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.)
- Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
- Subtract the smaller number from the bigger number.
- 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:
7641 – 1467 = 6174.
For example, choose 3524:
Iteration:
- 5432 – 2345 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 = 6174
- 7641 - 1467 = 6174
Using the above process, the number "0050" takes 7 iterations to reach 6174.
Try it and see!
Try it and see!
(Hat tip to Darren at http://rightontheleftcoast.blogspot.com/2011/01/how-would-someone-figure-this-out.html)
1 comment:
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
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