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Interesting... Thu, 09 October 2008 12:23 Go to next message
Ron is currently offline Ron

 
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Select any 4-digit number in which there are at least 2 different digits (e.g. 4474 is OK but not 4444). Arrange the digits in increasing order and also in decreasing order (e.g. chosen number 3395 arranged as 3359 and 9533). Subtract the smaller number from the larger one. Re-arrange the digits of this answer as before - increasing and decreasing order - and again subtract the smaller from the larger. Keep repeating these steps and see what happens.





Ron Miller
Stars! AutoHost

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Re: Interesting... Thu, 09 October 2008 18:07 Go to previous messageGo to next message
Effluviant Walrus is currently offline Effluviant Walrus

 
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3395 -> 9533-3359 = 6174 -> 7641-1467 = 6174

2426 -> 6422-2246 = 4176 -> 7641-1467 = 6174

8547 -> 8754-4578 = 4176 -> 7641-1467 = 6174

4117 -> 7411 - 1147 = 6264 -> 6642-2466 = 4176 -> 7641-1467 = 6174

What happens when a number has a 0 in it? That kind of screws up the sequence (or maybe it doesn't, I haven't taken anything past 4 or 5 steps).

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Re: Interesting... Thu, 09 October 2008 18:33 Go to previous messageGo to next message
Effluviant Walrus is currently offline Effluviant Walrus

 
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Hmm, it seems that 0s don't matter. I wrote a simple Python program to test this; all four digit numbers except for 1111,2222,etc. come out to 6174.

[Updated on: Thu, 09 October 2008 18:33]

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Re: Interesting... Thu, 09 October 2008 19:01 Go to previous messageGo to next message
Effluviant Walrus is currently offline Effluviant Walrus

 
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3-digit numbers seem to come out to 495.

Every 5-digit number I've tried seems to get stuck in one of two cycles:

71973 -> 83952 -> 74943 -> 62964 -> 71937...

or

82962 -> 75933 -> 63954 -> 61974 -> 82962...

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Re: Interesting... Fri, 10 October 2008 01:48 Go to previous message
Micha

 

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Registered: November 2002
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Looks like somebody has nothing better to do while waiting for the next gen. Wink

mch

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