[net.puzzle] time puzzle

dash@fluke.UUCP (11/01/83)

time puzzle

i thought of this puzzle but could not figure out an easy answer -- the
answer is from dick davison, university of washington physics department.

question:

all 3 hands on my watch are together at 12:00:00.  sometime around 1:05
they may be together again... at least the hour and minute hands might
be... but it wouldn't be exactly 1:05, since the hour hand would be
slightly past the '1' at that time.

so, are the hands all together at some time around 1:05?  if so, when?

answer -- rot13:

pbafvqre gur ubhe naq zvahgr unaqf.  gur zvahgr unaq znxrf gjryir
eribyhgvbaf va gjryir ubhef, juvyr gur ubhe unaq znxrf bar, fb gur zvahgr
unaq cnffrf gur ubhe unaq ryrira gvzrf va gjryir ubhef.

guhf gur zvahgr unaq pngpurf hc gb gur ubhe unaq rirel gjryir ryriraguf bs
na ubhe, fb gur unaqf ner gbtrgure bar ryriragu bs na ubhe nsgre bar
b'pybpx.

fvapr gurer ner fvkgl zvahgrf va na ubhe, naq fvkgl frpbaqf va n zvahgr,
lbh pna pbaivapr lbhefrys gung gur frpbaq unaq vf gurer ng gur fnzr gvzr
gbb. guvf frys-pbaivapvat vf yrsg nf na rkrepvfr gb gur fghqrag.

stekas@houxy.UUCP (J.STEKAS) (11/02/83)

Elegant though it may be Mike Dash's arguement is wrong.
So as not to spoil the fun I give the arguement rot13.


 Gur frpbaq unaq jvyy abg pbvapvqr jvgu gur zvahr unaq orpnhfr
vg jvyy unir geniryyrq 60k nf sne nf gur zvahgr unaq, be
frira-uhaqerq gjragl ryriraguf. Fhogenpgvat bss gur pbzcyrgr
eribyhgvbaf, gur frpbaq unaq vf qvfcynprq svir ryriraguf nf
pbzcnerq gb bar ryriragu sbe gur zvahgr unaq.
Va snpg gur svefg gvzr nyy 3 unaqf jvyy yvar hc ntnva vf 12:00
jura gur zvahgr qvfcynprzrag vf ryrira/ryriraguf naq gur
frpbaq qvfcynprzrag vf svsgl-svir ryriraguf.

                              Jim

usenet@abnjh.UUCP (usenet) (11/02/83)

I was unable to convince myself that the second hand was at the same
place as the hour and minute hand when the latter two coincided at
about 1:05.  In fact, I convinced myself that it was not there as
follows: (ROT13)

Gur ubhe naq zvahgr unaq pbvapvqr ng 1 ubhe, 5 zvahgrf naq 5/11
zvahgrf nsgre abba.  5/11 zvahgrf vf 27.2727.... frpbaqf.  Guhf jura
gur ubhe unaq naq zvahgr unaq pbvapvqr gurl jvyy or arne(naq fyvtugyl
nsgre) gur 1, ohg gur frpbaq unaq jvyy or arne (naq fyvtugyl orsber)
gur 6.

Ba gur bgure unaq, lbh znl unir n jngpu jurer gur unaqf pyvpx bire ol 6
qrterr vaperzragf vafgrnq bs zbivat fzbbguyl.  Gurer jvyy or n crevbq
bs bar shyy frpbaq sbyybjvat 1:05:05 qhevat juvpu gurl pbvapvqr.  Gur
cebbs bs guvf vf yrsg gb gur ernqre nf na rkrepvfr.

Dhrfgvba: Jung bgure gvzrf qbrf guvf bpphe?  Ner gurer nal jurer nyy
guerr unaqf pbvapvqr haqre gur pbagvahbhf zbgvba nffhzcgvba? (orfvqrf
abba naq zvqavtug, bs pbhefr.) Ng jung cbvag qbrf gur qvfpergr zbgvba
nffhzcgvba fgneg gb snvy gb cebqhpr gevcyr pbvapvqrapr.

jar@unc.UUCP (Jeff Raynes) (11/02/83)

The answer to the time puzzle was intriguing, but dead wrong.  The exact
time when the hour and minute hands line up is 5 and 5/11 minutes after
1.  5/11 of a minute is about 27 seconds, so the second hand will be
between the 5 and the 6 at that time.  All 3 hands will align only once
every 12 hours.  To see this, notice that the minute and hour hand are
aligned 11 times around the dial per cycle, while the second and minute
hands are aligned 59 times in their respective cycle.  11 and 59 being
relatively prime guarantees here that there will be no meetings except
at the trivial times of noon and midnight.

Jeff Raynes
{duke,mcnc,ulysses}!unc!jar

dmmartindale@watcgl.UUCP (Dave Martindale) (11/06/83)

	thus the minute hand catches up to the hour hand every twelve
	elevenths of an hour, so the hands are together one eleventh of
	an hour after one o'clock.

	since there are sixty minutes in an hour, and sixty seconds in
	a minute, you can convince yourself that the second hand is
	there at the same time too. this self-convincing is left as an
	exercise to the student.

Huh?  What does the fact that there are 60 minutes in an hour and 60
seconds in a minute have to do with it?  As the minute hand moves through
60 minutes, the hour hand moves through 1/12 of a revolution.  As the
second hand moves through 60 seconds, the minute hand moves through 1/60
of a revolution.  I fail to see how one is supposed to apply to the other.

And, in fact, the answer is wrong.  The hour and minute hands line up
at 12/11 hour after 12:00, which is 1:05:27.  The second hand is nowhere
near the hour and minute hands.

	Dave Martindale