New Ulm weekly review. [volume] (New Ulm, Minn.) 1878-1892, 1890-02-12
SOME OLD PUZZLES.
They Seem to Be Invested With Vigorous
Immortality.

1AlAu1 tc1lGys
Revival of Conundrums Supposed to Have
Been Satisfactorily Solved Fifty Years Ago
Problems in Which Interested People
Will Persist in Radical Disagreement.
There are certa in problems, chiefly
arithnletical embued with a vigorous
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
lips Of hundreds who have not seen the
reply or who either can not under
stand it or will not accept it.
The original question sent to us forty
years ago was how to find the product
of fl9 19s lid 81 multiplied by itself.
OF course if the parts of the pounds
were stated as fractions, and the
pounds as whole numbers, then 49,
Y5996Oths could be multiplied by it,
self. But money of account has not
two dimensions. II a 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
five pounds are f25, 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 child
rem has no meaning. So nineteen
pounds, nineteen shillings, eleven
pence, three farthings times nineteen
pounds, nineteen shillings, eleven
pence, three farthings,n is utter non
sense
The next puzzle on the list, and one
which comes. the oftenest to our desk,
in some form Of q problem which pro-
poses to divide a 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 man in his will had divis-
ed one-third, one-fourth, one-ffth, and
one-sixth of his property respectively
to his four children, supposing that he
had thus devised the whole of his
estate. The fractions mentioned only
made nineteen twentieths of whole
number. This is easily seen if they
are reduced to common Denomination.
One-third is twenty-sixtieths, one
fourth is ffteen-sixtieths, one-tifth is
twelve-siItieths, and one-sixth is ten
sixtieths, which together make but
fifty-seven sixtieths, leaving three
sixtieths Cor 1-2Oth to make up the
whole number.
This puzzle reappears in some form
ir
answered on the same principle involv-
ed in the Interpretation of the Arabs
will. He had fifteen horses and four
sons. He devised his estate, giving
one son a half, another q quarter, an
other an eighth, and the last 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, one-quarter, one
| eighth, or one-sixteenth would give
either son an even lot they had fierce
dispute over the division. A venerable
sheik rode up just as the quarrel was
at its height, and to compose their
differences dismounted and generously
offered to add his mare to the fifteen
belonging to the estate, agreeing that
each should take his allotted share
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 sheilz
mounted his mare and rode away. The
Arab boys regarded it as miracle,
and exclaimed that Allah had given a
horse to the sheik for his generous in
tale the problem still survives and au-
nually puzzlee hundreds OF our coun-
trymen.
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 divided by one-half?,'
The unthinking person would say that
as the half of two-thirds is one-third.
This must be the solution of the pro-
blem, but Dabol1 will easily refute it.
The quotient of : divided by J is Ia
that is, ] will go in 3 one and one
third times. The last form Of the
1 proplem is to find the quotient of
divided by J. Two partners in lead
| ing banking house, having disputed,
as they say, all one day over the re-
result, the senior mainting that /
divided by J is J, and defying any one
to refute it. We answer that when /
is divided by J the quotient is q; that
is, J will be found times in l. If 6
be divided by the answer is 70; that
is, there are twelve halves in six. We
should beg pardon of our readers for
repeating these demonstrations if it
Were not for the character and magni-
tude of the disputes which occur
Ieuery day concerning 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 world stands. We
printed $50 proofs of a former answer,
and they have all been distributed to
4 ,xv1,< !, -