The New Sudoku Players' Forum

Website · by **denis_berthier** » Fri Jan 10, 2025 8:43 am

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As I understand it:

An unavoidable set (UA) in a valid complete solution grid is a set of cells among which the values can be exchanged without changing the rest of the grid and still making a valid complete solution grid.
This notion is useful mainly for puzzle creators. Every single-solution puzzle for a grid must have a given from each of its unavoidable sets. But, even if one accepts the assumption of uniqueness, UAs can't be used directly by puzzle solvers.
References: I've found on an external disk a list of 525 minimal UAs, due to Blue (?), but I have no reference.

A deadly pattern (DP) in some resolution state RS of a possibly multi-solution puzzle is a set of cells such that, in RS, the candidates in these cells can be exchanged independently of the rest of the puzzle. As this is impossible in a single-solution puzzle, DPs can have a direct application in solving puzzles (provided one accepts the assumption of uniqueness): there can never be a deadly pattern and when one finds something close to one, i.e. a DP with additional candidates (guardians), one can assert a disjunction of the guardians (an OR relation between the guardians).
Reference: https://www.sudopedia.org/wiki/Deadly_Pattern, where there is the full catalogue of 17 minimal DPs on 9 or fewer cells (modulo isomorphisms)

Given a deadly pattern, the underlying set of cell is obviously an UA.
The converse is not so clear. Take for instance the following UA:
....................................................................1..2.....2..1 ( 4)
it clearly allows the simplest DP:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 . . 21 . . . . . 21 . . 12

But now, take this:
.................................................................1..2.34..3..4.21 ( 8)
Can one build a (unique?) DP based on this and how?

Other question: is there a more up-to-date catalogue of UAs and/or DPs?
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by **Serg** » Fri Jan 10, 2025 5:02 pm

Hi, Denis!

denis_berthier wrote:An unavoidable set (UA) in a valid complete solution grid is a set of cells among which the values can be exchanged without changing the rest of the grid and still making a valid complete solution grid.

I'd add some points to your definitions.
An order of UA set is a numder of cells, participating UA set. Particular UA set is denoted by letter "U", plus order of the set. For example, "U4" UA set. Nowadays is more popular another designation for UAs (with additional letter "A" in the name) - UA4 instead of U4, for example.

Set of UA cells values (digits), permitted the same valid completion of solution grid is called permutation of UA set. Any UA set has at least 2 permutations. Number of UA set's permutations is called valency of UA set.

UA set is minimal, if it doesn't contain any UA sets of smaller order as subset. An UA permutation is called minimal if each cell of this permutation contains unique digit compared to the same cell digits of other UA set's permutations. If all UA set's permutations are minimal, the UA set is called strongly minimal. If not all UA set's permutations are minimal, the UA set is called weakly minimal. It can be proved that strongly minimal or weakly minimal UA set is minimal in common sense, i.e. it doesn't contain any UA sets of smaller order as subset.

All observed strongly minimal UA sets have valency 2 (2 permutations), though this property isn't proved yet. Weakly minimal UA set must have valency > 2. All observed weakly minimal UA sets have the only minimal permutation, though this property isn't proved yet.

The highest observed order of minimal UA set - 62 (see dobrichev's post Two 2-valent strongly minimal U62 sets). The first minimal U62 discovered dobrichev in 2011, later, in 2022, jovi_al01 discovered another minimal U62.

A simple example of strongly minimal UA set is published below.

Code: Select all: Strongly minimal 2-valent 4-digit UA example (2 possible permutations) +-----+-----+-----+ |. . .|. . .|. . .| |. . 1|. . 2|. 3 4| |. . 3|. . 4|. 2 1| +-----+-----+-----+ +-----+-----+-----+ |. . .|. . .|. . .| |. . 3|. . 4|. 2 1| |. . 1|. . 2|. 3 4| +-----+-----+-----+

denis_berthier wrote:Given a deadly pattern, the underlying set of cell is obviously an UA.

Not quite true. Mladen Dobrichev just posted an example of 7-cell Deadly Pattern in the thread 7-cell Unavoidable Sets, which is not based on an UA.

denis_berthier wrote:The converse is not so clear.

Usually Deadly Patterns are built from strongly minimal UA sets, i.e. DP always have 2 candidates in each cell, according to "base" UA set valency.

denis_berthier wrote:But now, take this:
.................................................................1..2.34..3..4.21 ( 8)
Can one build a (unique?) DP based on this and how?

