u/onl-li

The fraction 1/7 is:

0.142857142857142857...

Now take the repeating part: 142857

Multiply it:

142857 × 2 = 285714
142857 × 3 = 428571
142857 × 4 = 571428
142857 × 5 = 714285
142857 × 6 = 857142

It’s the same six digits, just rotating around.

Then the magic breaks beautifully:

142857 × 7 = 999999

This is called a cyclic number, which sounds like something a wizard would write on a chalkboard before vanishing.

Pick any 3-digit number where the first and last digits are different by at least 2.

Now do this:

1. Reverse the number.
2. Subtract the smaller number from the larger one.
3. Reverse the answer.
4. Add those two numbers together.

You will always get 1089.

Example:

742 reversed is 247.

742 − 247 = 495

495 reversed is 594.

495 + 594 = 1089

Try another one:

931 − 139 = 792

792 + 297 = 1089

It feels like a magic trick, but it is just digit math being sneaky. No matter what valid 3-digit number you start with, the subtraction step creates a number whose digits are arranged in a way that forces the final sum to become 1089.

This is called Kaprekar’s routine. For any 4-digit number with at least two different digits, the process eventually lands on 6174, known as Kaprekar’s constant.

Example:

Start with 3524
5432 - 2345 = 3087
8730 - 0378 = 8352
8532 - 2358 = 6174

Once you hit 6174, it loops forever:
7641 - 1467 = 6174