A181874 Minute hand closest to hour hand on analog quartz clock. Best approximation for seconds.

0, 27, 55, 22, 49, 16, 44, 11, 38, 5, 33

Offset: 0

Author

Wolfdieter Lang, Jan 21 2011

Keywords

• nonn
• fini
• easy

Comments

At which a.m. times h:m:s is the minute hand closest to the hour hand on an analog quartz clock (discrete seconds)? For an analog clock with continuous seconds this is the overlap problem nr. 43 of the quoted Loyd/Gardner book where also the solution is given (pp. 41-2, solution pp. 180-1 in the German version). See A183032.

Examples

			The eleven times are:
00:00:00, 01:05:27, 02:10:55, 03:16:22,
04:21:49, 05:27:16, 06:32:44, 07:38:11,
08:43:38, 09:49:05, 10:54:33.
The next time would be 12:00:00
		

References

• 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.

Crossrefs

Cf.: A178181, A183032, A183033.

Formula

a(n) gives the second for the (a.m.) hour h=n = 0,1,2,...,10, when the minute hand is closest to the hour hand on an analog quartz clock (discrete seconds), provided the minute is A178181(n).

a(n)= round((300/11)*n) (mod 60), n=0..10. See the solution in the Loyd book with (27+3/11)s = 300/11 s.