A178181 Minute with hour hand overlap problem on analog clock.

0, 5, 10, 16, 21, 27, 32, 38, 43, 49, 54

Offset

0,2

Comments

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).

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 Publications, NY, 1959.

Links

Table of n, a(n) for n=0..10.

Formula

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.

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.

Note that 60/11 m = (5+5/11)m.

See the eleven times given in EXAMPLE.

a(n) = a(n-1)+a(n-2)-a(n-3) for n=4..10. - Colin Barker, Aug 19 2014

a(n) = (-3-(-1)^n+22*n)/4 for n=1..10. - Colin Barker, Aug 19 2014

Example

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.

Crossrefs

Cf. A183032 (seconds). A181874.

Sequence in context: A313893 A313894 A276853 * A277645 A075003 A313895

Adjacent sequences: A178178 A178179 A178180 * A178182 A178183 A178184

Keyword

nonn,easy,fini,full

Author

Wolfdieter Lang, Dec 20 2010

Status

approved