Back to the Zeros - Netflix
Runtime: 60 minutes
Back to the Zeros - 6174 (number) - Netflix
6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar. This number is notable for the following property: Take any four-digit number, using at least two different digits. (Leading zeros are allowed.) Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary. Subtract the smaller number from the bigger number. Go back to step 2 and repeat. The above process, known as Kaprekar's routine, will usually reach its fixed point, 6174, in at most 8 iterations. Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174. For example, choose 3524: 5432 – 2345 = 3087 8730 – 0378 = 8352 8532 – 2358 = 6174 7641 – 1467 = 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.
Back to the Zeros - Other "Kaprekar constants" - Netflix
Note that there can be analogous fixed points for digit lengths other than four, for instance if we use 3-digit numbers then most sequences (i.e., other than repdigits such as 111) will terminate in the value 495 in at most 6 iterations. Sometimes these numbers (495, 6174, and their counterparts in other digit lengths or in bases other than 10) are called “Kaprekar constants”.
Back to the Zeros - References - Netflix