Question

FUN ACTIVITY
Take any four digit number, follow these steps,
and you'll end up with 6174.
1. Choose a four digit number (the only condition
is that it has at least two different digits).
2. Arrange the digits of the four digit number in
descending then ascending order.
3. Subtract the smaller number from the bigger
one.
4. Repeat
Eventually you'll end up at 6174, which is known
as Kaprekar's constant. If you further repeat the
process you'll just keep getting 6174 over and
over again.​

Answer 1

Kaprekar's constant:

• The only four-digit integers for which Kaprekar's formula falls short of 6174 are repdigits like 1111, which provide the value 0000 after just one repetition. All additional four-digit integers eventually reach 6174 if leading zeros are employed to maintain the number of digits at 4. It is crucial to treat 3-digit numbers with a leading zero when dealing with numbers that have three identical numbers and a fourth number that is one number higher or lower (such as 2111); for instance, 2111 - 1112 = 0999, 9990 - 999 = 8991, 9981 - 1899 = 8082, 8820 - 288 = 8532, and 8532 - 2358 = 6174.
• There may be equivalent fixed points for digit lengths other than four; for example, if we use 3-digit numbers, the majority of sequences—aside from repdigits like 111—will end in the value 495 after a maximum of 6 repetitions. These figures (495, 6174, and their equivalents in other digit lengths or in bases other than 10) are also referred to as "Kaprekar constants" at times.

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