Iowa County democrat. [volume] (Mineral Point, Wis.) 1877-1938, 1914-11-19
CURIOUS FIGURING.
It's a Way the Russian Peasant
Has. and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.

It Is StmpI,city Itself ana Absolutely
Accurate. but the Why and Where.
tore of the Method and It's Hesults
Are Puzzle to Mathematician,
This is not meaningless. trraky
twiSter OF puzzle. Bur it is a puzzle
/ 1t is the method 10y which Russian
! peasants multiply. and us yet the
boosted mental superiority OF America
cannot solve the simple riddle OF the
Slav
suppose vou want 10 multiply two
/ numbers tuGrther Divide one OF the
numbers uN =. ignoring the frar
/ tons, Continue the process until the
/ divided column reaches one. Then don
bic the other number and continue the
! process until 1t equals in lines the nrSt
column rhrn whenever Il number Is
even in thu nrSt column strike it out
! together WITH lis corrcSpuudluG nam
! Der III the second column Add the ~r.
oNd column and, 10, thr answer Now
! why does II Do IL: rherr seems tr ur
no :.;J:.uu tut H. nut WHAT Is II: eau
/ you work il out:
1t is lWi;.jih,c II has never ueeu
! know t. ,.u. But what principle ct
mathematics is nchind il all: Perhaps
4 it is some queer freak OF numbers
soHr one says ont such things are not
! to be turned aside with such gcnCran
! ties. Mathematics is not built upon SO
/ lax a system There Is some rule be
! hind ii ali.
Take the Simple multiple L. by 10
! obviously the answer is l2O Try It
/ the russian way Place II in the first
column and 10 i'll the second Divide
II by and multiply 10 by and place
the respective answers beneath the
sums from which they were derived
1t will stand 6 and 20. Dividing 10y ;
/ equals 3. and multiplying 20 by :
equals 40 Continuing, 3 divided 10y ,
and throwing away all fractions wilt
be t. while 10 multiplied by will be
so. Now strike out all the numbers III
the first column which are even and
with it their parallels in the second
column-l2 and will go out, leaving
the last two parallel results. Ignoring
the first column and adding the mum
! berS in the second. the answer will he
the result of 10 and so, 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 T. to the
multiplying 1t will result like this
Ten and - will become 5 and -
/ which will in turn be changed to . and
As and finally into and sc. Then.
striking out the numbers 10 and with
their corresponding numbers y and
49, 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 10 even
numbers. Take % and Is Going
right down the column they become II
and 30; then and 60; then and l2O
then l and 240; IL and 6 go out taking
with them 80 and GO. Add 10, l20 and
240 Answer. 375. Multiply - by Is 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 ut all in the
addition
Ii is plain tC 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 Y IL. there is no
! complication: Is and 10 in the process
become and % then and ~ and
! finally ! ana lO4. Adding IL. 26. -
and lO4 equals 1875. the correct sum
/ There can be no multiplication In fig
ures which will divide down to a place
where there are no odd numbers. foi
the final number must always OF neces
/ Sity be |. In the sum lG 4. ~
sively. while becomes =. IT, 81 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 "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
"stnmper" can be demonstrated to be
simplicity itself
Another quiZZer: why must frac.
| lions he discHrdedi How is ii that the
result will be true when several units
are cast aside For example. consider
the number a. Dividing by ? the
result will he % One whole unit Is
thrown away Twenty three becomes