OFFSET
0,2
COMMENTS
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.
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.
FORMULA
a(n) = floor(300*n/11) (mod 60), n=0..10.
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.
MATHEMATICA
Table[ Floor@ Mod[300/11 n, 60], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,fini,full,easy
AUTHOR
Wolfdieter Lang, Dec 20 2010
STATUS
approved