Newspaper Page Text
CURIOUS FIGURING.
It’s a Way the Russian Peasant
Has. and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.
It la Simplicity Itself and Absolutely
Accurate, but the Why and Where
fore of the Method and Its Results
Are a Puzzle to Mathematicians.
This Is not n meaningless. freaky
twister of a puzzle. But It Is a puzzle.
It Is the method by which Russian
peasants multiply, and ns yet the
boasted mental superiority of America
cnnnot solve the simple riddle of the
Slav.
Suppose you want to multiply two
numbers together. Divide one of the
numbers by 2, ienorhiK the frac
tions. Continue the process until the
divided column reaches one. Then dou
ble the other number aud continue the
process until it equals in lines the first
column. Then whenever a number is
even in the first column strike it out,
together with its corresponding num
ber in the second column. Add the sec
ond column, and, lo, the answer! Now.
why does it do ItV There seems to be
no reason for it, but what is it’/ Can
you work It out?
It is infallible. It has never been
known to fall. But what principle of
mathematics is behind it all? Perhaps
it is some queer freak of numbers,
some one says, but such things are not
to be turned aside with such generali
ties. Mathematics is not built upon so
lax a system. There is some rule be
hind It all.
Take the simple multiple 12 bv 10.
Obviously the answer is 120. Try it
the Russian way. Place 12 in the first
column aud 10 in the second. Divide
22 by 2 and multiply 10 by 2 aud place
the respective answers beneath the
sums from which they were derived.
It will stand 0 aud 20. Dividing 0 by 2
equals 3. and multiplying 20 by 2
equals 40. Continuing. 3 divided by 2
and throwing away all fractions will
be 1, while 40 multiplied by 2 will be
80. Now strike out all the numbers in
the first column which are even and
with It their parallels in the second
column—12 and 0 will go out. leaving
the last two parallel results. Ignoring
the first column and addiug the num
bers in the second, the answer will be
the result of 40 aud 80. or 120.
The questions are: Who ever worked
It out? How did he start?
Now try working the problem by put
ting 10 in the first column and sub
jecting it to the dividing and 12 to the
muJtiplj*ing. It will result like this:
Ten and 12 will become 5 and 24,
which will in turn be changed to 2 aud
48 and finally into 1 and IH5. Then,
striking out the numbers 10 and 2 with
their corresponding utimbers 12 and
48, leaving the second column figures
24 and 9G to be added—this becomes
120.
There Is no escaping It- No matter
how large the score, it comes out right
with distressing surety. Take the odd
numbers. Perhaps ther* is some twist
in the scheme that applies to even
numbers. Take 25 and 15. Going
right down the column they become 12
and 30; then 0 and CO: then 3 and 120;
then 1 and 240: 12 and G go out, takiug
with them 30 and CO. -Add 15. 120 and
240. Answer. 375. Multiply 25 by 15 ac-
cording to our methods. Correct—375.
Now, why Is it that the even numbers
must be eliminated on the right side
when they do not count at all in the
addition?
It is plain to be seen that all the
numbers in the second column will be
even, hut by what freak of calculation
are those corresponding to the even
numbers In the first column ot uo con
sequence when the correct sum is to be
obtained?
Where no even number results in the
first column, ns in 15 x 13. there Is no
comDllcation; 15 and 13 in the process
become 7 and 20, then 3 and .52 and
finally 1 and 104. Adding 13, 20. 52
and 104 equals 195. the correct sum.
There can be no multiplication In fig
ures which will divide down to a place
where there are no odd numbers, for
the final nunjber must always ofyneces
8lty be 1. In the sum 10 x 4, 10
divides itself Into 8, 4. 2 and 1 succes
sively, while 4 becomes 8. 10, 32 and
64. AH of the pairs are crossed out,
with the exception of 1 nnd 64. In that
vase the addition ot the second column
will be 04.
Despite the puzzling nature of this
formula, there Is some mathematical
principle by which it can be explained.
There Is Borne rule awaiting the fertile
minds of the workers by which this
“stumper" can be demonstrated to be
simplicity ItselL
Another qulzzer: Why must frac
tions be discarded? How is it that the
result will be true when several units
are cast aside? For example, consider
| the number 47. Dividing by 2 the
result will be 23. One whole unit .is
thrown away. Twenty-three becomes
by the same process 11. another unit
I discarded. Eleven resolves itself Into
B. making the third unit passed by. The
next step results in 2 nDd then 1. but
I *hy Is it that these three units count
I for nothing?
The mere fact that the explanation
11-" near, that the whole thing is simple
I l f the key can be found, is one that
l r annot help bnt draw attention to this
luovei means of adding.—Philadelphia
1 North American.
The more 1 study the world the more
I 1 am convinced of the inability of force
| Tn create anything durable.—NapoUSm
Ibonaparu.
While the Supply Lasts
A Hand - Painted
Japanese Silk
TEA POT”
tt
Pin Cushion
To Every Purchaser of 10c Worth of TUXEDO Tobacco
This beautiful little novelty will delight every lady who receives
one. It is an excellent pin cushion and will make a dainty, attractive
ornament for the dressing table. Take home a tin of TUXEDO,
and take your wife this pretty “Tea Pot 5 ’ Pin Cushion.
Your gift will please her—that TUXEDO leaves no odor about
draperies and furniture, will also win her heartiest approval. The
clean, fresh fragrance of TUXEDO pleases everyone.
