Tuesday, January 11, 2011

Mentat training

For Christmas I received a "Lightning Calculation" calendar. It's a wall calendar that explains techniques for performing mental calculations, such as finding what day of the week a date fell on and performing fast multiplications. In addition, there are historical bits on famous individuals who have been able to perform incredibly complicated mental calculations. I've spent at least half an hour in my office every morning reading through it and trying the practice problems (of which there are hundreds, if not over a thousand).

Something I've learned is the anchor method for multiplication of two, two-digit numbers. It may seem complicated at first, but it's actually incredibly powerful. First consider the product to be found as a product of two sums, each one "anchored" to a nearby round number. This product can be written as

(a + c)(a + d) = a^2 + ac + ad + cd
(a + c)(a + d) = a(a + c + d) + cd

where a is the anchor. From the right-hand-side of the last line above, the anchor is multiplied by itself with the sum or difference terms c and d. Then the correction term cd is added or subtracted, depending on whether the signs of c and d were the same or not, respectively.

For example, consider the product 17 * 18. This can be written as (20 - 3) * (20 - 2) = 20(20 - 3 - 2) + (2 * 3) = 306. The algorithm is easy to carry out because the first product is 20 * 15 = 300. Cool stuff.

The information for the calendar can be found here: http://myreckonings.com/wordpress/2010/11/22/a-2011-%E2%80%9Clightning-calculation%E2%80%9D-calendar/. It's very nicely done and I highly recommend it for all those mentats in training =)