The Wahpeton times. [volume] (Wahpeton, Richland County, Dakota [N.D.]) 1879-1919, 1914-11-05
CURIOUS FIGURING.
It's a Way the Russian Peasant
Has, and It's an Enigma.

Has, and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.
N 10 Simplicity Itself and Absolutely
Accurate. but the Why and Where.
tore Of the Method and lts Results
Are Puzzle to Mathsn,atieians.
This is not meaningless, freaky
twister OF puzzle. But 1t is aspuzzle.
It u the method BY which Russian
peasants multiply. and as yet the
boasted mental superiority of America
cannot solve the simple riddle of the
Slav.
Suppose you want to multiply two
numbers together. Divide one of the
numbers BY 2, ignoring the frac.
lions. Continue the process until the
divided column reaches one. Then don.
bic the other number and continue the
process until It equals In lines the frst
column. Then whenever a number Is
even In the 6rst column strike 1t out,
together with its corresponding uum.
Der in the second column. Add the sec.
ond column, and, 10, the answerI Now.
why does 1t do It? There seems to be
no reason for It, but what Ia It'll Can
you work It QUIT
1t u tnfallible. It has never been
known to fail. But what principle Of
mathematics is behind it an7 Perhaps
1t 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 80
Lax q system. There Is some rule b.
hind It all.
Take the simple multiple II BY 10.
Obviously the answer Is 12O. Try 1t
the Russian way. Place II in the first
column and 10 in the second. Divide
IL by and multiply 10 by and place
the respective answers beneath the
sums from which they were derived.
1t will stand and 20. Dividing 6 by 2
equals 8. and multiplying 20 by =
equals 40. Continuing, 3 divided by
and throwing away all fractions will
be l, while 40 multiplied by 2 will be
80. Now strike out all the numbers IL
the FIRST column which are even and
with 1t their parallels In the second
column-12 and 6 will 60 out, leaving
the last two parallel results. Ignoring
the FIRST column and adding the num-
bers in the second. the answer will be
the result of 20 and 80. or 12Q.
The questions are: Who ever worked
It out? How did be start?
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. 1t will result like this:
Ten and IL will become and "a,
which will in turn be changed to 2 and
4S and finally into and 90. Then.
striking out the numbers 10 and with
their corresponding numbers II and
48, leaving the second column figures
"a and SO to be added-this becomes
l2O
There is no escaping 1t. No matter
how large the score. it comes out right
with distressing surety. Take the odd
numbers. Perhaps there Is some twist
In the scheme that applies to even
numbers. Take Is and Is. Going
right down the column they become IL
and 80; then and GO; then and 1870:
then and $40: IL and 60 out, taking
with them 30 and 60. Add Is. 12O and
24O. Answer. 375. Multiply 25 by Is &C.
c0rding 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. 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
obtained?
Where no even number results in the
drst column. as In Is Is. there Is NO
complications: IS and 10 in the process
become and 26. then 3 and 80 and
finally l and lO4. Adding IL. 70. 81
and 104 equals 1913. the correct sum.
There can be no multiplication In fig
ures which will divide down to place
where there are no odd numbers. fol
the fnal number must always Of neces
sity be I. In the cum Is 4, 16
divides itself into 8 4. and success
sively. while becomes y, Is. 80 and
"a. All Of the pairs are crossed out.
With the exception of and GA. In that
case the addition OF the second column
will be "a.
Despite the puzzling nature of this
formula. there is some mathematical
principle by which it can be explained
There Is some rule awaiting the fertile
minds of the workers by which this
'stnmper" can be demonstrated to be
sim lefty itself.
Another quizzer: Why must frac-
tio's be discarded? How Is 1t that the
result will be true when several units
are cast aside? For example, consider
the number AZ. Dividing by 2 the
result will be O. One whole unit Ia
thrown away. Twenty.three becomes