The New Sudoku Players' Forum

by **yzfwsf** » Mon Aug 23, 2021 12:15 am

Code: Select all: 1..2...7...8.4..39.....56..7......5.....349....9.....3.4...2.....7.9..1.5..4..... .-------.-------.-------. | 1 . . | 2 . . | . 7 . | | . . 8 | . 4 . | . 3 9 | | . . . | . . 5 | 6 . . | : ------+-------+-------: | 7 . . | . . . | . 5 . | | . . . | . 3 4 | 9 . . | | . . 9 | . . . | . . 3 | :-------+-------+-------: | . 4 . | . . 2 | . . . | | . . 7 | . 9 . | . 1 . | | 5 . . | 4 . . | . . . | '-------'-------'-------'

Standard Sudoku has the property of unique solution, while the "Just One Cell" variant problem has only one cell with a definite solution, while other cells have multiple solutions.

Website · by **denis_berthier** » Mon Aug 23, 2021 5:17 am

.
Not sure what you're looking for.

Code: Select all: Resolution state after Singles and whips[1]: +----------------------+----------------------+----------------------+ ! 1 3569 3456 ! 2 68 3689 ! 458 7 458 ! ! 26 2567 8 ! 167 4 167 ! 125 3 9 ! ! 2349 2379 234 ! 13789 178 5 ! 6 248 1248 ! +----------------------+----------------------+----------------------+ ! 7 12368 12346 ! 1689 1268 1689 ! 1248 5 12468 ! ! 268 12568 1256 ! 15678 3 4 ! 9 268 12678 ! ! 2468 12568 9 ! 15678 125678 1678 ! 12478 2468 3 ! +----------------------+----------------------+----------------------+ ! 3689 4 136 ! 135678 15678 2 ! 3578 689 5678 ! ! 2368 2368 7 ! 3568 9 368 ! 23458 1 24568 ! ! 5 123689 1236 ! 4 1678 13678 ! 2378 2689 2678 ! +----------------------+----------------------+----------------------+ 235 candidates

After applying T&E(2, W1), the resolution state is:

Code: Select all: +----------------------+----------------------+----------------------+ ! 1 39 456 ! 2 68 39 ! 58 7 458 ! ! 26 256 8 ! 17 4 167 ! 125 3 9 ! ! 2349 7 23 ! 39 18 5 ! 6 24 18 ! +----------------------+----------------------+----------------------+ ! 7 1368 1346 ! 1689 12 1689 ! 1248 5 12468 ! ! 268 12568 125 ! 15678 3 4 ! 9 268 2678 ! ! 468 12568 9 ! 15678 1257 1678 ! 1278 2468 3 ! +----------------------+----------------------+----------------------+ ! 389 4 136 ! 135678 1567 2 ! 3578 689 5678 ! ! 238 2368 7 ! 3568 9 368 ! 345 1 2456 ! ! 5 123689 1236 ! 4 17 13678 ! 378 2689 2678 ! +----------------------+----------------------+----------------------+ 196 candidates

i.e. 39 candidates have been eliminated but only one non-given decided value has been found: r3c2=7
This is not enough to prove that no other one could be found: although all the known valid puzzles are in T&E(2), this doesn't imply anything about multi-solution ones.

by **yzfwsf** » Mon Aug 23, 2021 5:33 am

For this Sudoku variant, as long as the solver finds a solution to a cell with a unique solution, the puzzle maker guarantees that all other cells have multiple solutions.

Website · by **denis_berthier** » Mon Aug 23, 2021 6:01 am

yzfwsf wrote:For this Sudoku variant, as long as the solver finds a solution to a cell with a unique solution, the puzzle maker guarantees that all other cells have multiple solutions.

OK, I've found such a cell, what am I expected to do now?

by **yzfwsf** » Mon Aug 23, 2021 6:14 am

denis_berthier wrote:OK, I've found such a cell, what am I expected to do now?

You have solved it.

Website · by **denis_berthier** » Mon Aug 23, 2021 6:20 am

yzfwsf wrote:
denis_berthier wrote:OK, I've found such a cell, what am I expected to do now?

You have solved it.

OK. I thought you were expecting some smart way to use the information that the other cells have multiple solutions.

by **marek stefanik** » Mon Aug 23, 2021 8:37 am

HP 39b2p37, X-Wing 4c18/r36

Code: Select all: .---------------------.-----------------------.--------------------. | 1 3569 3456 | 2 68 39 | 458 7 458 | |a26 2567 8 |a167 4 a167 | 125 3 9 | | 2349 b2379 b23 |b39 178 5 | 6 248 128 | :---------------------+-----------------------+--------------------: | 7 12368 12346 | 1689 1268 1689 | 1248 5 12468 | | 268 12568 1256 | 15678 3 4 | 9 268 12678 | | 2468 12568 9 | 15678 125678 1678 | 1278 2468 3 | :---------------------+-----------------------+--------------------: | 3689 4 136 | 135678 15678 2 | 3578 689 5678 | | 2368 2368 7 | 3568 9 368 | 23458 1 24568 | | 5 123689 1236 | 4 1678 13678 | 2378 2689 2678 | '---------------------'-----------------------'--------------------'

(7=126)r2c146 – (2=379)r3c234 => –7r2c2, –7r3c5 => 7r3c2

by **totuan** » Mon Aug 23, 2021 9:06 am

yzfwsf wrote:Standard Sudoku has the property of unique solution, while the "Just One Cell" variant problem has only one cell with a definite solution, while other cells have multiple solutions.

