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: . $1728$

$8721 - 1278 \:=\:7443$

$7443 - 3447 \:=\:3996$

$9963 - 3699 \:=\:6264$

$6642 - 2466 \:=\:4176$

$7641 - 1467 \:=\:6174$

$7641 - 1467 \:=\:6174$

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

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: . $1728$

$8721 - 1278 \:=\:7443$

$7443 - 3447 \:=\:3996$

$9963 - 3699 \:=\:6264$

$6642 - 2466 \:=\:4176$

$7641 - 1467 \:=\:6174$

$7641 - 1467 \:=\:6174$

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

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