..10. - _Colin Barker_, Aug 19 2014
%e A178181 The eleven overlap times are:
%e A178181 00:00:00 plus 0/11 s, 01:05:27 plus 3/11 s;
%e A178181 02:10:54 plus 6/11 s, 03:16:21 plus 9/11 s,
%e A178181 04:21:49 plus 1/11 s, 05:27:16 plus 4/11 s,
%e A178181 06:32:43 plus 7/11 s, 07:38:10 plus 10/11 s,
%e A178181 08:43:38 plus 2/11 s, 09:49:05 plus 5/11 s,
%e A178181 10:54:32 plus 8/11 s.
%e A178181 The next time would be 12:00:00.
%Y A178181 Cf. A183032 (seconds). A181874.
%K A178181 nonn,easy,fini,full
%O A178181 0,2
%A A178181 _Wolfdieter Lang_, Dec 20 2010