Daily Ohio statesman. [volume] (Columbus, Ohio) 1855-1870, 1867-10-12
THE pUzzLEw,s COLUMN.


GREEsvrLLE. o. Oct. 8, 1867.
Mr. EDITOR; Since Sammy has requested solu
tions will I'LL endeavor to give few. Here is my SO
Let denote the center of the circle an
Ah,S the e. ext extremity Sa3iy Of the Diameter fro!
in the direction the second body moves. lay off tn
ar arc J, . equals 50 degrees 50 minutes equal
then will the arc D equal minutes. Draw
E1S% "a II! .Sd 'sss
q COS O B EQUALS is 5usas7: and in the trisneI @
ID I'D; 20; We have . equals y . cos E . equal
Z minus F equals .ois5s5 Now the second bod;
move; from e D, while he first moves from i
equal o1454 4. then the velocity of the SEQ
oSd 6ody in moving rom to Dis el4s444 divided b
starting point. being the middle point of the arc
u. the velocity Of the body when passing this de
think some Of the boys will solve No. e3s No
21ol beautiful theorem. will give my aemon
Describe a circumference with any radius. De
note the radius by aud the diameter of the circl,
1y ID. Construct two regular hexasons. inscrib; ne
the circle. Denote these hsxasons bv Nj and N
lnscribe regular dodecaggn by bisecting the arc
the Denass this dodseasan by porn Noa
each side Of NJ equals R. the apothsm eqaaisK of
sef RI into the square root Of three. Each sid,
Q, N equal = Of into the sqaare root of 9. th.
into the square root Of three. By PROPOSE
Soh. We have ( ual the square ROOT eftM IN o Nd
toostit1ting the values Of a and in this equs;
equals of D2 that is the regular inscribed dode-
cagon is threefourths of the crcumscribing square
No. st4'sis 50: IS. .sh's' io-4i per cent
No. 245-l45s. ..i + .,,.-. +
and gain, A's capital was f20.
The answer to the, grindstone question is: A
No. 24s-l3.ls ,7s cubic feet. 81 -,.,,,,,,,.t,
NO. 24s-Eet KS Kay. x3y2, x2y3. xy4 and y5 eaus
equal sps9 s5xx
ing equation fe) from Cd, we have x4sXxsv2X KY
Xky4 squalls $40 3D. Let x=z-v, and y=zXv; sub
stituting in I'd snd (3l. aud reducing, We obtain
2zSxaozsyaX XiozE4=lo25 90. and IS minus Ev4=s'
t5l Make v=ts in lD and 5); then f nd the value oi
obtain ls75t4X IT0ot2-s55 IN which we ind ia s
saSns tie s.fnss q and % DS sDS
the numbers (which are I. a. l6, "a. s56. and l624
e. b. .
.s9Mas f-'a .. WASHINGTON. o., Oct 8. 1857
Mr.: EDIToR: The mathematical column looks
fine this week, although there several absent
Come. boys let US see your faces again. will now
proceed to give afew
.su0i' s,1i sss' i7oV ANSWERS. a-szt IS
- Problem No 2I3-Loss is q per cent ;-l,g
No. 244-I092 plus (not satisfactory to myself),
No. 945-lf Guernsey means to inclose the whole
circle by triangle, equilatera viii be the kind
as takes the least number of rails viz 1470 rails
but wants the area of triangle equal to circle
1t will take q less number.
see that there is a new contributor from Norris
is j. a. SmaiIbrains. who thinks that ou column is
for the express purpose of making him monied
them Good Don' write letters. as' but write SDts
problems, and answer them" Please and car you
ten me why YOU. J. A. did not DO this you self
been worn out long ago. The last Of his communi-
cation is a problem. though old. will answer: A
must grind and grind until the stone will measure
is PIX inches in aeter when it will be found that
he has used 7ss inches of diameter.
More next time. SIX
CoLLINsvILLs. O., Oct. 8, lsa7
Mr.. EDIToR:-Your paper failed to reach me last
week. and so this week have nothing to do; mean
! have No. answers to send. have tried some Of
and now think can learn a good deal from the
brethren in review In the me.a time will wait
last weeks paper to me? As i am making them
into book to preserve them. I don't ike to lose
men to be present at roll call more iarly in
tend to be rgular as my paper comes to me.
Here is Prob EN- for Limestone:
-,.,.-, PROBLEM NO. 250. 81 80. b, ~
In rectangular field go rods long and 40 rqas
wide, hare starts in the and runs along te
fence. tthe long side9 and across the end right
aneles TO the bare in the other corner deg starts
after the hare and runs directly toward the hare
the time thus forming a curve. He catches the
hare just as she reaches the other end of the field
- aSs>-H-s -a. Fl. "SAMxY.n
81. toqsd 81 PROBLEM NO. 251. az
In field of unequal Sides the sgonal between
the most distant is 40 rods and the perpen-
diculars are 4s and "a rods how many acres does it
contain? .-l .s = - :
rola-i.-e SIX
------- PROBLEM NO. 252.
How long tube can be made from a G, Hinder of
lead inches long and inches in diameter and
through the center of which is hole 4 of an inch
Der and q of an inch ick?
SIX.
PROBLEM NO. 253.
How many cannon balls. six inches in diameter,
can be put in box six feet long, four feet DE- and
four feet one incn deep? E. B.
PROBLEM NO. 254.
Find two numbers whose difference is equal to the
difference of their cubes and whose product equal
to the difference of their squares. Please give