Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-07-20
IT ii U J t-E-
GUERNSEY.
BELLE Po1Nr, ONO. July 18th, 1867.

t BELLE POINT. OHIO. July 18th, 1867.
Mr.. EDITOR The puzzer's column did not reacf
me this week, and content myself by writing
s2lution for two or three unanswered problems
No. 70 may be solved as follows: Let x2 plus W :
(x-ay)2. whence x=>a2-1, divided by 2a)y which
substituted in xs plus y3. gives an expression con.
tanning y3 equal to square. and since y2=a
fady y in terms Of and and and : may be tafeI I
at pleasure; Taking aI2 we get y==4be divided By
for our answer x=a73 and y336l ~
Here is my method of solution for the following
product is equal to the difference of their squares
and the sum of their squares equal to the difference
problem5 Let X the less and KY the gSeatel e
number: Then form equations per eond ditions and
Of Nh plus (1 into the square root of 81. Ther
divide the second equaton by x2. and with little
and Ky divided by 4, plus u into the SQUARE l
root OF So can give thre four solutions for this
problem. Here is my solution for No. 9. my wine
The tumbler is full of water at first. and at the
end is half and half, therefore half the water must
flow away. Now the quantity of wine in the over
flow increases uniformly from nothing to equality
The flow of water diminishes just as much as the
flow of water is equal to the whole flow of wine
Now substract this from the whole flow of water and
equal to twice the average flow of wine
win, from nothing, to equality with. the
uniform flow ofwater averages just halD
tines the flow of wine but the whole q W Of water
is balf tumbler. hence one third of this or one
sixth of tumbler would be the flow of wine. and
SINCE half a tun,bler of wine remains in the tumb-
Ter it will take two-thirds of tumbler of wine to
afulfll the conditions of the question.
My age question is solved something like Robins
digit questions. Let x and represent the num-
bers respectively: then from conditions form equa-
and we have equati of the 4th degree which may
be stwrn'd solved by the general rule fOI finding
numbers are found to be 10 and s. hence the answer
is 20 years old. tOur family record makes me some
MY pulley question is an easv question in trigo.
nometry, but little tedious The work cannot be
PTgbashed a in in the paper vii give you the result
trigouometry. 1t il .312 inches Then find the
diameter of wheels bysuccessive trials and the three
SMALL LARGE
Sd s5Ff; f.. ss.4s sIs9 in
80 ft. 33 1923 in.
I.32 ft. 80 AL in.
will solve the rest Of the unanswered problems
SAMMY"
DUBLIN. OHIO. July IL. 1867.
MIR. EDITOR: After coll citing the fragments Of
my strGaO n'Gn which we are told by Broths Innis
was torn TO pieces with such violence and binding
them together. | sat him (the straw mani down up
on a largs limestohe.. and charged him with the
ing problems / then got Problem No. n as given
by Geo. A. Smith and read it to him very carefully
exactly what Mr.. mith meant in No 81 After read
the wheels of the cars running the rails" &C.,
and the latter part of the sentence which
says liter giving the dimensions of axle and its
two Wheels " that the axle will ALWAYS be in DO
stion square across the two rails" He (the straw
its verbal part denotes action (not being5 in the
present ten'e and progressive form, which shows
time. but extending into the future The preced eo
ing words !" wheels of the cars" plural number)
also indicates bs that s there nd is not only sing loaded
correspondent has it stated, but includes all or any
ears passing over the curve t7at have similar axes
and wheels to the one described in the problem;
and, consequently the axes will take the same po:
sition as the first 4 e. ?gusrs across the rails
position, taken in connection with the words. the
cars running on the rails" as spoken of at first
the axes bear the same relations before mentioned
In regard to making his conditions for problems
the natural or customary situation Of the thing
spoken of for granted therefore, in speaking of a
rail is eIeoGted because that rail is always elevated
at and if it is not, it is contrary to the gen.
eral CUSTOM and should therefore be mentioned.
After hearing his Ghe straw man's) defense and
summing the evidence. pronounced him honorably ~
tions," snd told him If he would tel me the pToba-
biry of similar event not happening again by Civ.
What is the probaby That an event viii bapSe2
atleast times in trials? he might have recess.
He answers That depends . upon Ts crcum tances
icy in the "breakneck the probabilities are at eas
toe that no accident will happen to him, If the
ton to six young ladies' and the young should
not reciprocate his affection. and should each an
swer no. the probabilities that the event of hi.
marriage with one of them would not happen at all
hence his conclusion in this
LIMESTONE.
COLUMBUS. OHTo, July Is. 1867.
Mr.. EDIToR-Hurrah for Sammyl He has in
deed sent fine oution to Problem No. 72 fol
which am very than. full. am much Obliged tC
Guernsey for giving Sammy his hat for next to the
one 9 who sol solved this Problem. | am under obliga
sey and Delta thought | was ill-natured when
wrote my st letter, but can assure them thai
there was never a better natured Robin picked I
cherry or mulberry than was at that time
The answer to Problem No. 100 is-Satinet q
yards; muslin 81 yards; ribbon Is yards.
No. .12l-There must be rods in each lot
No. I22-No. Brother Guernsey; Won were %
rods from La Ponta, and only l94.67 rods from tn,
vessel. ~
No. Iss-Sammy had 81 marbles. Dixie %, anG
Delts 16. - "-0
The answer to No. 12s is-The number is so.
ROB N
SIDNEY. o., July Il, Is 2.
Mr. ED1TER-Sir: Sammy's memorv n.n =
possibly be as good for remembering some things s.
Il is for remembering mathematician or else =
would certainly know his own age but since he he