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R F O SN LBIEIY

74 THE FASCINATION OF NUMBERS

digits, the first digit is written to the left, and the second
digit is written to the right of the diagonal. Next, the digits
within the squares are added diagonally irrespective of the
squares, and the results are written in order backwards along
the bottom and continuing upwards along the left-hand side
of the quadrilateral. As in ordinary addition, tens are carried
forward to the next diagonal.

The answer, 207336, can then be read off starting at the
top of the left-hand side and continuing along the bottom of
the quadrilateral.

" There is another old method, whereby any two numbers
may be multiplied together, which involves only actual mul-
tiplication by the number 2. The procedure, known as
Russian Multiplication, is as follows. Form two columns,
headed respectively by the two numbers to be multiplied; it
does not matter which number goes in which column. The
number in the left column is progressively divided by 2, any
remainders being ignored. The number in the right column is
in equal stages progressively multiplied by 2. When the
number 1 is reached in the left column, both columns are
ruled off. All even numbers in the left column are crossed out,
as also are the numbers in the same lines in the right column.
The remaining numbers in the right column are then added
and their total gives the answer to the multiplication.

397 x 196 would be calculated:

397 196
198 392
99 784
49 1568
24 3136
12 bz
6 o544
3 25088
I 50176

 

Total 77812 =397 X 196