The sun. [volume] (New York [N.Y.]) 1833-1916, 1910-06-12


matter whether the second hand bsats
halves or quarters or nfths. e. there
must be a time az which Il Il jumping
from one half second 10 the other. should
| this fraction he ESSENTIAL 10 the solution.
Strange 70 nay, not a single solver
pointed this out. although several implied
L in their statemsnt Of the reasons that
prevented the solution Of the problem.
4 large number Of interesting letters
have come "a hand about this clock puEgle
each giving In different way the scientific
reasons for concluding that there 10 no
| time az which The three hands, hour.
minute and sweep second, would BE-
exactly 40 degrees apart " they were
properly adjusted.
Morrison Z. ColyeF AVS: IL the second
hand Il In 40 positions during one revO-
luton there are 10 times la the twelve
hours when the hour hand could be 100
degrees distant from d. These are on
the hour and 9. n, ~. -. 80. g. a. ~
and 81 minutes after the hour
when the hour hand 10 At q point
| indicating an even minute a. all these are,
the second hand would have 20 be a. ~,
and a. i20 degrees from n would he either
4 OF the minute hand could not Be at u
minutes before or after the hour
2. n A puts the same idea IN another
NANt ~ AllH aENuAu MAAu WAAnUN NN0
beats q second Il stops at either the minute
or the half minute, and 10 BE- 40 degrees
from u the hour hand must be az some
minute or half minute space. A. this
hour hand moves over one minutes space
In u minutes and half a minutes space
IN minutes, Il cannot he 40 degrees
from tho second hsEd except o. the exact
minute % acme hour. the hOurs available
beng lands
These are fair Examples % the mistake
in assuming that tie second hand IL never
passing from one beat 20 the next.
AlgeYnon Bray sAys; When the hour
and minute hands are 10 degrees apart
the minute hand must point 70 one Of
the angles Of a regular hendecagon one
% whose angles 10 AZ the top OF the clock.
Il IA evident that Al the same time the
second hand also points a. nearly 70 OD9
Of these angles a. ita isrky motion will
permit
The distance between the minute hand
and the second hand az these times may b.
approximately any number % elevenths
81 the circumference, from 70 In either
direction. but cannot be nearer 20 100
degrees than 100 degrees 10 minutes n
seconds. which will he very nearly the
distance az houu minutes n seconds
n. d. ". says: Beginning az u O'Clock
the minute hand gains on the hour hand
every "a ell minutes. while the second
hand gains on the minute hand az the rate
Of 10 degrees every 20 Soths Of a minute
Find the lowest common multiple Of
thess two numbers. =. minutes. or
7sO minut - when reduced which II
every four hours But a. and O. clock.
when the hour and minute hands are
placed correctly. the second hand has
gained not only q multiple Of 100 degrees
but also a multiple Of 3oO. which makes
IL coincide with the minute hand
Hence this second hand 10 never 40
degrees from both the others when they
are I'D degrees from each other
Roy y Lynd sAys. AS the distance the
minute hand travels less the distance ths
hour hand travels will be II times a. far
a. the hour hand travels. the three hands
can never be I'D degrees apart We
cannot divide twenty plus a multiple
Of Ave minutes by eleven and get a result
which will be a multiple Of half a second
others Who correctly argued out that
the solution sought was imDoasib bic were
y. D. ", John Beatiie. Morrison &
Coiyer. o. T. Hand. p NJ. A.. AlgernOn
Bray. 4. y Bogart, Roy y. Lynd and
J l. Lazarus
A THIcET CHESS PROBLEM
No ono came anywhere near solving
chess problem No. - They Ohered al
kinds % defencea 20 the move Of NJ Obs.
such a. RIP. r kt1 ch. r X 90 and
all sorts % kinks after tho key. but not
one Of them ever guessed his heoom-
ing . bishop
II white nov continues the proposed
attack by pinning the rock With B QS.
black n stalemated
Given the hey move making the P=B.
and there 10 no way for white 20 mate In
three. because there h always the check
with the black rock a. OBS
II should be observed that this does not
prove the problem 10 b. unaOund. hut
only Shove that the key move offered by
those who thought they had solved u.
kt-QB9. was not the correct one. Per
haps some % the cracks can discover the
proper key move which would have 80
cured the desired mate In threei
Some players with the advantage q
the exchange on their side and none the I
worst % the position fTitter away valua-
bic time and opportunity by not seeing |
clearly what should be done 20 bring |
matters 10 a head a. once Take the !
following position a. an example
CHEss PROBLEM No. -
Biack.