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Kaprekar transformation

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1 Nov 2011 07:41:53 IST
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1 Nov 2011 07:41:53 IST
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Kaprekar transformation
Engineering Entrance , JEE Main , JEE Advanced , General Knowledge

The Kaprekar transformation is defined as follows for three-digit numbers:

1. Start with a three-digit number with at least two digits different.
2. Arrange the digits in ascending and then in descending order to get two three-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2.

Repeating this process will always reach 495 in a few steps. Once 495 is reached, the process stops because 954 – 459 = 495.

### Example

For example, choose 589:

985 − 589 = 396
963 − 369 = 594
954 − 459 = 495

The only three-digit numbers for which this function does not work are repdigits such as 111, which give the answer 0 after a single iteration. All other three-digits numbers work if leading zeros are used to keep the number of digits at 3:

211 – 112 = 099
990 – 099 = 891 (rather than 99 - 99 = 0)
981 – 189 = 792
972 – 279 = 693
963 – 369 = 594
954 − 459 = 495

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