What is Kaprekar's constant ?

 6174 is known as Kaprekar's constant, a magical number in mathematics. The "magic" lies in a process discovered by the Indian mathematician Dattatreya Ramchandra Kaprekar in 1949. Here's how it works:

The Kaprekar Routine:

1. Take any four-digit number, using at least two different digits. (If the number has fewer than four digits, pad it with leading zeros to make it four digits).
2. Arrange the digits in descending order and then in ascending order to get two four-digit numbers.
3. Subtract the smaller number from the larger number.
4. Repeat the process with the result.

No matter what four-digit number you start with, after a few iterations, you'll always reach 6174. Once you reach 6174, repeating the process will continue to yield 6174. This is why 6174 is often called a "self-repeating number" or Kaprekar's constant.

Example:

Start with 3524:

• Descending: 5432
• Ascending: 2345
• Subtract: 5432 - 2345 = 3087

Now repeat the process:

• Descending: 8730
• Ascending: 0378
• Subtract: 8730 - 378 = 8352

Continue:

• Descending: 8532
• Ascending: 2358
• Subtract: 8532 - 2358 = 6174

From here, any further iteration gives 6174, no matter the starting number.

Background:

Kaprekar, a mathematician from India, had a deep interest in number theory and developed several interesting results, though he worked without formal affiliation to a major academic institution. Despite his achievements, Kaprekar's work was often overlooked by the mathematical community, but over time, his discovery of 6174 has fascinated both mathematicians and amateur enthusiasts.

The routine works because of the unique properties of base 10 arithmetic and the way subtraction of rearranged digits causes numbers to converge to this constant, making 6174 a sort of attractor in this system.