Submitted by Michael Frankfort @mfrank_76
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Kaprekar’s Constant is a fascinating mathematical phenomenon involving four-digit numbers. Here’s how it works:
- Take any four-digit number (with at least two different digits).
- Rearrange the digits to form the largest and smallest possible numbers.
- Subtract the smaller number from the larger one.
- Repeat the process with the resulting number.
No matter which number you start with, you will eventually reach the number 6174 in at most seven steps, and then it will stay at 6174. This number is known as Kaprekar’s Constant.
For example, starting with 3141:
- 4311 – 1134 = 3177
- 7731 – 1377 = 6354
- 6543 – 3456 = 3087
- 8730 – 0378 = 8352
- 8532 – 2358 = 6174
- 7641 – 1467 = 6174
The process always leads to 6174, demonstrating a unique cycle in base 10 for four-digit numbers. This phenomenon highlights the intriguing patterns and cycles that can occur in mathematics.