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Ah, the Kaprekar Constant — a beautiful bit of mathematical magic! ✨
Here’s the idea:
🧮 The Kaprekar Constant (6174)
The Kaprekar Constant is 6174, discovered by Indian mathematician D. R. Kaprekar in 1949.
It’s known for its fascinating property in a process called Kaprekar’s Routine.
⚙️ The Kaprekar Routine (for 4-digit numbers)
- Start with any 4-digit number that has at least two different digits.
(e.g. 3524) - Arrange the digits:
- In descending order → 5432
- In ascending order → 2345
- Subtract the smaller number from the larger:
5432 − 2345 = 3087 - Repeat the process with the new number (3087):
- Descending: 8730
- Ascending: 0378
→ 8730 − 0378 = 8352 - Do it again:
- Descending: 8532
- Ascending: 2358
→ 8532 − 2358 = 6174
💫 The Magic
Once you reach 6174, the process stays there forever:
7641 − 1467 = 6174
No matter which 4-digit number you start with (as long as it isn’t a repdigit like 1111, 2222, etc.), you’ll reach 6174 in at most 7 steps.
🧠 Fun facts
- There’s also a 3-digit version of this process — its constant is 495.
- The Kaprekar routine is an example of digit manipulation mathematics, a field where Kaprekar discovered several beautiful patterns.
Would you like me to show a Python-style example or table of how different numbers converge to 6174 step by step?
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