Newnan herald & advertiser. (Newnan, Ga.) 1909-1915, November 20, 1914, Image 5

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CURIOUS FIGURING. It’s a Way the Russian Peasant Has. and It's an Enigma. A UNIQUE WAY TO MULTIPLY. It la Simplicity Itself and Absolutely Accurate, but the Why and Where fore of the Method and Its Results Are a Puzzle to Mathematicians. This Is not n meaningless. freaky twister of a puzzle. But It Is a puzzle. It Is the method by which Russian peasants multiply, and ns yet the boasted mental superiority of America cnnnot solve the simple riddle of the Slav. Suppose you want to multiply two numbers together. Divide one of the numbers by 2, ienorhiK the frac tions. Continue the process until the divided column reaches one. Then dou ble the other number aud continue the process until it equals in lines the first column. Then whenever a number is even in the first column strike it out, together with its corresponding num ber in the second column. Add the sec ond column, and, lo, the answer! Now. why does it do ItV There seems to be no reason for it, but what is it’/ Can you work It out? It is infallible. It has never been known to fall. 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 lax a system. There is some rule be hind It all. Take the simple multiple 12 bv 10. Obviously the answer is 120. Try it the Russian way. Place 12 in the first column aud 10 in the second. Divide 22 by 2 and multiply 10 by 2 aud place the respective answers beneath the sums from which they were derived. It will stand 0 aud 20. Dividing 0 by 2 equals 3. and multiplying 20 by 2 equals 40. Continuing. 3 divided by 2 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 It their parallels in the second column—12 and 0 will go out. leaving the last two parallel results. Ignoring the first column and addiug the num bers in the second, the answer will be the result of 40 aud 80. 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 12 to the muJtiplj*ing. It will result like this: Ten and 12 will become 5 and 24, which will in turn be changed to 2 aud 48 and finally into 1 and IH5. Then, striking out the numbers 10 and 2 with their corresponding utimbers 12 and 48, leaving the second column figures 24 and 9G to be added—this becomes 120. There Is no escaping It- No matter how large the score, it comes out right with distressing surety. Take the odd numbers. Perhaps ther* is some twist in the scheme that applies to even numbers. Take 25 and 15. Going right down the column they become 12 and 30; then 0 and CO: then 3 and 120; then 1 and 240: 12 and G go out, takiug with them 30 and CO. -Add 15. 120 and 240. Answer. 375. Multiply 25 by 15 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? It is plain to be seen that all the numbers in the second column will be even, hut by what freak of calculation are those corresponding to the even numbers In the first column ot uo con sequence when the correct sum is to be obtained? Where no even number results in the first column, ns in 15 x 13. there Is no comDllcation; 15 and 13 in the process become 7 and 20, then 3 and .52 and finally 1 and 104. Adding 13, 20. 52 and 104 equals 195. the correct sum. There can be no multiplication In fig ures which will divide down to a place where there are no odd numbers, for the final nunjber must always ofyneces 8lty be 1. In the sum 10 x 4, 10 divides itself Into 8, 4. 2 and 1 succes sively, while 4 becomes 8. 10, 32 and 64. AH of the pairs are crossed out, with the exception of 1 nnd 64. In that vase the addition ot the second column will be 04. Despite the puzzling nature of this formula, there Is some mathematical principle by which it can be explained. There Is Borne rule awaiting the fertile minds of the workers by which this “stumper" can be demonstrated to be simplicity ItselL Another qulzzer: 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 2 the result will be 23. One whole unit .is thrown away. Twenty-three becomes by the same process 11. another unit I discarded. Eleven resolves itself Into B. making the third unit passed by. The next step results in 2 nDd then 1. but I *hy Is it that these three units count I for nothing? The mere fact that the explanation 11-" near, that the whole thing is simple I l f the key can be found, is one that l r annot help bnt draw attention to this luovei means of adding.—Philadelphia 1 North American. The more 1 study the world the more I 1 am convinced of the inability of force | Tn create anything durable.