The daily Alaskan., 1914-12-07
CURIOUS FIGURING.
It's a Way the Russian Peasant
 Has, and It's an Enigma.
A UNIQUE WAY TO MULTIPLY.

fore of the Method and Its Results
 Are Puzzle to Mathematicians.
 This is not a meaningless, freaky twlster of puzzle But it is a 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- ble the other number and continue the process until it equals in lines the first column. Then whenever q 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 dees it do 1t? There seems to be no reason for it, but what is it? Can you work it out?
 It is infallibIe. It 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 generali- ties. Mathematics is not built upon so lax q system. There is some rule be- hind it all.
 Take the simple multiple 12 by TO- Obviously the answer is 120. Try 1t the Russian way. Place l2 in the first column and 10 in the second. Divide F by and multiply 10 by and place the respective answers beneath the sums from which they were derived. It will stand and 20. Dividing by 2 equals 3, and multiplying 20 by 2 equals 40. Continuing, 8 divided by ? and throwing away all fractions will be l, while 40 multiplied by ? 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 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 1ecting it to the dividing and F to the multiplying. It will result like this: Ten and F will become 5 and 24 which will in turn be changed to 2 and 4S and finally into 1 and 96. Then, striking out the numbers 10 and with their corresponding numbers F and 4S, leaving the second column figures 24 and 96 to he 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 numbers. Take 9 and 15. Going right down the column they become F and 30: then and GO; then and 12O; then and 24O; 12 and 6 go out, taking with them 30 and 60. Add b, 12O and 24O. Answer. 375. Multiply 9 by 15 ac- cording to our methods. Correct-3Io.
 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 10 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 tue correct sum is to be obtained?
 Where no even number results in the first column. as in 15 13, there is no complication; 15 and 13 in the process become I and PC. then 3 and 52 and finally and 1O4. Adding 13, 26, g md l04 equals 195. 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, 16 divides itself into 8. 1, and l success sively, while 4 becomes s, 16, 32 and G4. All of the pairs are crossed out, with the exception of and 64. 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 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 discarded2 How Is it that the result will be true when several units are cast aside? For example, consider the number 47. Dividing by the result will be 23. One whole unit is thrown away. Twenty-three becomes by the same process II, another unit discarded. Eleven resolves itself into 5, making the third unit passed by. The next step results in 2 and then l, but why is it that these three units count for nothing?