1. Ever notice this?

Select a four-digit number (other than a multiple of 1111).

(1) Arrange the digits in decreasing order.
(2) Arrange the digits in increasing order.
(3) Subtract these two numbers.
(4) Repeat steps (1), (2), (3) with this new number.

Repeat step (4) until you are sleepy.

Exanple: .$\displaystyle 1728$

$\displaystyle 8721 - 1278 \:=\:7443$

$\displaystyle 7443 - 3447 \:=\:3996$

$\displaystyle 9963 - 3699 \:=\:6264$

$\displaystyle 6642 - 2466 \:=\:4176$

$\displaystyle 7641 - 1467 \:=\:6174$

$\displaystyle 7641 - 1467 \:=\:6174$

. . . $\displaystyle \vdots$ . . . . . . . $\displaystyle \vdots$

2. Originally Posted by Soroban
Select a four-digit number (other than a multiple of 1111).

(1) Arrange the digits in decreasing order.
(2) Arrange the digits in increasing order.
(3) Subtract these two numbers.
(4) Repeat steps (1), (2), (3) with this new number.

Repeat step (4) until you are sleepy.

Exanple: .$\displaystyle 1728$

$\displaystyle 8721 - 1278 \:=\:7443$

$\displaystyle 7443 - 3447 \:=\:3996$

$\displaystyle 9963 - 3699 \:=\:6264$

$\displaystyle 6642 - 2466 \:=\:4176$

$\displaystyle 7641 - 1467 \:=\:6174$

$\displaystyle 7641 - 1467 \:=\:6174$

. . . $\displaystyle \vdots$ . . . . . . . $\displaystyle \vdots$

Yes, you get Kaprekar numbers

3. What happens with 5 digits, 6 digits, etcetera? Are there any 4 digit nbrs that don't wind up at 6174, apart from 1111 etc?

4. Originally Posted by ray_sitf
What happens with 5 digits, 6 digits, etcetera? Are there any 4 digit nbrs that don't wind up at 6174, apart from 1111 etc?
Kaprekar Number