The Butler County press. [volume] (Hamilton, Ohio) 1900-1946, 1914-11-20

1t Is 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 meaningless. freaky
twistcr Of a puzzle. But it is a puzzle.
1t is the method by which Russian
peasants multiply. aud 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 ,, ignoring the frac-
tions Continue the process until the
divided column reaches one. Then dou-
BILE the other number and continue the
process until 1t equals in lines the first
column. Then whenever number Is
even in the FIRST column strike it out,
together with its corresponding num-
Der In the second column. Add the Sec
ond column, and. 10, the answer. Now,
why does it do it? There seems to be
no reason for it, but what is it? Can
you work it out?
1t is infallibIe. 1t has never been
known to fail But what principle of
mathematics is behind 1t all? Perhaps
1t Is some queer freak of numbers,
some one says. but such things are not
to be turned aside with such generali
firS ic
lax q system. There is some rule be-
hind 1t 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 by 2
equals 3, aud multiplying 20 by 2
equals 40. Continuing. 3 divided by 2
and throwing away all fractions will
be l. 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 will go out, leaving
the last two parallel results. ignoring
the Grst column and adding the num-
bers In tie second. the answer will be
the result of 40 and 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 IL to the
multiplying 1t will result like this:
Ten and II will become and "a,
which will in turn be changed to and
48 and finally into | and 90. Then,
striking out the numbers 10 and with
their corresponding numbers II and
4S. leaving the second column figures
"a and 90 to be added-this becomes
120
There is no escaping it, No matter
how large the score. 1t comes out right
with distressing surety Take the odd
numbers. Perhaps there is some twist
in the scheme that applies to even
numbers Take % and ID Going
right down the column they become IL
then and 240: II and 6 go out. taking
with them 80 and 60 Add 10. 120 and
240. Answer. 375 Multiply % by 10 ac-
cording TO our methods Correct-375
Now. why is it that the even numbers
must be eliminated on the right side
addition2
1t 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
obtained2
Where no even number results in the
first column. as in Is l3. there Is no
complication; 10 and 13 in the process
become and 26. then 3 and 81 and
finally ! and l04 Adding l3. 26, SO
and 104 equals 1875, the correct sum
There can be no multiplication In fig
ures which will divide down to place
where there are no odd numbers. for
the final number must always of neces
sity be |. In the sum l6 4, 16
divides itself into 8. 4. and / success.
sively, while becomes 8, IT, 80 and
GA. All OF the pairs are crossed out.
with the exception OF | and "a In that
case the addition OF the second column
will be GA
Despite The puzzling nature of this
formula, there is some mathematical
principle by which 1t can be explained
There Is some rule awaiting the fertile
minds of the workers by which this
"stumper" can be demonstrated to be
simplicity Itself