St. Johnsbury Caledonian. [volume] (St. Johnsbury, Vt.) 1867-1919, 1914-12-30


This is not a meaningless, freaky
twister of a puzzle. But it is a puzzle.
1t is the method by which Russian
peasants multiply. and as yet the
boosted 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-
tons. Continue the process until the
divided column reaches one. Then dou-
BILE the other number and 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 it's 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 infaIlible. 1t has never been
known to fail. 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 generai-
ties. Mathematics is not built upon so
lax a system. There is some rule be-
hind it all.
Take the simple multiple II by 10.
Obviously the answer is 120. Try it
the Russian way. Place Il in the first
column and 10 in the second. Divide
IL by 2 and multiply 10 by and place
the respective answers beneath the
sums from which they were derived.
It will stand and 20. Dividing by
equals 3, and multiplying 20 by 2
equals 40. Continuing, divided by 2
and throwing away all fractions will
be 1, while 40 multiplied by will be
80. Now strike out all the numbers in
the first column which are even and
with it their parallels in the second
coIumn-12 and will go 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 40 and 80, or 12O.
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 II to the
multiplying. 1t will result like this:
Ten and II will become 5 and "a,
which will in turn be changed to 2 and
4S and finally into l and SO. Then.
striking out the numbers 10 and 2 with
their corresponding numbers Il and
|
"a and 90 to be added-this becomes
| 12O.
There is no escaping it. 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 25 and Is. Going
right down the column they become II
and 30; then and 60; then and 120;
then and 24O; u and go out, taking
with them 30 and 60. Add Is, 120 and
24O. Answer, 375. Multiply 25 by 10 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?
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
obtained?
Where no even number results in the
first column, as in 10 K ID, there is no
complication; Is and 13 in the process
become Z and 20, then 3 and 90 and
finally 1 and 1O4. Adding ID, 20, 81
and 1O4 equals 1876, 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 number must always of neces-
sity be /. In the sum 16 4, 10
divides itself into 8. 4, and success
Bively, while 4 becomes 8, 16, 80 and
a. All Of the pairs are crossed out,
with the exception of and "a. 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
"stumper" can be demonstrated to be
simplicity itself.
Another quizzer: Why must frac-
lions be discarded? How is it that the
result will be true when several units
are cast aside? For example. consider
the number Al. Dividing by the
result will be %. One whole unit is
thrown away. Twenty-three becomes
by the same process II. another unit
discarded. Eleven resolves itself into
5. making the third unit passed by. The
next step results in and then 1. but
why is it that these three units count
Tor nothing?
The mere fact that the explanation
b near. that the whole thing is simple
If the key can be found. is one that
cannot help but draw attention to this
rDoanc IF adding DbsJaIoIwbfa