The New Sudoku Players' Forum

[m_b_metcalf]

Here an real example:

Thanks, this solves when treated as an x-sukaku, but, if I'm not mistaken, has multiple solutions if only the givens are used as a standard x-sudoku, which, I thought, is our topic.

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     6                    7
  5     9              2   
     7              6  9   
  1        7  2        6   
        6        9        8
                 6         
  6              2  9     4
        2                 6
  9     7              1   

 Multiple solutions found, example:

  2  6  8  1  9  3  4  5  7
  5  1  9  6  4  7  8  2  3
  3  7  4  2  8  5  6  9  1
  1  4  3  7  2  8  5  6  9
  7  2  6  5  3  9  1  4  8
  8  9  5  4  1  6  7  3  2
  6  8  1  3  5  2  9  7  4
  4  5  2  9  7  1  3  8  6
  9  3  7  8  6  4  2  1  5

Regards,

Mike

[creint]

Pasting in your solver does not work correctly.
I am confident that it has a single solution, checked both formats.

Solution:

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8 6 3 2 9 5 1 4 7
5 1 9 4 6 7 8 2 3
2 7 4 8 1 3 6 9 5
1 3 5 7 2 8 4 6 9
4 2 6 1 3 9 5 7 8
7 9 8 5 4 6 2 3 1
6 5 1 3 7 2 9 8 4
3 4 2 9 8 1 7 5 6
9 8 7 6 5 4 3 1 2

[m_b_metcalf]

I get your solution treating it as an x-sukaku, but if I feed just this

Code: Select all

 . 6 . . . . . . 7
 5 . 9 . . . . 2 .
 . 7 . . . . 6 9 .
 1 . . 7 2 . . 6 .
 . . 6 . . 9 . . 8
 . . . . . 6 . . .
 6 . . . . 2 9 . 4
 . . 2 . . . . . 6
 9 . 7 . . . . 1 .

into SukakuExplainer with X activated, I get

This Sudoku is not valid
This Sudoku has multiple solutions. Two different possible solutions can be viewed by selecting the "View 1" or the "View 2" under the grid. The solutions are highlighted in orange.

Regards,

Mike

[creint]

Yes it is an x-sukaku because those are easier to manually create.
Should have used the term puzzle/sukaku instead of sudoku.

[m_b_metcalf]

THE END

[tarek]

Yes it is an x-sukaku because those are easier to manually create.
Should have used the term puzzle/sukaku instead of sudoku.

SE reports that it has multiple solutions. Nevertheless the logic stands. Thanks for the example.

I suspect that Mike - like me - would like to see an example that comes from an x-sudoku ... Had I had time then I would have implemented it in Sukaku explainer and tweaked the generator to look for that specifically but I have so many things on my to-do list that I have to finish first.

tarek

[creint]

Hidden single in hidden constraint (r28c28+r5c5) => 5r5c5

Code: Select all

7 . . . . . . . .
. . . 6 7 8 9 . 5
. . . . . . . . .
. . . . . . . . .
1 7 . . . . 3 . .
. . 5 . 9 . . . 2
. . . . 6 . . . .
. . 6 7 8 9 5 . .
. . . . 4 3 . . .

This time it saves at least a forcing chain of rating 7.1.

[tarek]

We need to find a name for these "Forced cell sets" or "Forced cages" as they would like to call them in killer sudoku. The group of cells are forced to have different symbols.

These cell sets will need to be known & declared to be useful for players. I'm not sure if Jean-Christophe had this feature in JSudoku! If anyone implemented it, it would be him.

You will have many examples of similar cluster of cells. SE's Generalized intersections when used will show you several examples. Examples of the magnitude of 5 or more cells covering several constraints is most likely what we are searching for here although it appears that any number of forced cell sets can be useful.

If there is a puzzle variant with forced cell set with more than 9 cells then the puzzle variant will be invalid by nature. Very interesting branching topic starting here creint!

Tarek

[creint]

JSudoku:
R28C28 forms a generalized naked Quad on {1234} -> not in R5C5
R5C5 = 5

No awareness of constraint else it should have found it as hidden single.

