The Wahpeton times. [volume] (Wahpeton, Richland County, Dakota [N.D.]) 1879-1919, 1914-10-08
CURIOUS FIGURING.

GUkluUS flGUkllyGj.
It's a Way the Russian Peasant
Has, and It's an Enigma.
A UNIQUE WAY 10 MULTIPLY.
h Il Simplicity ltssif ana Abseisfsly
Accurate. but tiss Why and Wt.srs.
fore of the Method and ~ Rssults
Arr Puzzle 60 Mathsmatleisns..
This b NOT meaningless, treaty
twister Of puzzle But Il b Q puszla.
It = the method By witch Russian
peasants multiply. and 40 yet the
boasted mental superiority Of America
cannot solve the simple riddle Of the
slav. n 8
Suppose you want to multiply two
numbers together. Divide one OF the
numbers By 2 ignoring the frac.
tiona Continue the process until the
divided column reaches one. Then dou-
BILE the other number and continue tho
process until It equals In lines the flrst
column. Then whenever q number u
even in the frst column strike It out,
together with its corresponding num-
Der In the second column. Add the sec.
ond column. and, 10, the answeri Now.
why does It do it7 There seems to be
no reason for It. but what 10 It'll Can
you work It QUIT
1t - infanible. It has never been
known to fail. But what principle Of
mathematics IL behind It an3 Perhaps
It u some queer freak Of numbers,
some one says, but such things are not
to be turned aside with such general.
ties. Mathematics Is not built upon 90
lax system. There Il some rule be-
hind It all.
Take the simple multiple ~ By 10.
Obviously the answer u 12O. Try It
the Russian way. Place IL In the first
column and 10 In the second. Divide
12 BY 3 and multiply 10 By 2 and place
the respective answers beneath the
sums from which they were derived
It win stand and 20. Dividing 6 By 2
equals B. and multiplying 20 By 2
equals 20 Continuing, 3 divided BY 3
and throwing away all fractions will
be I. while 40 multiplied by 2 win be
80. Now strike out all the numbers In
the 6rst column which are even and
with It their parallels in the second
column-12 and 6 will 60 out, leaving
the last two parallel results. Ignoring
the 6rst column and adding the mum.
bers In the second, the answer will be
the result of 20 and 80. or 120.
The questions are: Who ever worked
e out? How did he start7
Now try working the problem BY put
ting 10 In the first column and sub
jecting It to the dividing and II to the
multiplying. It win result like this:
Ten and u will become s and "A.
which win in turn be changed to 2 and
g and finally into and 90 Then.
striking out the numbers 10 and 2 With
their corresponding numbers II and
g. leaving the second column figures
"a and o6 to be added-this becomes
100
There u no escaping II. No matter
how large the score. It comes out right
with distressing surety. Take the odd
numberA Perhaps there u some twist
In the scheme that applies to even
numbers Take Is and Is Going
right down the column they become IL
and 30; then 6 and 60; then 8 and 120;
then and 240; II and 6 60 out, taking
with them 30 and 60. Add IS. 12O and
240 Answer. 87h Multiply Is by 15 &C.
cording to our methods. Correct-875.
Now. why is 1t that the even numbers
must be eliminated on the right side
when they do not connt at all in the
addition1
It IL plain to be seen that all the
Numbers in the second column will be
even. but by what freak Of calculation
are those corresponding to the even
numbers In the first column Of no con.
sequence when the correct sum is to be
obtained7
Where no even number results In the
1rst column. as in Is Z Is. there u no
complication: Is and 10 In the process
become and e. then 8 and &c and
finally I and 1O4. Adding 10, Is, 80
and 104 equals 1875 the correct sum.
There can be no multiplication In DC.
ures which will divide down to q place
where there are no odd numbers, for
the 0nal number must always Of neces-
sity be l. In the sum 16 Z Z, 10
divides itself into 6. Z. 3 and success.
sdvely. while Z becomes 6, l6. Sc and
e. All Of the pairs are crossed ont,
With the exception Of and "a. In that
case the addition Of the second column
viii be e.
Despite the puxsling nature Of this
formula. there b some mathematical
principle BY which It can be explained
There II some rule awaiting the fertile
minds Of the workers BY which this
'stnmper" can be demonstrated to b
simplicity itSelf
Another quixSer: Why must frac-
lions be discarded How b It that ths
result will be true when several units
49, nS@R a~aNn0 Uo~