Two permutations of your 2-valent strongly minimal U8 are published above. So, DP can easily be constructed from those permutations:

Code: Select all: Deadly Pattern example |. . .|. . .|. . .| |. . 13|. . 24|. 32 41| |. . 31|. . 42|. 23 14|

Serg

Website · by **denis_berthier** » Fri Jan 10, 2025 7:08 pm

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Hi Serg
Thanks for all these precisions.

Regarding the last UA:
.................................................................1..2.34..3..4.21 ( 8)
OK, for the associated DP.
But my question was more general. As I now understand it, there's no systematic way of finding a DP, even from a strongly minimal UA. And it seems that the notation doesn't help, even in this case.

As I'm mostly interested in DPs, my question is now: is there a larger known set of minimal DPs than the one I mentioned before?
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by **Serg** » Fri Jan 10, 2025 8:21 pm

Hi, Denis!

denis_berthier wrote:As I now understand it, there's no systematic way of finding a DP, even from a strongly minimal UA. And it seems that the notation doesn't help, even in this case.

If you know some strongly minimal UA set, you can systematically construct Deadly Pattern from it.

denis_berthier wrote:As I'm mostly interested in DPs, my question is now: is there a larger known set of minimal DPs than the one I mentioned before?

I have no high order DP list. Such DPs, to my mind, have limited practical use. Humans cannot use high order DPs in Sudoku solving.

Serg

Website · by **denis_berthier** » Sat Jan 11, 2025 4:20 am

Serg wrote:
denis_berthier wrote:As I'm mostly interested in DPs, my question is now: is there a larger known set of minimal DPs than the one I mentioned before?

I have no high order DP list. Such DPs, to my mind, have limited practical use. Humans cannot use high order DPs in Sudoku solving.

OK.
My purpose was to test their resolution power systematically, but it already appears that even the 9-cell ones appear rarely. Calculations are still running. I'll say more about this in the ORk thread (http://forum.enjoysudoku.com/ork-forcing-whips-ork-contrad-whips-and-ork-whips-t40189.html)
Thanks for your answers; they allowed me to concentrate on the questions of direct interest to me.

Just out of curiosity, what's the procedure for finding a DP from a strongly minimal UA (given in the same standard(?) form as:
.................................................................1..2.34..3..4.21 ( 8)
Does one have to test all the possible minimal permutations?
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Website · by **denis_berthier** » Sat Jan 11, 2025 9:46 am

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Here's a puzzle with a DP9. It's a rare case. Unfortunately for the usability of a DP9, it is useless here.
I haven't yet found a DP9 that would be effectively used in the resolution.

Notation: DPc-k-n(s):
c = number of cells
k = number of digits
n = place with the previous 2 parameters in the Sudopedia list
s = diagonal symmetric version

Code: Select all: Puzzle cbg-000 #2743 +-------+-------+-------+ ! 1 . . ! . 5 . ! . 8 . ! ! 4 5 6 ! . 8 . ! . . . ! ! 7 . . ! . . 2 ! . . 6 ! +-------+-------+-------+ ! . . . ! 9 . . ! 3 7 . ! ! . 1 . ! 6 . 4 ! . . . ! ! . . 8 ! . . 5 ! . . . ! +-------+-------+-------+ ! . . . ! . . . ! 2 . . ! ! . 3 . ! . 4 . ! 8 9 . ! ! 8 . 2 ! . 6 . ! . 1 . ! +-------+-------+-------+ 1...5..8.456.8....7....2..6...9..37..1.6.4.....8..5.........2...3..4.89.8.2.6..1. 731667

Code: Select all: Resolution state after Singles and whips[1]: +----------------+----------------+----------------+ ! 1 2 39 ! 347 5 6 ! 479 8 479 ! ! 4 5 6 ! 137 8 1379 ! 179 23 279 ! ! 7 8 39 ! 134 139 2 ! 1459 345 6 ! +----------------+----------------+----------------+ ! 25 6 45 ! 9 12 8 ! 3 7 124 ! ! 239 1 7 ! 6 23 4 ! 59 25 8 ! ! 239 49 8 ! 137 1237 5 ! 6 24 1249 ! +----------------+----------------+----------------+ ! 59 479 145 ! 8 1379 1379 ! 2 6 3457 ! ! 6 3 15 ! 2 4 17 ! 8 9 57 ! ! 8 479 2 ! 5 6 379 ! 47 1 347 ! +----------------+----------------+----------------+ 114 candidates.

There are 3 DPs in 4 cells plus one in 9 cells. The 4 are useless.

