[Edu-sig] Mystery Number 6174
Tim Peters
tim.peters at gmail.com
Mon Jul 7 00:07:17 CEST 2008
[Massimo Di Pierro]
> This is interesting
[Tim Peters]
>> trying 7 digits
>> 0000000 reached by 10 inputs
>> 8429652 reached by 9999990 inputs
[Massimo]
> The probability of a single fixed point in in 10**7 numbers is quite small.
Well, note that the program was looking for cycles, not for fixed
points. In fact, the only 7-digit fixed point is 0000000. 8429652 is
not a fixed point, but turns out it's part of a cycle everything other
than multiples of 1111111 eventually falls into:
8429652 -> 7619733 ->
8439552 -> 7509843 ->
9529641 -> 8719722 ->
8649432 -> 7519743 ->
8429652
It may be easier to think about the 2-digit results, where again 00 is
the only fixed point, but everything other than multiples of 11
eventually falls into a cycle containing 09:
09 -> 81 -> 63 -> 27 -> 45 -> 09
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