## Saturday, 7 June 2008

### The Kaprekar Number

The number 6174 is called the Kaprekar number.

The Indian mathematician D.R.Kaprekar made the following discovery in 1949.

(1) Take a four-digit number with different digits (acbd with .a<b<c<d)..

(2) Form the largest and the smallest number from these four digits (dcba and abcd)..

(3) Find the difference of these digits. Maybe this is 6174 (dcba - abcd = 6174?).

If it is not, form the largest and the smallest  number from the difference and subtract these numbers again. You may have to repeat this procedure.

The end result is always 6174, but there are no more than 7 steps.

1st example: Take the number 1746.

1st step:  7641 - 1467 = 6174

2nd example: Take the number 5644.

1st step:  6544 - 4456 = 2088

2nd step:  8820 - 0288 = 8532

3rd step:  8532 - 2358 = 6174

3rd example: Take the number  7652.

1st step:  7652 - 2567 = 5085

2nd step:  8550 - 0558 = 7992

3rd step:  9972 - 2799 = 7173

4th step:  7731 - 1377 = 6354

5th step:  6543 - 3456 = 3087

6th step:  8730 - 0378 = 8352

7th step:  8532 - 2358 = 6174