The Perfect Tobacco for Pipe and Cigarette
Thousands of famous Americans emphatically endorse
TUXEDO. They find in this mild, delightful tobacco com
plete relaxation, soothing comfort and healthful enjoyment.
A week’s trial of TUXEDO will convince you. That is the
reason this unusual free offer is made.
TUXEDO is the very best Kentucky Burley tobacco
—carefully ripened, cured and mellowed—then treated by the
original “Tuxedo Process,” that takes out the “bite” and “sting”
absolutely, fully developing the wonderful mildness, fragrance
and flavor of the Burley leaf.
YOU CAN BUY TUXEDO
EVERYWHERE
Convenient Pouch, innerlincd _
with moisture-proof paper . . DC
Famous green tin, with gold ^ rf"\ _
lettering, curved to fit pocket A V/C
In Tin Humidors, 40c and 80c
In Glass Humidors, 50c and90c
FREE
Take advantage of this Free Offer today and avoid
disappointment. Dealers have only a limited supply
of these Pin Cushions and cannot get more. Look
for Free Offer sign in a dealer’s window — get 10c
worth of TUXEDO and ask for the “Tea Pot” Pin Cushion, FREE.
THE AMERICAN TOBACCO COMPANY
Special Notice to Dealers:
WE want every dealer in Newnan to be supplied with these Pin Cushions. All dealers who have not yet secured a
supply of these Pin Cushions can do so by applying at TUXEDO headquarters, E. W. BEALL, Virginia House.
Professional Cards. |
W. L. WOODROOF,
PHYSICIAN ANDSURGEON.
Office 11 Vs Greenville street Residence 9 Perry
street Office ’phone 401; Residence ’phone 451.
ID. A. HANEY,
PHYSICIAN ANDSURGEON.
Offers his professional service to the people of
Newnan, and will answer all calls town or coun
ty. Office in the Jones Building. E. Broad Street
Office and residence ’phone 289.
THOS. J- JONES,
PHYSICIAN AND SURGEON.
Office on E. Broad street, near public square.
Residence next door to Virginia House.
T. B. DAVIS,
PHYSICIAN ANDSURGEON.
Office-Sanitorium building. Office 'phone 5—1
•all; residence ’phone 6—2 calls.
Court Calendar.
COWKTA CIRCUIT.
R. W. Freeman, Judge; J. Render Terrell, So
licitor-General.
Meriwether—Third Mondays in February and
August.
Cowetfr—Flrst Mondays In March andSeptem.
her.
Heard—Third Mondays in March and Suptem-
ber
Carroll—Firs* Mondays in April and Octolier
'Iroup—First Mondays in February and Aug
CITY COURT OF NEWNAN.
W. A. Post, Judge; W. L. Stalling)*. Solic
itor.
Quarterly term meets third Mondays in Janu
ary, April, July and Octolrer.
BANKRUPTCY COURT.
A. I). Freeman.Newnan.Oa., Referee in Bank
ruptcy for counties of Coweta. Troup, Heard.
Meriwether, Carroll, Douglas and Haralson.
W. A. TURNER,
PHYSICIAN AND SURGEON.
Special attention given to surgery and diseases
»f women. Office 19Mi Spring Btreet. ’Phone 230 ,
F. I. WELCH,
PHYSICIAN AND SURGEON.
Office No. 9 Temple avenue, opposite public
«chool building. 'Phone 234.
THOS. G. FARMER, JR.,
ATTORNEY AT LAW
Will give careful and prompt attention to all
egal buaines entrusted to me. Money to loan
Office in court-house.
Laundry Lists for sale here.
For Shoe and Har
ness Repairing
and
NEW HARNESS
go to
A. J. BILLINGS
6 SPRING ST.
Only high-class materials used
in my work.
Give us a trial order on
job printing.
Atlanta and West Point
RAILROAD COMPANY
ARRIVAL AND DEPARTURE
OFTRAINS AT NEWNAN. GA.
EFFECTIVE NOV.
1, 1914.
Subject to change and typographical
errors.
No. 3ft
. 7:2ft a. m.
No. 19
. 7:50 a. m.
No 18
. U :4ft a. m.
. 10:40 a. m.
No. 39.
. 3:17 p. m.
No 20
, 0:3ft p. in .
No 34
. 5 :37 p. in.
No 38
No 40
19 :40 fl . m
. 12:52 p. in.
No. 17
. 1:12p.m.
No. 41
. 7:20 p. in.
No. 37
. 0:23 p. m.
No. 30
.10:28 I*, in.
All trains daily. Odd numbers,
HMiihhound; even numbers, north
bound.
Old newspapers for sale
at this office at 25c. per
hundred.
T. S. PARROTT
Insurance—All Branches
Representing
Fire Association, of Philadelphia
Fidelity and Casualty Co., of New York
American Surety Co., of New York
Mutual Benefit Life Insurance Co.,
of Newark, 'N. J.
14 1-2 Greenville st., Over H. C. Glover Co.
CENTRAL OF GEORGIA RAILWAY CO.
CURRENT SCHEDULES.
ARRIVE FROM
Griffin 11:10 A.M. 7:17 p, m. ’
Chattanooga 1:40 p. M.
Oedartown 6:36 A. M.
Col urn boa 9:00 a M. , 8:36 p.m.
DEPART FOR
Griffin 1-.4AP. M.
Griffin 0:3b a. m,
Chattanooga 11 :|0 a. M .
Cedartown 7:17 p.m.
Columbus 7:40 A.M.