Edited by brifri238, 16 November 2012 - 12:07 PM.
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A Boggle-like Challenge
Posted 16 November 2012 - 09:11 PM
into a bit of trouble trying to keep the dimension down to two or three. Also,
curr3nt's solution makes for an easy second part solution. I had hoped that
someone would go a bit further and hint at some algorithm for generating these
things. I know of no way to generate a random one -- i.e. an algorithm which
can choose one with probability 1/N where N is the total number of possible
adjacencies. I don't even know how to find N. Thanks for working on it.
Posted 18 November 2012 - 07:41 AM
Spoiler for assuming curr3nts
N is not going to be that simple to calculate. Any given adjacency you find could have multiple possible cycles that could be found within it (So it may incorrectly be counted multiple times). Adjacencies don't need to be as neatly organized as curr3nt's answer was.
Posted 19 November 2012 - 07:58 PM
Posted 19 November 2012 - 11:06 PM
Spoiler for Why wouldn't phil's approach for N work?
Posted 19 November 2012 - 11:39 PM
shed light on this problem. I wrote a little program
to generate all possible ways of making adjacencies on
an alphabet of size 8 with each letter having 3 adjacencies.
The number of these I got was 19,355.
Posted 20 November 2012 - 01:47 AM
Time to look at 3-regular graphs... which aren't as simple and quite possibly don't have this property.
Posted 20 November 2012 - 04:21 PM
Spoiler for can you "cube" this?
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