The diamond drill. (Crystal Falls, Iron County, Mich.) 1887-1996, 1890-02-22
SOME OLD PUZZLES.
Thy Seem to Be Invested With Vigorous
Immortality.
Revivai'of conundrums Supposed to Have
Been Satisfactorily Solved Fifty Years Ago
Problems in Which Interested People
VIII Persist In Radical Disagreement

There are certain problems. chiefly
arithmetical, embued with 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 IL or will not acceptit
The original question sent TO us forty
years ago was how 10 find the product
OF El9 los lid 81 multiplied by itself.
OF course II the parts OF the pounds
were stated rs fractions, and the
pounds as whole numbers, then 49,
g59960ths could be multiplied by it
self But money OF account has not
two dimensions. IL 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 arthings," is utter nom
sense.
The next puzzle on the list. and one
which comes the oftenest 10 our desk,
In some form OF 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 man in his will had dlvis-
ed one-third. one-fourth. one-ffth, 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 twenticths OF whole
number. This Is easily seen II they
are reduced 10 a common denominator.
One-third is twcnty-sixtieths, one
fourth is fifteen-sixtieths one-flfth Is
twelve-sixtieths. and one-sixth Is ten
sixtieths, which together make but
tfty-seven sixtieths. leaving three
sixticths (or 1-2Oth) TO make up the
whole number.
This puzzle reappears in some form
every few days the year round. II is
answered on the same principle involv-
ed in the Interpretation OF the Arabs
will. He had fifteen horses aud four
sons. He devised his estate. giving
one son half, another "A quarter, an
other an eighth, and the last six
teenth. They found IL impossible 10
ngree on u 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
DC 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
Mt its height and TO compose their
differences dismounted and generously
offered 20 add his mare to tho fifteen
belonging 10 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 sheix
mounted his mare and rode away. The
Arab boys regarded IL as "A miracle,
and exclaimed that Allah had given a
horse 70 the sheik for his generous In
tcrfercnce. In spite OF this oft-told
tale the problem still survives and an
IL -
trymen.
A more recent problem, which we
have already answered several times.
but which Is repeated every week from
some quarter, Is tho division OF one
fraction by another. The original
question. which we answered several
years ago. was What is the quotient
OF two-ihirds divided by one-halfP''
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 Daboll will easily refute IL |
The quotient OF divided by is l.
that Is. will go In I one and one
third times. The last form OF the !
proplem Is 10 find the quoticnt OF |
divided by J. Two partners in n lead
ing banking house. having disputed. I
as they say, all one day over the re-
result. the senior mainting that l |
divided by Is !. and defying any one
10 rofutc H. We answer that when !
Is divided by 4 tho quotiont Is ?; that .
is. ! will be found ? times In l. IL |
be divided BY ! the answer Is ~; that
Is. there are twelve halves Ia six. We |
should beg pardon OF our readers for |
repeating these demonstrations II II
were not for the character and magni-