The Olneyville times. (Olneyville [Providence, R.I.]) 1887-1917, 1914-10-02

Are a Puzzle to Mathematician.
This Is not a meaningless, freaky
twister Of a puzzle. But 1t is puzzle.
It is 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-
tions. Continue the process until the
divided column reaches one. Then dou-
process until 1t 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 it2 Can
you work 1t out?
1t Is infallible. 1t has never been
known to fail But what principle OF
mathematics is behind 1t 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 1t all.
Take the simple multiple IL by 10.
Obviously the answer Is 12O. Try 1t
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 6 and 20. Dividing 6 by 2
equals 3, and multiplying 20 by
equals 40. Continuing, 3 divided by
and throwing away all fractions Will
be 1, while 40 multiplied by 2 will be
80 Now strike out all the numbers In
the first column which are even and
with 1t their parallels In the second
column-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
1t out? How did he start?
Now try working the problem by put
ting 10 in the first column and sub
Secting It to the dividing and II to the
multiplying. 1t will result like this:
Ten and IL will become 8 and "a,
which will in turn be changed to 2 and
4S and finally into 1 and 06. Then,
striking out the numbers 10 and z with
their corresponding numbers II and
AZ, leaving the second column figures
"a and 90 to be added-this becomes
12O.
There is no escaping 1t. 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
numbas. Take % and 10. Going
right down the column they become IL
and 80; then and 60; then and 12O;
then and 240; II and 9 go out, taking
with them 30 and GO. Add Is, 12O and
24O. 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
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 x 13, there Is no
complication; Is and 13 In the process
become and 26, then 3 and 81 and
finally / and 104. Adding 13, 26, 81
and 1O4 equals 1915, 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 1. In the sum 16 4, 10
divides itself into 8, 4, 2 and l success
sively, while 4 becomes 8, 16, 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 64.
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.
Another quizZer: Why must frac-
lions be discarded? How Is Ii that the
result will be true when several units
are cast aside? For example, consider
the number ~. Dividing by 2 the
result will be %. One whole unit is
thrown away. Twenty three becomes
by the same process IL, another unit
discarded. Eleven resolves itself into
5, making the third unit passed by. The
next step results in 2 and then 1, but
why is It that these thrye units count
Tor nothingl
The mere fact that the explanation
% near. that the whole thing Is simple
II the key can be found, is one that