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   number strings and sub-strings
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   Author  Topic: number strings and sub-strings  (Read 424 times)
Brian
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number strings and sub-strings  
« on: Aug 26th, 2004, 1:38pm »
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consider all m-digit strings made of n different numbers.  for example, with (m,n)=(2,3), they are:
 
11    21    31
12    22    32
13    23    33
 
note that there are always n^m different strings.  now consider a longer string containing these m digits.  the minimum size it has to be to be able to contain all the m-digit substrings would be n^m + n - 1.  for example, with (m,n)=(2,3) again, one possible string would be 1121322331.  is it always possible to construct such a string with this minimum length?
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william wu
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Re: number strings and sub-strings  
« Reply #1 on: Aug 26th, 2004, 4:18pm »
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Hi Brian. Thanks for the puzzle, but this is already on the site under a unnecessarily complicated problem description written by yours truly. See
 
http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_har d;action=display;num=1063089039
 
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brian
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Re: number strings and sub-strings  
« Reply #2 on: Aug 27th, 2004, 9:34am »
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o sorry.  but i didnt see a clear proof of the general case over there, so do you or anyone else have that?
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