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Saturday, January 15, 2011

Weird Numbers - Kaprekar's constant

Amaze your nerd friends and win bar bets:

6174 is known as Kaprekar's constant after the Indian Mathematician D. R. Kaprekar. This number is notable for the following property:

Take any four-digit number, using at least two different digits (Leading zeros are allowed.)
  1. Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary. 
  2. Subtract the smaller number from the bigger number.
  3. Using the result, go back to step 1.

The above process, known as Kaprekar's routine, will always reach 6174 in at most 7 iterations. Once 6174 is reached, the process will continue yielding:
7641 – 1467 = 6174. 

For example, choose 3524:
Iteration:
  1. 5432 – 2345 = 3087
  2. 8730 – 0378 = 8352
  3. 8532 – 2358 = 6174
  4. 7641 - 1467 = 6174

Using the above process,  the number "0050" takes 7 iterations to reach 6174. 
Try it and see!

(Hat tip to Darren at http://rightontheleftcoast.blogspot.com/2011/01/how-would-someone-figure-this-out.html)

1 comment:

Anonymous said...

I like this! I copied it to use with older students when I need something to occupy them when they have their work done. Thanks, NE. sub