Kaprekar's Constant
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6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following rule: (1) Take any four-digit number, using at least two different digits. (Leading zeros are allowed.) (2) Arrange the 4 digits from highest to least to form the greatest number possible with those 4 digits. Then do the opposite and arrange those digits from least to highest to form the smallest number. Subtract the smaller number from the bigger number. Go back to step 2 and repeat. The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations. Once 6174 is reached, the process will continue yielding 6174. The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single iteration. All other four-digit numbers eventually reach 6174 if leading zeros are used to keep the number of digits at 4.
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