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Brad Klee
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&[Wolfram Notebook][1] [1]: https://www.wolframcloud.com/obj/d5362aba-7efd-4a41-8ba6-46b0a3b4bbda
Hey Peter! Thanks for your interest. We're still actively working on the proof (and now a few others including [this one from nks][1]). It turns out after some decently involved combinatorics that the Hat tile is actually a combinatorial hexagon, as...
In [your other recent post][1], there's now some competitive timing statistics, where it looks like DancingLinksX (DLX) wins the race. A similar approach is possible for the queens problem, but it looks like DLX is not especially fast in this case....
> Ignoring one's currently available pieces and half-completed puzzles > (which is a very big ignore!), the value of a piece should look > something like v=v(points,rewardPiece,complexity,t), where t is the > mean number of remaining rounds until...
Actually, it's not even a mystery if you read the code. Somehow the word clouds must get included in the graphics, and that is done through g1 and g2. But yes, you're right the code is incomplete, thanks for noticing. Here attached is the fix, just...
This is a nice follow-up to [your previous post][1], especially because DepthFirstSearch doesn't lead to a timely solution. However, it's well-known that Sudoku is a good use case for Donald Knuth's DancingLinksX algorithm, so it's also possible to...
> Why L^N? and not L*N, for instance. Either is fine. If the probability of avoiding a dead end is $1/L$ and you have $N$ dead ends, then the probability of successful finish is $1/(L^N)$. I probably should have said this in the original write-up,...
Thanks! This is probably exactly what I was asking about, but now I need to take a closer look at the combinatorics how the alternative super-tiles fit together and form larger copies. For reference, we're trying to do something similar to [this post...
The nomenclature doesn't worry me too much, but would using "game graph" or optionally "directed acyclic game graph" at least avoid the pitfall of throwing around acronyms? As to your important question--The tools we developed are highly...
Thanks again to Maestro Michael, making this problem a little more interesting. If you didn't see my updated code on the other thread, it looks like we have the same results up to the 20-gon. I'll have to do a timings comparison for our approaches...