## Invalid (incompletable) 4-template(s)

Everything about Sudoku that doesn't fit in one of the other sections

### Re: New Solving Technique (I think)

dobrichev wrote:
Code: Select all
`... .12 .34.13 4.. 2...42 3.. 1...21 .34 ...3.. 1.. .424.. 2.. .13.34 ... .211.. .23 4..2.. .41 3..`

What i don't understand now:
When i change some digits in this pseudo puzzle, i can get this one, which has a nice box symmetry (boxes 159, 267, 348), and - as i see it - is not equivalent. It has no solution for the same reasons. Why isn't it in your list ?
Code: Select all
`... .12 .34.23 4.. 1...41 3.. 2...34 ... .121.. .23 4..2.. .41 3...12 .34 ...4.. 1.. .233.. 2.. .41`
eleven

Posts: 1999
Joined: 10 February 2008

### Re: New Solving Technique (I think)

eleven wrote:What i don't understand now:
When i change some digits in this pseudo puzzle, i can get this one, which has a nice box symmetry (boxes 159, 267, 348), and - as i see it - is not equivalent. It has no solution for the same reasons. Why isn't it in your list ?

It is easy to understand - because I am wrong.
eleven wrote:I cant see, what you are out for.

You proved the ratio 119 503 485 completable : 1 non-completable 4-templates isn't correct.
Maybe the ratio 2 648 603 completable : 1 non-completable 4-rookeries is still correct.
There is chance that I messed up only templates with rookeries during my computation, but who knows...
k-templates which are the only representatives of its k-rookery are not uncommon. Maybe I somehow wrongly determined that this is the case for this template. I still keep the 10GB list with the 4-templates and can compress it somehow and send it to those who are interested.

BTW, at which "clue" in the holdout's grid generation algorithm (thank you, Danny) the continuation list will be emptied? Are there min and max "clue" depending on the choice of the 5-th template? (a different view point to the "15 combinations" discussed above).

eleven wrote:It is easy to generate puzzles, which have this template as option, mostly it is destroyed by singles early. These 2 have it after basics (found in 30 min):
Code: Select all
`..7..2.3...349.2...42...1.8.21.3.......1.....48..6.....3.....2.1....34...9.84..........9.4..348.........617.62.5.4.......7.6....9..8..3.3.....2.1.6...4..........5`

Yes, "mostly". Maybe it couldn't be determined w/o years of computations whether the puzzles having this template as an option in the solution path trend to be harder than average.
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: New Solving Technique (I think)

denis_berthier wrote:
dobrichev wrote:Its existence could be cause or effect of some still undiscovered symmetries/asymmetries of the sudoku space.

About "still undiscovered" : the definition of Sudoku doesn't leave much liberty for finding other symmetries than those in the obvious well known Sudoku symmetry group.

It depends of definitions.
Any puzzle which givens entirely cover the cells of an unavoidable sets has a complementary puzzle (a twin) with the same givens outside of the UA and permuted givens within the UA. Is't this a symmetry? To me it is.
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: New Solving Technique (I think)

ronk wrote:If this were extended to canonicalized 5-templates, would there be more incompletables?

It is good to know how incompletables grow, but the task requires CPU and disk space...
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: New Solving Technique (I think)

dobrichev wrote:Any puzzle which givens entirely cover the cells of an unavoidable sets has a complementary puzzle (a twin) with the same givens outside of the UA and permuted givens within the UA.

This is interesting, but I'm afraid your meaning isn't very clear to me.
Are you saying this will always be true or just in specific instances?
Are you assuming minimal puzzles?
It would help me a lot if you would provide an example.

DPB
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

### Re: New Solving Technique (I think)

David P Bird wrote:
dobrichev wrote:Any puzzle which givens entirely cover the cells of an unavoidable sets has a complementary puzzle (a twin) with the same givens outside of the UA and permuted givens within the UA.

This is interesting, but I'm afraid your meaning isn't very clear to me.
Are you saying this will always be true or just in specific instances?

Always

David P Bird wrote:Are you assuming minimal puzzles?

No matter

David P Bird wrote:It would help me a lot if you would provide an example.

Here is an example by eleven.
dobrichev
2016 Supporter

Posts: 1634
Joined: 24 May 2010

### Re: Invalid (incompletable) 4-template(s)

MD, Thanks for your response which helped me realise how ignorant on this subject I am. I'm tempted to ask more questions but feel they would only take this thread way off-topic and would just cover old ground for many players here.

DPB
David P Bird
2010 Supporter

Posts: 1040
Joined: 16 September 2008
Location: Middle England

Previous