>Hi all,
>
>I''m searching a prove of a little problem.
>You take a four digit number where not all digits are equal such
>5957 and reorder the digits such that the biggest digit is at the
>first place, the second at the second place etc. Then subtract the
>smallest possible reoredering from the the other number and restart
>the process. As result you will get 6174.
>
>Example: 5957
>
>9755-5579=4176; 7641-1467=6174; 7641-1467=6174
>
>If you take a five digit number, the result will be a period of
>74943, 62964, 71973, 83952. With six digits it will be a period too.
>Have anyone got a prove tor that?
For a poor man's proof, I wrote a quick app to exhaustively search.
The results differ slightly from your assertion:
3 digit numbers: 495->495
4 digit numbers: 6174->6174
5 digit numbers:
96988 #s: 74943->62964->71973->83952->74943
3002 #s: 59994->53955->59994 (example: 16531)
6 digit numbers:
941993 #s: 851742->750843->830862->862632->642654->420876->851742
56181 #s: 631764 (example: 142486)
1816 #s: 549945 (example: 551616)
7 digit numbers:
9999990 #s: (all possible):
8649432->7519743->8429652->7619733->8439552->
7509843->9529641->8719722->8649432
8 digit numbers:
86326632->64326654->43208766->85317642->75308643->84308652->86308632
or
86526432->64308654->83208762
or
97508421
(I didn't let it finish, so don't have the counts of each sequence)
-- Tim
Tim Charron
[EMAIL PROTECTED]
[EMAIL PROTECTED]
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