The New Sudoku Players' Forum

by **StrmCkr** » Fri Dec 23, 2016 1:47 am

http://hodoku.sourceforge.net/en/tech_ur.php covers the following:
Unique rectangles types 1-6
Hidden rectangle types 1-2 {avoidable}
B.u.g http://forum.enjoysudoku.com/the-bug-bivalue-universal-grave-principle-t2352.html
B.u.g lite (bug+1)

http://forum.enjoysudoku.com/post63659.html#p63659
Unique rectangle 1.1
{creates the use of UR's missing 1 candidate}

M. U. G http://forum.enjoysudoku.com/post21050.html#p21050
Aur http://forum.enjoysudoku.com/post22180.html#p22180
Revers bug http://forum.enjoysudoku.com/the-reverse-bug-t4431.html
Reverse bug lite http://forum.enjoysudoku.com/reverse-bug-lite-t4957.html

Chains/technique ± any uniqueness argument

Are all based around avoiding any one of the unavoidable sets
Which can be as simple as 4 cells and two digits to the monster of an empty grid.

I'll provide hyper links
To the list later tonight.

by **eleven** » Fri Dec 23, 2016 1:17 pm

ghfick wrote:I suppose the empty puzzle has the maximum solution count. [combinatorics here?]. I wonder what the maximum solution count would be for a puzzle with 17+ givens?

The empty grid should have 6670903752021072936960 solutions, 5472730538 of them being essentially different (see here and here).
I guess, that it is not easy to calculate the maximum for puzzles with N givens (apart from trivial cases N=1 or N>76)

Could you please post a list of 100 puzzles with the first hundred solution counts?

Here is an arbitrary list:

Hidden Text: Show

Note that for each solution count you may have puzzles with so different solution paths as you have with unique puzzles.

by **eleven** » Fri Dec 23, 2016 3:53 pm

ghfick wrote:I now see we also have MUG [Multi-Value Universal Grave] and so I found:
layered-bug-lite-t4432.html
Again MUGs could be findable by humans but slightly tougher, for sure.
The examples found are very helpful. Is there a place that gives precise definitions for these terms?

For MUGs see also these threads:
Forming MUGs from BUG-Lite composites
Layered BUG-lite
You will see, that it is not trivial to decide, if a pattern is a MUG. I don't know, if there is an academic definition for a MUG, e.g. i think, that two independent MUG's "combined" would not be called a MUG.
But the basic property is (as for BUG lites), that whatever numbers/candidates you have outside the MUG pattern, there would always remain at least 2 solutions (inside the MUG cells).

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