DIR Return Create A Forum - Home
       ---------------------------------------------------------
       gworld
  HTML https://gworld.createaforum.com
       ---------------------------------------------------------
       *****************************************************
   DIR Return to: MATH FACTS
       *****************************************************
       #Post#: 112--------------------------------------------------
       MAGIC 1089
       By: eba95 Date: July 30, 2010, 6:43 am
       ---------------------------------------------------------
       Magic 1089
       Here's a cool mathematical magic
       trick. Write down a three-digit
       number whose digits are
       decreasing. Then reverse the digits
       to create a new number, and
       subtract this number from the
       original number. With the resulting
       number, add it to the reverse of
       itself. The number you will get is
       1089!
       For example, if you start with 532
       (three digits, decreasing order), then
       the reverse is 235. Subtract 532-235
       to get 297. Now add 297 and its
       reverse 792, and you will get 1089!
       Presentation Suggestions:
       You might ask your students to see if
       they can explain this magic trick
       using a little algebra.
       The Math Behind the Fact:
       If we let a, b, c denote the three
       digits of the original number, then
       the three-digit number is 100a+10b
       +c. The reverse is 100c+10b+a.
       Subtract: (100a+10b+c)-(100c+10b+a)
       to get 99(a-c). Since the digits were
       decreasing, (a-c) is at least 2 and no
       greater than 8, so the result must be
       one of 198, 297, 396, 495, 594, 693,
       792, or 891. When you add any one
       of those numbers to the reverse of
       itself, you get 1089!
       *****************************************************