The Kennewick courier-reporter. [volume] (Kennewick, Wash.) 1914-1938, 1914-10-01
CURIOUS FIGURING.
IFS a Way the Russian Peasant
Has, and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.

Il Il Simplicity Itself and Absolutely
Accurate. but the Why and Where
fore Of the Method and Its Results
Are Puzzle to Mathematieians.
This is not meaningless. freaky
twister of puzzle. But 1t is puzzle.
II IS the method by which Russian
peasants multiply. and as yet the
Roasted 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 dou-
ble 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 it's corresponding num-
her In the second column. Add the Sec
oud column. and, 10, the answer! Now,
WHY does 1t do It? There seems to be
no reason for it, but what is It? Can
you work it out?
Il is infallible. 1t has never been
known to fail. But what principle of
mathematics is behind 1t all? Perhaps
II Is some queer freak of numbers,
some one says. but such things are not
10 be turned aside with such general
ties. Mathematics Is not built upon SO
lax a system. There Is some rule be-
hind 1t all.
Take the simple multiple IL by 10.
Obviously the answer is 100. Try it
the Russian way. Place IL In the first
column and 10 In the second. Divide
IL by 2 and multiply 10 by 2 and place
the respective answers beneath the
sums from which they were derived.
Il will stand 6 and 20. Dividing by 2
equals 3, and multiplying 70 by 2
EQUALS 40. Continuing, 8 divided by 2
and throwing away all fractions will
be 1, while 40 multiplied by 2 will be
so, Now strike out all the numbers In
the first 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 first column and adding the num-
bers In the second. the answer will be
the result of 40 and so. or 40.
The questions are: Who ever worked
4 out? How did he start?
Now try working the problem by put
ding 10 In the first column and sub
1ecting 1t to the dividing and II to the
multiplying. It will result like this:
Ten and IL will become 5 and "a.
which will in turn be changed to 2 and
48 and finally into I and 96. Then.
striking out the numbers 10 and 2 with
their corresponding numbers IL and
IS, leaving the second column figures
"a and SO to be added-this becomes
10.
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 10. Going
right down the column they become II
and 30; then 6 and GO: then 3 and 100:
then and 24O: II and go out. taking
with them 80 and 60. Add Is. 12O and
90. Answer. 1915. Multiply % by 10 ac-
c0rding to our methods. COrrect-310.
Now. why Is 1t that the even numbers
must he eliminated on the right SIDE
when they do not count at all In the
addition?
II il plain to be seen that all the
numbers In the second column Will De
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 De
obtained?
Where no even number results In the
first column. as in 10 13, there Is no
complication; Is and Is In the process
become and &c. then 3 and o. ana
dnally / and 1O4. Adding IL, 70. o.
and lO4 equals 1876. the correct sum-
There can be no multiplication In hg-
ores which will divide down to place
where there are no odd numbers. TOT
the final number must always OF neces-
fty be !. In the SUM IL Z T. 40
divides itself into 8. 4. 2 and success.
sively. while 4 becomes g. 16. 81 ana
a. All Of the pairs are crossed OUT.
with the exception Of ] and "a. In tnat
case the addition Of the second Column
will be "a.
Despite the puzzling nature OF tnls
formula. there Is some matnemalca'
principle by which 1t can be expialneu
There Is some rule awaiting the fertiie
minds of the workers by which tnis
'stumper" can be demonstrated 20 DC
simplicity itself.
Another quizzer: why must frac-
dons be discarded? How Is II that tue
result will be true when several units
are cast aside? For example. consiuel
the number AZ. Dividing Dy Tug
result will be %. One whole uhit -
thrown away. Twenty-three becomes
oy the same process IL. another ul.
discarded. Eleven resolves itseiI lm1o
.. making the third unit passed Dy. II. LIZ.