Steps to find the Kaprekar Constant :
1) Choose any 3-digit number whose digits are not all the same.
2) Using these 3 digits, form the largest and smallest numbers possible.
3)Subract the smaller number from the larger number.
4) Take the result and repeat steps 2 and 3. to illustrate :
ex. no.1 : 517 751 - 157 = 594 954 - 459 = 495
ex. no.2 : 397 973 - 379 = 594 954 - 459 = 495
ex. no.3 : 263 632 - 236 = 396 963 - 369 = 594 954 - 495 = 495
Note that each cycle ends at the number 495.
495 is called the Kaprekar Constant.

Number: 211. 211-112 = 99 99-99 = 0

Number 212 221-122= 99 99-99=0
Number: 767 776 - 677= 99 99-99 =0
Other 3 digit numbers (60 in total) that don't converge to 495 are:

100, 101, 110, 111, 112, 121, 122, 211,
 212, 221, 222, 223, 232, 233, 322, 323,
 332, 333, 334, 343, 344, 433, 434, 443,
 444, 445, 454, 455, 544, 545, 554, 555,
 556, 565, 566, 655, 656, 665, 666, 667,
 676, 677, 766, 767, 776, 777, 778, 787,
 788, 877, 878

Karmanaut:
Number: 211.
211-112 = 99
99-99 = 0


Number 212
221-122= 99
99-99=0

Number: 767
776 - 677= 99
99-99 =0

Other 3 digit numbers (60 in total) that don't converge to 495 are:

100, 101, 110, 111, 112, 121, 122, 211,
 212, 221, 222, 223, 232, 233, 322, 323,
 332, 333, 334, 343, 344, 433, 434, 443,
 444, 445, 454, 455, 544, 545, 554, 555,
 556, 565, 566, 655, 656, 665, 666, 667,
 676, 677, 766, 767, 776, 777, 778, 787,
 788, 877, 878

The three digits must be different eg 345, 985 etc there a constant for four digits number too. Do you notice that you just discover something else?
Let start with 325 re-arrange highest three digits number 532 and re-arrange to the smallest three digits number possible 235
do the maths the result is 495

Awoofawo:


The three digits must be different eg 345, 985 etc

The rule was that all the numbers must not be the same, eg 111.

there a constant for four digits number too.

Yep. 6174.

There's also one for 6 digit numbers: 549945,

There's also one for 10 digit numbers: 9975084201.

Do you notice that you just discover something else?
Let start with 325 re-arrange highest three digits number 532 and re-arrange to the smallest three digits number possible 235
do the maths the result is 495

Counter example:
656.

665 - 566 = 99

99 - 99 = 0

Karmanaut:

The rule was that all the numbers must not be the same, eg 111.


Yep. 6174.

There's also one for 6 digit numbers: 549945,

There's also one for 10 digit numbers: 9975084201.

Counter example:
656.

665 - 566 = 99

99 - 99 = 0

In your last example, you can only have 6 or 9 once. No digit should appear twice! That is general rule to theorem!

Awoofawo:


In your last example, you can only have 6 or 9 once. No digit should appear twice! That is general rule to theorem!

Okay.