The daily Alaskan., 1915-01-29
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 It's Results
 Are a Puzzle to Mathematcians.
 This is not a meaningless, freak3 twister of a puzzle. But it Is puzzle. It Is the method by which Russian peasants multiply, and as yet the boasted mental superiority of America candot solve the simple riddle of the SlaV.
 Suppose you want to multiply two numbers together. Divide one of the numbers by ?, ignoring the frae' tions. Continue the process until the divided column reaches one. Then dou- ble the other number and continue the process until 1t equals in lines the first column. Then whenever number is even in the first column strike it out, together with its corresponding num- Der in the second column. Add the sec- Und column. and, 10, the answeri Now. why does it do 1t? There seems to be no reason for it, but what is it? Can you work it out?
 It is infallibe. 1t has never been known to fail. But what principle Of mathematics is behind it 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 ak q system. There is some rule be hind It ali.
 Take the simple multiple l2 by 10. Obviously the answer is l2O. Try it the Russian way Place F in the first column and 10 in the second. Divide l2 by ? and multiply 10 by 7 aud place the respective answers beneath the sums from which they were derived. 1t will stand 6 and 20. Dividing by 7 equals 3, and multiplying 70 by 7 equals 10 Continuing, 3 divided by Z and throwing away all fractions will be I. 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 l2 and 6 will go out, leaving the last two parallel results. Ignoring the first column and adding the mum bers in the second. the answer will be the result of 4U and 80. or l2O.
 The questions are: Who ever worked If out? How did he start?
 Now try working the problem by put ting 10 in the first column and sub ;ecting it to the dividing and F to the multiplying It will result like this; Ten and l2 will become and "A. which will in turn be changed to and 4S and finally into l and 96. Then. striking out the numbers 10 and with their corresponding numbers F ana +S, leaving the second column figures 24 and 9G to be added-this becomes l2O.
 There Is no escaping it. No matter how large tbe 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 25 and 15. Going right down the column they become F and 30; then and 60; then 3 and l2O: then and 24O; l2 and go out, taking with them 30 and 60. Add l5, l2O and 24O. Answer, 3T5. Multiply 25 by b ac. cording to our methods. Correct-3I5.
 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?
 It 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 seouence when the correct sum is to be obtained?
 Where no even number results In the first column, as in l5 X 13, there is no complication; 15 and l3 in the process become and 2G, then and 52 and finally 1 and 104. Adding l3. 26. 52 and 1O4 equals l95. 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 I. In the sum l6 4, l6 divides itself into S. 4. ? and success, sively, while becomes s, l6. 32 and ct. All of the pairs are crossed out, with the exception of and G4. In that ease 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 "stnmper" can be demonstrated to be simplicity itself.
 Another quizzer: Why must frac' tions be discarded? 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 Il, another unit discarded. Eleven resolves itself into B. making the third unit passed by The next step results in and then l, but