Salute to great Karpekar

The following note I am writing is for real maths lovers i.e. who love to learn new concepts .

I want to write about "Karpekar's Constant"

1) First I would like to mention a simple experiment of playing with numbers.

2) Take any 4-digit number. Eg: Lets take 6384

3) Now arrange this number in its descending order of digits. like: 6384 will be written as 8643... [let this number be 'x']

4) Now arrange the original number in its ascending order of digits. like 6384 will be written as 3468....[let this number be 'y']

5) Now subtract numbers x and y like x-y=8643-3468=5175

6) Now do the same process with the 5175 i.e. arrange in descending order and then in ascending order and then subtract.

7) You will get another number.

8) Do this till you get 6174 as the number.

9) Now if you carry out this process with 6174 then you will observe that in any case this number (6174) remains constant.

10) This number is known as the "Karpekar's Constant".

The specialty of this number is that if you treat any 4-digit number (using at least two different digits) by the above given process then within 7 steps you get the Karpekar's Constant.

If you can construct any sums based on this concept then please write me on atharvabagul2000@gmail.com

Thank You

#NumberTheory #Karpekar'sConstant

Note by Atharva Bagul
5 years, 7 months ago

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Comments

See this

Pi Han Goh - 5 years, 7 months ago

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Sorry I didn't see that problem but this is the general form popularly known as Karpekar' Constant

Atharva Bagul - 5 years, 7 months ago

Even I posted the same thing long time ago.

See this.

Akshat Sharda - 5 years, 3 months ago
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