Thursday, September 16, 2010

Kaprekar’s Constant-A unique constant in Mathematics by an Indian, D.R. Kaprekar.

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Mathematics always have been a nightmare for majority of students during school days. Learning various angles, remembering trigonometry tables was not everybody’s cup of tea. Somehow, we managed to pass these initial classes. However, many used to very brilliant in Mathematics and answers were just on their tips. While studying Mathematics and other Science subjects we have come across many constants like Planck’s constant, c=speed of light etc.

Here, I am going to tell you a unique and interesting constant in Mathematics that was discovered in the year 1946 by D.R. Kaprekar. This constant is known as Kaprekar’s Constant. The value of the Kaprekar’s Constant is equal to 6174. There is a very interesting procedure of calculations after which we always get Kaprekar’s constant as final value.

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D.R. Kaprekar

Procedure of getting Kaprekar’s Constant:

1. Take any four digit number of your choice, but the number should not be repetitive numbers like 1111, 2222, 3333 etc. Let’s suppose we take 6359.

2. Now arrange this number in descending order (9653) and ascending order (3569) and subtract the ascending order values from descending order one. That is, 9653-3569=6084.

3. Keep on repeating step 2 for the result you obtain every time. That is now we have to take descending and ascending order values of 6084 which are 8640 and 0468 respectively.
(a) 8640-0468=8172.
(b) 8721-1278=7443.
(c) 7443-3447=3996.
(d) 9963-3699=6264.
(e) 6642-2466=4176.
(f) 7641-1467=6174 (Kaprekar’s Constant).

Performing these steps for any value of 4 digit number will give Kaprekar’s Constant=6174 in any of the steps. We cannot take repetitive numbers like 1111, 9999 etc. because it will result in 0 values at the very first step.

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