The times. [volume] (Richmond, Va.) 1890-1903, 1890-01-28

has charge OF that department is very
clever. and we think he is playing a little
with his inquisitor
The original question sent to us forty
years ago and involving the same point
submitted to The Eagle was, how to find
the product OF SO los. Id 81. multi
/ piled by itself. OF course il the parts Of
the pounds were stated as fractions. and
the pounds as whole numbers. then
10 9j9-060ths could be multiplied by
itself But money Of account has not
two dimensions. il table is 4 feet wide
and 4 feet long. then 4x4-1G feet
and we have the number Of squar,
feet on the surface. Five times five
pounds are e2j, but five pounds time.
FIVE pounds is unmeaning. as money
does not measure itself in that fashion.
Twice two children are four. children
but twice children two children has No
meaning. SO nineteen pounds, nineteen
shillings, eleven pence, three farthings
times nineteen pounds, nineteen shill
ings, eleven pence, three farthings." i,
utter nonsense.
TROUBLESOME MILLS.
The next puzzle on the list, and one
which comes the oftencst TO our desk, in
some form Of a problem which proposes
to divide a whole sum into fractions that
together did not make the dividend
The original OF this in our columns was
an answer to an actual case where
man in his will had devised one-third.
one-fourth. one-ffth and one-sixth OF
his property respectively 10 his fom
children. supposing that he had thus de
vised the whole Of his estate. The frac
tons mentioned only made nineteen.
twentieths Of a whole number. This il
easily seen il they are reduced to com.
mon denOminator. One-third is twenty
sixtieths, one-fourth is fifteen-sixtieths
one-fifth is twelve-sixtieths, and one
sixth is ten-sixtieths, which together
make but ffty-seven sixtieths, leaving
lhree-sxtieths (or l-20th) to make NJ
the whole number.
This puzzle reappears in some form
every few days the wear round. 1t is
answered on the same principle involved
in the Interpretation Of the Arabs will
He had fifteen horses and four sons. II,
devised his estate, giving one son a half
another quarter, another an eighth
and the last 4 sixteenth. They found j.
impossible 20 agree on a division. Tn,
eldest son insisted that rs seven horses
would not be half Of fifteen he SHOULD
have eight: but the other sons objected
and as neither onc-half, One-fOurth, one.
eighth nor Onc-sixtccnth would give
either son an even lot they had fierce
dispute over the division. A venerable
sheik rode up just rs the quarrel was at it.
height, and to compose their difference
dismounted and generously offered e
add his mare 10 the fifteen belonging {,
the estate, agreeing that each should
take his allotted share from the Who'll,
sixteen, only STIMULATING that his should
be the last selected The addition made
an easy solution of the difficulty. The
first then took eight as his half OF
the sixteen, the next tool, four for hi,
quarter, the third took two for his
eighth, and the fourth took ono for his
sixteenth. As this made but fifteen the
sheik mounted his mare and rode away
The Arab boys regarded it as a miracle
and exclaimed that Allah had given q
horse TO the sheik for his generous inter
ference. In spite Of this oft told tale tn,
problem still survives and annually puz
zles hundreds Of our countrymen.
JUGGLING WITH FRACTIONS.
a more recent problem which we have
already answered several times, but
which is repeated every week from some
quarter. is the division Of one fraction
by another. The original question which !
we answered several years ago was
what is the quotient Of two-thirds di |
vided by one-half?" The unthinking per
son would say that as the half Of two |
thirds is one-third, this must be the solu. |
ton Of the problem, but Daboll will east
" refute IT, The quotient of % divided |
by is Is; that is, I will go in 2-3 one
and one-third times. The last form OF |
the problem, received as we write this |
is to find the quotient Of l divided by I /
two partners in leading banking house. |
having disputed, as they say, all one day i
over the result. the senior maintaining |
that divided by is !. and defying any
one to refute it, We answer that when
1 is divided by the quotient is ?; that
is, ! will be found two times in /. If
be divided by I the answer is 10; that is
there are twelve halves in six. We
should beg pardon Of our readers for re-
pcating these demonstrations if it were
not for the character and magnitude OF
the disputes which occur every day con
cerning them.
We have reserved for the last Of the
puzzles the century question, which will
never be laid TO rest, we believe, as long
As the would stands. We printed $50
proofs Of a former answer, and they
nave all been distributed to parties who
nave Quarreled over it. A writer whose
initials are r. L. b. asks rs in letter
ust 10 hand whether the Twentieth |
century begins with Jan. !. 1900. or Jan
1901. and declares that of all whom he
Addressed for an answer about half took
ne date and half the other. There
hould DO no question about 1t. ms
entury ends with the last moment OF
he wear 1900. and the next begins with
an. /, 1901. IL
The middle grows out of the fixed
iea which some people have that the
eckonine of time begins with a cipher
nd that one is counted when the hour,
ay. month or year has closed; whereas
n the counting of time begins with one
nd at the end of the first period two
eoins 10 count. Thus. when child Is
on. he enters on his first day OF the
rst month Of the first year OF his HE
lis ten years are finished. not when ne
nters in his tenth year, but at It's close
nd his hundred years are compieted'
OF when the hundredth year Is begun
at ended. When we write lsVV we
ave begun the last year of the century, ,
ot ended it. The centuries 40 NOT
III n f0o 900 hut with i, lOl,