Kaprekar's Constant for 4-Digit Numbers: 6174
Kaprekar's constant of 6174 is notable for the following property:
1) Take any four-digit number with at least two digits different.2) Arrange the digits in ascending and then in descending order to get two four-digit numbers, adding leading zeros if necessary.
3) Subtract the smaller number from the bigger number.
4) Go back to Step #2.
The above operation will always reach 6174 in at most seven steps and it stops there.
Once 6174 is reached, the process will keep yielding 7641 – 1467 = 6174.
The only four-digit numbers for which this function does not numbers whose digits are all identical (e.g., 2222) as they yeild zero after a single iteration.Example #1:
3165 yields:
6531 – 1356 = 5175
7551 – 1557 = 5994
9954 – 4599 = 5355
5553 – 3555 = 1998
9981 – 1899 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174
Example #2:
1000 yields:
1000 – 0001 = 0999
9990 – 0999 = 8991
9981 – 1899 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174
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