Telegram-herald., 1890-01-30
SOME ANCIENT PUZZLES
ghey seem % Be Invested Win q
vigorous ImmorsllTy
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There are certain problems. chiefly
a-itfaet.eAI. sudu=d ~ith . Vigorous
ilsnorsahtv ~ matter hos often the
solution IS printed. or hos ~i1e.. an ex-
hsllsngs ans~er Is pa3llsheds uls ques-
usn comes up a-aiu. before the mA Is
f.srly dri-d o. lhe Eps d hundreds ~ho
have uot seen the reply, ~ ~ho eithef
cannot understand ig oE sil not accept
IL There are several ~ these which @s
h4Fs printed 50 often. o9t which s11
ksDt coming lhar O. save fuuher tme
vre srracE oH a huaared proofs % e4cn.
snd mailed one 90 che Iuq4lrers 10 sue
cession without comment These proofs
are exhausted. AM .se have accumulated
from q score or more ~ cores Pondents
tie same OLD questions. with urgent re-
quests for fresh solution We notice
that The Brooklyn Eagle has been strug-
z.lnz sslIn ole of these. The editor who
bias charge ~ thAt department Is very
clever. and gse think he IS play lng little
0ith his iuqus-tor.
The original question sent 10 us forty
years ago and involving the same point
submitted 70 The Eagle was how 10 find
the product Of SO l9s. I'D 81. multi
piled by itself OF course II the parts Of
the pounds were stated ss fractions, and
the pounds as whole numbers, then
10 gJ9 -g60ths could be multiplied by
itself But money OF account has not
two dimensions. Ii a table IS 4 feet wide
and feet long. then 4x4-l6 feet.
and we have the number Of square
feet on the surface. Five times five
pounds are SO, bat five pounds times
five pounds Is uumeaning as money
does not measure itself ia 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-
iugs, eleven pence. three farthings. IS
utter nonsense.
TROUBLESOME MILLS.
The next puzzle on the list and one
some form of problem which proposes
TO divide q 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 a
man in his will had devised one-third,
one-fourth, one-fifth and one-sixth of
his property respectively 10 his four
children. supposing that he had thus de-
vised the whole of his estate The frac-
tions mentioned only made nineteen
twentieths of a whole number. This is
easily seen if they are reduced to a com
mon denominatCr. One-third is twenty
sixtieths, one-fourth IS Il en-sixtieths,
one ffth Is twelve-sixtieths and one
sixth is ten-sixtieths, which together
make but fifty-seven sixtieths, leaving
three-sixtieths (or 1-20th) to make up
the whole number.
This puzzle reappears in some form
every few days the year round. Il is
answered on the same principle involved
in the Interpretation of the Arabs will
lie had fifteen horses and four sons. He
devised his estate, giving one son a half,
another a quarter, another an eighth
and the last a sixteenth. They found il
impossible to agree on a division. The
eldest son insisted that as seven horses
would not be half Of fifteen he should
have eight; but the other sons objected
and as neither one-half, one-fourth, one
eighth nor 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 tC
add his mare TO the fifteen belonging tC
the estate, agreeing that each should
take his allotted share from the whole
sixteen, only stipldating that his should
be the last selected. The addition made
an easy. solution Of the difficulty. Tn,
first then took eight as his half o
the sixteen, the next took four for hi
quarter, the third took two for hi
eighth, and the fourth took one for hu
sixteenth. As this made but fifteen tn,
sheik mounted his mare and rode away
The Arab boys regarded it as a miracle
and exclaimed that Allah had given
horse To the sheik for his generous inter
ference. In spite of this oft told tale IN.
problem still survives and annually puz
zles hundreds Of our countrymen.
JUGGLING WITH FRACTIONS
A more recent problem which we hav'
already answered several times, bu
which is repeated every week from som.
quarter. Is the division Of one Fraction
by another. The original question which
We answered several years ago was
"What is the quotieat Of two-thirds di
videj by one-halfy7 The unthinking per
son would say that as tho half Of two
thirds rs one-third. this must De the solu
tion Of the problem, but Daboll will easi
ly refute 1t. The quotient Of 2-3 divide
by is Is. that is. VIII 60 in % on
and oue-third times. Tie last form O
the problem, received as We write this
"a 90 find the quotient Of 1 divided by .
two partners IN a leading banking house
having disputed. as they say. AL one ia,
over the result the senior maintainiu.
that 3 divided hy is :. and defvirg an,
one 81 refute b. W answer that wher
( is divided bT the qaoteut Is Q. tba
1874 wi be found two times in /. II
ca divided b7 = the answer is p, that ia
there are twelve halves ia SIX ",
sra.l aer pardon = our readers for re