From: rusin@washington.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: Trachtenberg Math Date: 21 Mar 1995 03:40:02 GMT In article <3kc8mj$f7s@ns1.arlut.utexas.edu>, Shirlene Pearson wrote: [in re: 'The Trachtenberg Speed System of Basic Mathematics'] >Sorry, I haven't heard of this particular system, but if it's >like most of the tricks to gain efficiency it might suffer from >a lack of generality. That is, the tricks tend to be for very >special circumstances and are not rules that can be widely applied. >That is one reason such short cuts tend to be of interest only >to those who are already quite knowledgeable, and fast, when it >comes to math! In this category I'll toss out the following method for multiplying one-digit numbers greater than 5. On each hand, label your fingers "6" thru "10" (yes, I know that's not a one-digit number) from the thumb outwards. To multiply two of these numbers together, place together the corresponding fingers from the two hands and read off the two-digit answer as follows: the first digit is the number of fingers from thumb to thumb, crossing over from one hand to the other where the fingers touch. (Don't forget to count the touching fingers as well). the second digit of the answer is the product of the numbers of fingers not yet counted on each hand. Example: to compute 7 x 8, touch the left index finger to the right middle finger. Count left thumb, left index, right middle, right index, right thumb: 5 fingers. Now multiply 3 (middle, ring, pinky on left) times 2 (ring and pinky on right) to get the second digit, 6. The results are accurate for {6,...,10} x {6,...,10}, although the cases 6 x 6 and 6 x 7 need to be properly interpreted. This is not "accidental"; it works for n-fingered beasts who count base n (as long as they have those fingers on precisely 2 hands!) dave