The Value of Mathematical Tricks

    While tricks are not universally applicable, they can come in handy in certain situations. Sure you can slogg through dimensional analysis or other universal rules to solve a great many problems, but often a trick can do the work MUCH easier.

    Let me give you three examples:

• Is this number evenly divisible by three: 49,672,069,376,593,597
  • You could slogg through the long-division to check it out to see whether or not you get a remainder. BUT...
  • There is a faster way: add up all the digits and do they sum to a number that is divisible by three?
  • Let's see: 4+9+6+7.... = 111, which is, of course, evenly divisible by three since 1+1+1=3

• Is this number evenly divisible by eleven: 49,672,069,375,593,597
  • The trick here is to sum all the even digits and substract the sum of all the odd digits. If the answer is zero, the number is evenly divisible by 11.
  • (4+6+2+6...)-(9+7+0+9....) = 48 - 48 = 0
• Much more frequently than above, you are called upon to multiply two numbers that differ by 2 - such as 4 x 6, or 14 x 16, or 39 x 41. The trick here is to square the number in the middle and then substract one.
  • 4 x 6 = 5² - 1 = 25 -1 = 24
  • 14 x 16 = 15² - 1 = 225 - 1 = 224
  • 39 x 41 = 40² - 1 = 1600 -1 = 1599
  • The reason for this you may remember from high school algebra:
    (X-1)(X+1) = X² - 1

  Now let's look at some tricks regarding making solutions.