Code: Select all: *-----------------------------------------------------------------------------* | 1 3569 3456 | 2 68 3689 | 458 7 458 | | 26 2567 8 | 167 4 167 | 125 3 9 | | 2349 2379 234 | 13789 178 5 | 6 248 1248 | |-------------------------+-------------------------+-------------------------| | 7 12368 12346 | 1689 1268 1689 | 1248 5 12468 | | 268 12568 1256 | 15678 3 4 | 9 268 12678 | | 2468 12568 9 | 15678 125678 1678 | 12478 2468 3 | |-------------------------+-------------------------+-------------------------| | 3689 4 136 | 135678 15678 2 | 3578 689 5678 | | 2368 2368 7 | 3568 9 368 | 23458 1 24568 | | 5 123689 1236 | 4 1678 13678 | 2378 2689 2678 | *-----------------------------------------------------------------------------*

Just lucky

- check for UR(48)r18c79 => r3c9=8, right?

totuan

by **DEFISE** » Mon Aug 23, 2021 9:16 am

yzfwsf wrote:For this Sudoku variant, as long as the solver finds a solution to a cell with a unique solution, the puzzle maker guarantees that all other cells have multiple solutions.

My DFS (Depth First Search) program calculates all the solutions and also the intersection of the solutions (see below).
I added the starting puzzle just after this intersection to be able to compare the two.
We can see that r3c2 is the only unresolved cell at the start which has a value common to all the solutions.

Hidden Text: Show

by **DEFISE** » Mon Aug 23, 2021 9:36 am

totuan wrote:Just lucky - check for UR(48)r18c79 => r3c9=8, right?
totuan

There is indeed a solution with 8r3c9 (solution_161 in my results above) but all other solutions contain 1r3c9.

by **yzfwsf** » Mon Aug 23, 2021 9:39 am

totuan wrote:Just lucky - check for UR(48)r18c79 => r3c9=8, right?
totuan

This Sudoku variant cannot use UR or any technology that relies on unique solutions to puzzles.

by **yzfwsf** » Mon Aug 23, 2021 9:42 am

DEFISE wrote:My DFS (Depth First Search) program calculates all the solutions and also the intersection of the solutions (see below).
I added the starting puzzle just after this intersection to be able to compare the two.
We can see that r3c2 is the only unresolved cell at the start which has a value common to all the solutions.

This is the rule of this kind of Sudoku variant.

by **JPF** » Mon Aug 23, 2021 12:35 pm

Just One cell... Why not Just 12 cells?

Code: Select all: +---+---+---+ |...|...|432| |...|...|716| |...|...|589| +---+---+---+ |...|726|...| |...|451|...| |...|938|...| +---+---+---+ |287|314|695| |416|895|327| |935|267|148| +---+---+---+

ED=7.2/2.0/2.0, thanks to 999_Springs

see here

JPF

Website · by **denis_berthier** » Mon Aug 23, 2021 1:10 pm

Code: Select all: +----------------+----------------+----------------+ ! 1568 56 18 ! 16 7 9 ! 4 3 2 ! ! 3 49 49 ! 5 8 2 ! 7 1 6 ! ! 167 267 12 ! 16 4 3 ! 5 8 9 ! +----------------+----------------+----------------+ ! 18 49 3 ! 7 2 6 ! 89 5 14 ! ! 678 267 289 ! 4 5 1 ! 89 67 3 ! ! 567 567 14 ! 9 3 8 ! 2 67 14 ! +----------------+----------------+----------------+ ! 2 8 7 ! 3 1 4 ! 6 9 5 ! ! 4 1 6 ! 8 9 5 ! 3 2 7 ! ! 9 3 5 ! 2 6 7 ! 1 4 8 ! +----------------+----------------+----------------+

Obtained without computing all the solutions, but by eliminating the candidates that can't be in any of the solutions and asserting the 12 values that must be in any solution.

by **yzfwsf** » Mon Aug 23, 2021 2:13 pm

Hi JPF, please check.

qiuyanzhe wrote:This type is called "Just One Cell Sudoku", seemingly first appeared in WSC2010(in the USA).
The concept is the same as ours, multi-solution puzzles are provided but exactly one cell can be determined. Some descriptions and sample puzzles can be seen in https://motris.livejournal.com/102237.html

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Just One Cell

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