Yes this should be moved to a new topic.
Detecting all hidden houses would be helpful for new variants. Maybe I can add this to my solver.

But this affects rating of SE for variants, users/solvers who don't know this would struggle but a others don't.

[tarek]

If nobody but you has used this to their advantage then you've just become more powerful. The rest of us need to play catch up now. I'm surprised that this wasn't used by Ruud, JC or Andrew Stuart.

The cells = digits should be easy to check in any "Forced cell set" which allows to use Hidden sets! That could be the novel aspect here which hasn't been exploited by many before. You will find that we use the Naked sets aspect indirectly in generalized intersections or generalized naked sets because the "forced cell set" aspect is not needed to detect the naked set. Only the cells that form the (almost) naked set is needed.

tarek

[m_b_metcalf]

Hidden single in hidden constraint (r28c28+r5c5) => 5r5c5
[snip]
This time it saves at least a forcing chain of rating 7.1.

I simulated the use of this hidden single by setting 5r5c5 directly, and the SE rating stays at 9.1/1.2/1.2. I think I'll give that new coding a miss. Anyway I'm soon away from home for a while.

Regards,

Mike

[tarek]

These are my thoughts about the New rating tweak which should go into the next release (New Rating option) in the next release unless there are any objections

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Hidden Triple    --> 3.7
Swordfish       <--> 3.8
2 Strong Links   --> 3.9-4.2
XY wing          --> 4.3
XYZ Wing        <--> 4.4

UL  Type1   Type2  Type3+NP/HP Type3+NT/HT  Type3+NQ/HQ  Type4
4   4.5     4.5    4.6         4.7          4.8          4.5
6   4.6     4.6    4.7         4.8          4.9          4.6
8   4.7     4.7    4.8         4.9          5.0          4.7
10  4.8     4.8    4.9         5.0          5.1          4.8
12  4.9     4.9    5.0         5.1          5.2          4.9
14  5.0     5.0    5.1         5.2          5.3          5.0
16  5.1     5.1    5.2         5.3          5.4          5.1

Naked Quad      <--> 5.0
Jellyfish        --> 5.1
Hidden Quad      --> 5.2

[m_b_metcalf]

Hidden single in hidden constraint (r28c28+r5c5) => 5r5c5

Code: Select all

7 . . . . . . . .
. . . 6 7 8 9 . 5
. . . . . . . . .
. . . . . . . . .
1 7 . . . . 3 . .
. . 5 . 9 . . . 2
. . . . 6 . . . .
. . 6 7 8 9 5 . .
. . . . 4 3 . . .

This time it saves at least a forcing chain of rating 7.1.

Coming back to this after a while, I realize that I don't understand why there's a 'hidden single' here. The five cells must contain five different values, but that means that there are four values that they don't contain. The value 5 could be one of them (in general).

Consider also the case that the five cells each contain just the five values 1 to 5. How can I use that in a solver to make eliminations in other cells?

Or that case again, but where one cell additionally contains the value 6. Maybe the five cells solve to 1, 2, 3, 4, 6. How can I use this information for an elimination? I don't see it.

Regards,

Mike

[mith]

I would think of it as a naked quad on 1234, eliminating the 2 in r5c5, resulting in a naked single. The 5 isn't forced into r5c5 in general, just in the absence of other options in r28c28 eliminating the 2.

[creint]

Because of the constraint 5 cells and only 5 digits left in constraint, you can apply the single in constraint rule. This rule cannot be used when there are more than 5 digits, because then you don't know which ones will be true. In this case you could also see it as a naked quad.
Take my example puzzle and you can directly (first step) see 5 digits in 5 cells, while digit 5 can only go in one place in that constraint.
Naked quad/singles can be applied to constraints without requiring digits = cells.
Hidden subsets/singles can only be applied when digits = cells.

Because there are no cells outside this constraint that can see all four cells of quad it can only exclude inside the same constraint. But if you find a triple you can find common cells outside constraint.
Best way is just to implement digitcount = cellcount logic and apply constraint that you want to use. (those 3 + 84 other hidden constraint that are probably less usefull)
Because of all constraints in SudokuExplainer have 9 cells there were no implementation problems.