Ellsworth American. [volume] (Ellsworth, Me.) 1855-current, 1915-03-03
CURIOUS FIGURING.
It's a Way the Russian Peasant
Has, and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.

fore o. the Method and lite Hesults
Il Are Puzzle to Mathsmaticians.
This Is not. a meaningless, freaky
twister Of puzzle. But 1t is puzzle.
1t p the method by which Russian
peasants multiply, and as yet the
boosted mental superiority Of America
cannot solve the simple riddle of the
6lav.
Suppose you want to multiply two
Numbers together. Divide one Of the
aumbers by 2. ignoring the frac.
lions. Continue the process until the
divided column reaches one. Then dou-
bic the other number and continue the
process until It equals in lines the first
column. Then whenever number Is
even In the first column strike 1t out.
together with its corresponding num-
Der In the second column. Add the Sec
ond column. and. 10, the answer! Now,
why does 1t do It? There seems to be
no reason for 1t, but what is 1t? Can
you work 1t out?
known to fail. But what principle of
mathematics is behind 1t all7 Perhaps
1t Is some queer freak Of numbers,
some one says. but such things are not
to be turned aside with such generaii.
ties. Mathematics Is not built upon so
lax a system. There Is some rule be-
hind 1t all.
rut. otv L. hu IN
Obviously the answer IL 100. Try 1t
the Russian way. Place IL In the first
column and 10 In the second. Divide
II by 2 and multiply 10 By 2 and place
the respective answers beneath the
sums from which they were derived.
1t will stand q and 20. Dividing 9 by 2
equals 3. and multiplying 20 by 9
equals 40. Continuing, divided by 2
and throwing away all fractions will
be /. while 40 multiplied by will b.
So Now strike out all the numbers In
the first column which are even and
with II their parallels In the second
column-12 and viii 60 out, leaviiAs
the last two parallel results. Ignoring
the first column and adding the num-
beers In the second. the answer Will be
the result of 40 and so. or 100.
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 IL will become 5 and "a.
which will In turn be changed to 2 and
4S and finally into | and 96. Then.
striking out the numbers 10 and 2 with
their corresponding numbers IL and
4S, leaving the second column figures
"a and 96 to be added-this becomes
100.
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 IS and 10 Going
right down the column they become II
and 30; then 6 and GO; then 3 and 40:
then and 240: IL and go out, taking
with them 80 and 60. Add Is, 100 and
240. Answer. 375. Multiply Is by 10 &C.
cording to our methods. Correct-375.
Now. why is 1t that he even numbers
must be eliminated on the right side
when they do not count at all In the
addition?s
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 l5 13, there is no
complication: Is and 10 in the process
become and %. then and - and
finally l and 104. Adding Is. 26. 81
and i04 equals l95. 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 IL 4. 1G
divides itself into :. 4. 2 and ] succes-
sively, while becomes 8. 10. 80 ana
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 Gi.
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 1t that the
result will be true when several units
are cast aside? For example. consider
the number Al. Dividing by 2 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
8. making the third unit passed by. The
next step results In and then l. but
why ia II that these three units count