Kaprekar's constant is the number 6174, which has a fascinating property discovered by Indian mathematician D. R. Kaprekar.
Here's how it works (for 4-digit numbers):
Start with any four-digit number, using at least two different digits.
Arrange the digits in descending and then in ascending order to get two numbers.
Subtract the smaller number from the larger one.
Repeat the process with the result.
After a few iterations (at most 7), you’ll always arrive at 6174. Once you reach 6174, the process becomes a loop:
7641 - 1467 = 6174
Why does Kaprekar's routine always converge to 6174 for four-digit numbers?
Is there a similar constant for numbers with different digit lengths?
What mathematical properties make 6174 unique?