Introduction

1. Suppose 4-figure decimal A.
2. Arrange the 4 numbers in descending order, then let the arranged number L as follows.  

   

   where a,b,c,d are one-figure numbers and

   

3. As well, arrange the 4 numbers in ascending order, then let the ascending number S as follows.

   

4. Let the difference L-S as A=L-S.  
5. Repeat 2-4.

The above algorithm gives the trivial number 0 or the non-trivial number 7641 within 8 steps.

In short,

1. Make , from A.  
2.  

If you repeat i and ii, you will finally get a fixed number A=7641.

e.g.    (Suppose 3982)

   A=3982 ---> L=9832, S=2389     L-S = 7443
   A=7443 ---> L=7443, S=3447     L-S = 3996
   A=3996 ---> L=9963, S=3699     L-S = 6264
   A=6264 ---> L=6642, S=2466     L-S = 4176
   A=4176 ---> L=7641, S=1467     L-S = 6174

           A=6174