Juniata sentinel and Republican. [volume] (Mifflintown, Juniata County, Pa.) 1873-1955, 1890-11-19
: SOME OLD PUZZLES.
Th.y BEEN to Be Invested With Vigorous
Immortality.
Revival Of conundruns Supposed TO Have
Been satisfactorily Solved Fifty Years Ago
Problems IN which interested People
VII Persist in Radical Disagreement

Immortality. says the New York Jour-
nal OF Commerce. No matter how
often the solution is printed or how
widely an exhaustive answer Is pub
lished the question comes up again,
before the ink is fairly dried. to the
lip Of hundreds who have not seen the
reply or who either can not under
stand il or will not accept it
The original question sent to US forty
years ugo was how TO find the product
OF fl9 l9s lid 81 multiplied by itself
Oh course if the parts of the pound 5
were stated as fractions, and the
pounds as whole numbers, then l9-
s59yo0ths could De multiplied by it
self But money OF account has not
two Dimensions If q table is four
feet wide and four feet long,
then four times four equal six
teen feet, and We have the number of
square feet on the surface Five times
Eve pounds are E25, but five pounds
time i've pounds is unmeaning. as
money does not measure itself in that
fashion Twice two children are four
children, but twice children two. child
ron has no meaning. So nineteen
pounds, nineteen shillings, eleven
pence, three farthings times nineteen
pounds, nineteen shillings, eleven
pence, three fsrthings," IS utter nom
sense.
The next puzzle on the list, and one
which comes the oftenest TO our desk,
In some form of a problem which pro-
poses 10 divide whole sum into frac-
tions that together did not make the
dividend The original Of this In our
columns was an answer to an actual
case where 3 man in his will had divis-
ed one-third. one-fourth, one-6lth, and
one-sixth of his property respectively
10 his four children, supposing that he
had thus devised the whole OF his
estate. The fractions mentioned only
made nineteen twentieths OF 8 whole
number This is easily seen IL they
are reduced to a common denominator.
One-third is twenty-sixtieths, one
fourth is fifteen -sixt!eths, one-fifth Is
twelve-sixtIeths. and one-sixth Is ten
siItieths, which together make but
tfty-seyen siXtieths, leaving three
whole number.
This puzzle resppeRrs IN some form
every few days the year round. It is
answered on the same principle involv-
ed in the Interpretation OF the Arabs
will He hai fifteen horses and four
cons He devised his estate. giving
one son half, another quarter, an
other an eighth, and the last a six
teenth. They found It impossible to
agree on a division. The eldest son
insisted that as seven horses would not
be half Of fifteen horses he should have
eight, but the other sons objected, and
as neither one-half, oue-quarter, one
eighth, or oue-siNteenth would give
either son an even lot they had a fierce
dispute over the division. A venerable
sheik rode up Just as the quarrel was
at itz height and to compose their
differences dIsmOuuted aud generously
offered TO add his mare TO the fifteen
belonging to the estate, agreeing that
each should take his allotted ehare
from the whole sixteen. only stipulat-
ing 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 took four for his quarter, the
the third took two for his eighth, and
the fourth took one for his sixteenth.
AS this made but fifteen the sheik
mounted his mare and rode away. The
Arab boys regarded it as e miracle,
and exclaimed that Allah had given a
horse 10 the shsik for his generous in
terfereuce- In spite or this oft-told
tale the problem still survives and au-
nually puzzlce hundreds of our coua-
tTymen.
a more recent problem, which va
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 divided By one-halfsr
The uuthluking person would say that
as the half OF twO-thirds /. one-third,
| This must De the solution of the pro-
blem, but DaboIl will easily refute il
The quotient Of : divided by is II
that il, ! will go in Z one and one-
third times The last form of the
! prOp!en is 20 find the quotient of 1
| divided by J. Two partners in a lead
| ing banking house, having disputed,
as they say, all one day over the re-
result the senior mainting that l
divided by is :, and defying any one
/ to refute il We answer that when l
Is divided by ! the quotient Is 2; that
/ Is will be found 2 times in l. II 8
! be divided By the answer is y; that
[ Is, there are twelve halves in six. We
| should beg pardon of our readers for
/ repeating these demonstrations IL il
| were not for the character and magui-
tude OF the disputes which occur
every day concern ing them
We have reserved for the last OF the
/ puzzles the century question, which
/ will never be laid to rest We believe,
IS long as the world stands We
| printed 25O proofs OF a former answer.
aud they have all been distributed TO
/ parties who have quarreled over it
/ A writer asks US whether the twenti.
eth century begins with Jan l, 1900,
or Jan l, 1901, and declares that all
/ OF whom he addressed for an answer
about half took one date and hall
/ tuc oIner. Iuerc sIUuIvE YU-~
ton about it This century ends with
the last moment Of the year 1900,
and the next begins with Jan 1. 1901.
The muddle grows out OF the fixed
l idea which some people have that the
/ reckoning Of time begins with cipher
/ and one that's counted when the hour,
| day, month, or year has closed; where
/ as all the counting of time begins with
/ one, and at the end Of the first period
/ two begins to count Thus, when a
child is born no enters on his fist day
I OF the first month OF the first year o
his life. His ten years are finished.
not when he enters In his tenth year
but at its close; and his hundred year:
are completed, not when the hundredth
4 year Il begun, but ended When We
write 1900 We have begun the last yeal
I of the century, not ended it The cen
I turies do not begin with 0, loo, 200
/ but with i, 1Ol, 2Ol, and thus the
I twentieth century begins with 1901 a
the first moment of that year. The
I quoted date comes with the beginning 9
I not the close OF the twelve months
and therefore, while We quote the year
/ 1900 as we do every other year at il:
/ beginning, VIC must wait till il ends &c