The New Sudoku Players' Forum

[nazaz]

Here's a nice GDP-7:

Code: Select all

    12  24  |  14
    13  .   |  12
    --------+----
    23  12  |  .

It's a bivalue deadly pattern but not a BUG-lite. Is it known by any other name?

[champagne]

Here's a nice GDP-7:

Code: Select all

    12  24  |  14
    13  .   |  12
    --------+----
    23  12  |  .

It's a bivalue deadly pattern but not a BUG-lite. Is it known by any other name?

2 4 | 1
1 . | 2
--------+----
3 12 |

seems valid,
I have difficulties to qualify this as a deadly pattern

[nazaz]

Here's another GDP on the same set of cells.

Code: Select all

    23  14  |  12
    14  .   |  12
    --------+----
    13  13  |  .

And another:

Code: Select all

    24  14  |  12
    13  .   |  12
    --------+----
    13  14  |  .

Both deadly in the generalised sense of the word, but neither of them a BUG-lite.

[eleven]

2 4 | 1
1 . | 2
--------+----
3 12 |

seems valid,
I have difficulties to qualify this as a deadly pattern

There is a deadly 1212 pattern in r12. With 1r1c1 you get one in c12.

[champagne]

2 4 | 1
1 . | 2
--------+----
3 12 |

seems valid,
I have difficulties to qualify this as a deadly pattern

There is a deadly 1212 pattern in r12. With 1r1c1 you get one in c12.

OK it fits with the definition given in the first post.

[denis_berthier]

Here's a nice GDP-7:

Code: Select all

    12  24  |  14
    13  .   |  12
    --------+----
    23  12  |  .

It's a bivalue deadly pattern but not a BUG-lite. Is it known by any other name?

1) About vocabulary:
"A deadly pattern is a set of cells whose candidates form a pattern that causes the puzzle to have multiple solutions." (Sudopedia)
Your pattern is not a deadly pattern at all. And it's not a "generalised deadly pattern" in any possible meaning of the word "generalised".
It seems you're more interested in UAs than in DPs, so maybe you should rename it generalised UA, but you'll still have to explain the "generalised" part.

2) About making definitions:
A definition that allows no conclusion is useless.
What can you conclude from the above pattern? How can you use it in any way?
.

[eleven]

This pattern is as deadly according to this short Sudopedia definition as all the bivalue samples there. You can't have it in a unique puzzle.
However it does not fit Sudopedia's formal description, that all solutions have the same footprint. So it is generalized. Not a bad name for me.

However i still have not seen a useful real world sample with a GDP. Maybe you could you try to find one for one of these patterns, Denis.

[Added:] btw for me these patterns are double "generalized hidden UR's", i.e. patterns, where a digit forces a deadly pattern by short chains (e.g. i remember examples, where this could be done with strong links and locked candidates).
Found this old sample eliminating 4r2c7: 4r2c7 => 5r2c4 and 5r3c7, 4r2c7 => 4r1c3 => 4r3c4.

[nazaz]

btw for me these patterns are double "generalized hidden UR's", i.e. patterns, where a digit forces a deadly pattern by short chains

Not all GDPs are constructed solely out of URs. For example, each solution of the following contains a single minimal UA; some on four cells, some on six.

Code: Select all

13  | .  123 . | 123
123 | .  .   . | 12
123 | .  23  . | .

I do agree with you that the patterns can be explained by wrapping some logic around the underlying UAs, though.

[denis_berthier]

This pattern is as deadly according to this short Sudopedia definition as all the bivalue samples there. You can't have it in a unique puzzle.

Can you prove this?

However i still have not seen a useful real world sample with a GDP. Maybe you could you try to find one for one of these patterns, Denis.

Don't revert the charge of the proof.

[eleven]

Hi Denis,

i proved it above, you must have missed that: whatever solution a puzzle with this pattern has, it will contain one of the 2 digit 12-UA's (similar in the other 2 samples), therefore there must be another solution.

I asked you to to try to find a sample, because i have seen, that you found some for other bivalue deadly patterns. I don't have a proper tool to do that.

[eleven]

Code: Select all

13  | .  123 . | 123
123 | .  .   . | 12
123 | .  23  . | .

I do agree with you that the patterns can be explained by wrapping some logic around the underlying UAs, though.

Yes, it needs some case distinctions.
case 1r1c1:

Code: Select all

    1 # | . *23  . |*23#
   *23# | .  .   . |*12#
   *23  | . *23  . | .

2r2c5 -> 6 cell 23 UA (*)
1r2c5 and 1c5=r2c1 (2 or 3) -> 12 or 23 UA (#)
So you can eliminate 1r1c1.
case 3r1c1:

Code: Select all

    3   | .  12  . | 12
    12  | .  .   . | 12
    12  | .  23  . | .

same (depending on r2c4)

[denis_berthier]

Hi eleven

i proved it above, you must have missed that: whatever solution a puzzle with this pattern has, it will contain one of the 2 digit 12-UA's (similar in the other 2 samples), therefore there must be another solution.

OK, I see. I had indeed overlooked it. But then, we're back to the old UR1.1 case, for which I already provided a counter-example.

I asked you to to try to find a sample, because i have seen, that you found some for other bivalue deadly patterns. I don't have a proper tool to do that.

What I have (all available in CSP-Rules) is:
- tools to solve collections of puzzles with/without deadly pattern(s)
- tools to compare ratings of solutions with/without using deadly patterns
- tools to extract puzzles from a collection.

What I would have to do here is
1) code the above particular DP (not too hard)
2) try so solve some collection with it (easy but time consuming)

This also supposes to decide where I put it in the hierarchy of rules. For all the DPs I considered (Blue's list of 603), I put them immediately after Singles, in order to give them as high chances of possible. However, even this may be too late, as in the example alluded to above.
.

[nazaz]

we're back to the old UR1.1 case, for which I already provided a counter-example.

If you mean the old thread that StrmCkr linked to, then all that does is to show that a propositional calculus whose variables are only of the form "candidate d@(r,c) is true" cannot handle uniqueness techniques. That argument is irrelevant for more expressive logical systems, for example that allow predicates of the form IsGiven(X). Don't be ashamed that CSP-Rules can't handle uniqueness, but do please take care not to draw nonsensical conclusions outside of your CSP-Rules domain. UR1.1 is just fine.

[denis_berthier]

we're back to the old UR1.1 case, for which I already provided a counter-example.

If you mean the old thread that StrmCkr linked to, then all that does is to show that a propositional calculus whose variables are only of the form "candidate d@(r,c) is true" cannot handle uniqueness techniques. That argument is irrelevant for more expressive logical systems, for example that allow predicates of the form IsGiven(X). Don't be ashamed that CSP-Rules can't handle uniqueness, but do please take care not to draw nonsensical conclusions outside of your CSP-Rules domain. UR1.1 is just fine.

You shouldn't talk of what you don't know. You'd better take time to learn the basics of logic.
CSP-Rules is based on first order logic (FOL). It can perfectly handle non-uniqueness, as shown by the work I've done recently with Blue's 630 deadly patterns (and long ago with UR or BUG).
Introducing a predicate isGiven(X) would be totally useless in FOL, as a proof in FOL (or any logical system) can't make any difference between axioms and their consequences (theorems).
.

[eleven]

Interesting, that your logical system, which mainly works with memory chains, is suffering from dementia, and can't remember, which numbers were given.