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

0, 3, 6, 9, 1, 4, 7, 10, 2, 5, 8

Offset: 0

Author

Wolfdieter Lang, Dec 20 2010

Keywords

• nonn
• fini
• full
• easy

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 referenced Loyd/Gardner book, which also gives the solution (pp. 41-42, solution pp. 180-181 in the German version).

Examples

			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.
		

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.

Programs

Mathematica

Table[ Mod[ Floor[300/11 n], 12], {n, 0, 10}]

Formula

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.

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.)