205. 6174

I was reading “Our Scientists”; National Book Trust Publication of 1986. Reading this book was long overdue, so I was determined to finish it. As the title says, the book introduces various scientists – from past to present – very briefly. If NBT has brought out this book for children, I wonder whether they would find this engrossing enough.

I came across an article where a process of finding a “Constant” is described.

Let us see it.

1. Take any four digit number; which uses at least two different digits. Numbers like 1111, 2222 will not serve the purpose. (I write 4632)
2. Arrange the digits in descending order. (I write 6432)
3. Reverse the order of the digits. (I write 2346)
4. Subtract step 3 from step 1. (4632-2346= 2286)
5. For the number arrived at step 4, repeat steps 2 to 4.

So, I arrange the digits in descending order: 8622

Then I reverse the order of the digits: 2268

I subtract: 8622-2268= 6354

Repeat steps 2 to 4.

Here it goes.

6543

3456

6543-3456 = 3087

Repeat steps 2 to 4.

Here we go.

8730

0378

8730-0378=8352

Go on.

8532

2358

8532-2358=6174

  

Repeat.

7641

1467

7641-1467= 6174

Oh! 6174 is reappearing.

Let us try another number;

9423

9432-2349=7083

8730-0378=8352

8532-2358=6174

7641-1467=6174

Hmm...

Third try:

8417

8741-1478=7263

7632-2367=5265

6552-2556=3996

9963-3699=6264

6642-2466=4176

7641-1467=6174

This number 6174 is known as Kaprekar’s Constant.

I don’t know what the constant is used for. But it is fun.

I don’t know how and why Mr. Kaprekar arrived at this constant. Need to know more about him and his work.

For those who are interested, here are some links to know more about the number and the man.

http://en.wikipedia.org/wiki/6174_(number)

http://en.wikipedia.org/wiki/D._R._Kaprekar

http://www.math.hmc.edu/funfacts/ffiles/10002.5-8.shtml