—NapoUSm Ibonaparu. While the Supply Lasts A Hand - Painted Japanese Silk TEA POT” tt Pin Cushion To Every Purchaser of 10c Worth of TUXEDO Tobacco This beautiful little novelty will delight every lady who receives one. It is an excellent pin cushion and will make a dainty, attractive ornament for the dressing table. Take home a tin of TUXEDO, and take your wife this pretty “Tea Pot 5 ’ Pin Cushion. Your gift will please her—that TUXEDO leaves no odor about draperies and furniture, will also win her heartiest approval. The clean, fresh fragrance of TUXEDO pleases everyone. The Perfect Tobacco for Pipe and Cigarette Thousands of famous Americans emphatically endorse TUXEDO. They find in this mild, delightful tobacco com plete relaxation, soothing comfort and healthful enjoyment. A week’s trial of TUXEDO will convince you. That is the reason this unusual free offer is made. TUXEDO is the very best Kentucky Burley tobacco —carefully ripened, cured and mellowed—then treated by the original “Tuxedo Process,” that takes out the “bite” and “sting” absolutely, fully developing the wonderful mildness, fragrance and flavor of the Burley leaf. YOU CAN BUY TUXEDO EVERYWHERE Convenient Pouch, innerlincd _ with moisture-proof paper . . DC Famous green tin, with gold ^ rf"\ _ lettering, curved to fit pocket A V/C In Tin Humidors, 40c and 80c In Glass Humidors, 50c and90c FREE Take advantage of this Free Offer today and avoid disappointment. Dealers have only a limited supply of these Pin Cushions and cannot get more. Look for Free Offer sign in a dealer’s window — get 10c worth of TUXEDO and ask for the “Tea Pot” Pin Cushion, FREE. THE AMERICAN TOBACCO COMPANY Special Notice to Dealers: WE want every dealer in Newnan to be supplied with these Pin Cushions. All dealers who have not yet secured a supply of these Pin Cushions can do so by applying at TUXEDO headquarters, E. W. BEALL, Virginia House. Professional Cards. | W. L. WOODROOF, PHYSICIAN ANDSURGEON. Office 11 Vs Greenville street Residence 9 Perry street Office ’phone 401; Residence ’phone 451. ID. A. HANEY, PHYSICIAN ANDSURGEON. Offers his professional service to the people of Newnan, and will answer all calls town or coun ty. Office in the Jones Building. E. Broad Street Office and residence ’phone 289. THOS. J- JONES, PHYSICIAN AND SURGEON. Office on E. Broad street, near public square. Residence next door to Virginia House. T. B. DAVIS, PHYSICIAN ANDSURGEON. Office-Sanitorium building. Office 'phone 5—1 •all; residence ’phone 6—2 calls. Court Calendar. COWKTA CIRCUIT. R. W. Freeman, Judge; J. Render Terrell, So licitor-General. Meriwether—Third Mondays in February and August. Cowetfr—Flrst Mondays In March andSeptem. her. Heard—Third Mondays in March and Suptem- ber Carroll—Firs* Mondays in April and Octolier 'Iroup—First Mondays in February and Aug CITY COURT OF NEWNAN. W. A. Post, Judge; W. L. Stalling)*. Solic itor. Quarterly term meets third Mondays in Janu ary, April, July and Octolrer. BANKRUPTCY COURT. A. I). Freeman.Newnan.Oa., Referee in Bank ruptcy for counties of Coweta. Troup, Heard. Meriwether, Carroll, Douglas and Haralson. W. A. TURNER, PHYSICIAN AND SURGEON. Special attention given to surgery and diseases »f women. Office 19Mi Spring Btreet. ’Phone 230 , F. I. WELCH, PHYSICIAN AND SURGEON. Office No. 9 Temple avenue, opposite public «chool building. 'Phone 234. THOS. G. FARMER, JR., ATTORNEY AT LAW Will give careful and prompt attention to all egal buaines entrusted to me. Money to loan Office in court-house. Laundry Lists for sale here. For Shoe and Har ness Repairing and NEW HARNESS go to A. J. BILLINGS 6 SPRING ST. Only high-class materials used in my work. Give us a trial order on job printing. Atlanta and West Point RAILROAD COMPANY ARRIVAL AND DEPARTURE OFTRAINS AT NEWNAN. GA. EFFECTIVE NOV. 1, 1914. Subject to change and typographical errors. No. 3ft . 7:2ft a. m. No. 19 . 7:50 a. m. No 18 . U :4ft a. m. . 10:40 a. m. No. 39. . 3:17 p. m. No 20 , 0:3ft p. in . No 34 . 5 :37 p. in. No 38 No 40 19 :40 fl . m . 12:52 p. in. No. 17 . 1:12p.m. No. 41 . 7:20 p. in. No. 37 . 0:23 p. m. No. 30 .10:28 I*, in. All trains daily. Odd numbers, HMiihhound; even numbers, north bound. Old newspapers for sale at this office at 25c. per hundred. T. S. PARROTT Insurance—All Branches Representing Fire Association, of Philadelphia Fidelity and Casualty Co., of New York American Surety Co., of New York Mutual Benefit Life Insurance Co., of Newark, 'N. J. 14 1-2 Greenville st., Over H. C. Glover Co. CENTRAL OF GEORGIA RAILWAY CO. CURRENT SCHEDULES. ARRIVE FROM Griffin 11:10 A.M. 7:17 p, m. ’ Chattanooga 1:40 p. M. Oedartown 6:36 A. M. Col urn boa 9:00 a M. , 8:36 p.m. DEPART FOR Griffin 1-.4AP. M. Griffin 0:3b a. m, Chattanooga 11 :|0 a. M . Cedartown 7:17 p.m. Columbus 7:40 A.M.