Code: Select all: DP4-2-1s-OR8-relation in cells (marked #): (r6c5 r6c4 r3c5 r3c4) with 8 guardians (in cells marked @) : n3r6c5 n7r6c5 n3r6c4 n7r6c4 n3r3c5 n9r3c5 n3r3c4 n4r3c4 +----------------------+----------------------+----------------------+ ! 1 2 39 ! 347 5 6 ! 479 8 479 ! ! 4 5 6 ! 137 8 1379 ! 179 23 279 ! ! 7 8 39 ! 134#@ 139#@ 2 ! 1459 345 6 ! +----------------------+----------------------+----------------------+ ! 25 6 45 ! 9 12 8 ! 3 7 124 ! ! 239 1 7 ! 6 23 4 ! 59 25 8 ! ! 239 49 8 ! 137#@ 1237#@ 5 ! 6 24 1249 ! +----------------------+----------------------+----------------------+ ! 59 479 145 ! 8 1379 1379 ! 2 6 3457 ! ! 6 3 15 ! 2 4 17 ! 8 9 57 ! ! 8 479 2 ! 5 6 379 ! 47 1 347 ! +----------------------+----------------------+----------------------+ DP4-2-1-OR5-relation in cells (marked #): (r6c9 r6c5 r4c9 r4c5) with 5 guardians (in cells marked @) : n4r6c9 n9r6c9 n3r6c5 n7r6c5 n4r4c9 +----------------------+----------------------+----------------------+ ! 1 2 39 ! 347 5 6 ! 479 8 479 ! ! 4 5 6 ! 137 8 1379 ! 179 23 279 ! ! 7 8 39 ! 134 139 2 ! 1459 345 6 ! +----------------------+----------------------+----------------------+ ! 25 6 45 ! 9 12# 8 ! 3 7 124#@ ! ! 239 1 7 ! 6 23 4 ! 59 25 8 ! ! 239 49 8 ! 137 1237#@ 5 ! 6 24 1249#@ ! +----------------------+----------------------+----------------------+ ! 59 479 145 ! 8 1379 1379 ! 2 6 3457 ! ! 6 3 15 ! 2 4 17 ! 8 9 57 ! ! 8 479 2 ! 5 6 379 ! 47 1 347 ! +----------------------+----------------------+----------------------+ DP4-2-1-OR7-relation in cells (marked #): (r6c5 r6c1 r5c5 r5c1) with 7 guardians (in cells marked @) : n3r6c5 n7r6c5 n3r6c1 n9r6c1 n3r5c5 n3r5c1 n9r5c1 +----------------------+----------------------+----------------------+ ! 1 2 39 ! 347 5 6 ! 479 8 479 ! ! 4 5 6 ! 137 8 1379 ! 179 23 279 ! ! 7 8 39 ! 134 139 2 ! 1459 345 6 ! +----------------------+----------------------+----------------------+ ! 25 6 45 ! 9 12 8 ! 3 7 124 ! ! 239#@ 1 7 ! 6 23#@ 4 ! 59 25 8 ! ! 239#@ 49 8 ! 137 1237#@ 5 ! 6 24 1249 ! +----------------------+----------------------+----------------------+ ! 59 479 145 ! 8 1379 1379 ! 2 6 3457 ! ! 6 3 15 ! 2 4 17 ! 8 9 57 ! ! 8 479 2 ! 5 6 379 ! 47 1 347 ! +----------------------+----------------------+----------------------+ DP9-3-2-OR8-relation in cells (marked #): (r4c5 r4c9 r5c5 r5c1 r6c4 r6c9 r6c1 r3c5 r3c4) with 8 guardians (in cells marked @) : n4r4c9 n9r5c1 n7r6c4 n4r6c9 n9r6c9 n9r6c1 n9r3c5 n4r3c4 +----------------------+----------------------+----------------------+ ! 1 2 39 ! 347 5 6 ! 479 8 479 ! ! 4 5 6 ! 137 8 1379 ! 179 23 279 ! ! 7 8 39 ! 134#@ 139#@ 2 ! 1459 345 6 ! +----------------------+----------------------+----------------------+ ! 25 6 45 ! 9 12# 8 ! 3 7 124#@ ! ! 239#@ 1 7 ! 6 23# 4 ! 59 25 8 ! ! 239#@ 49 8 ! 137#@ 1237 5 ! 6 24 1249#@ ! +----------------------+----------------------+----------------------+ ! 59 479 145 ! 8 1379 1379 ! 2 6 3457 ! ! 6 3 15 ! 2 4 17 ! 8 9 57 ! ! 8 479 2 ! 5 6 379 ! 47 1 347 ! +----------------------+----------------------+----------------------+

The solution is in W3 and is irrelevant here.
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by **Serg** » Sat Jan 11, 2025 10:18 am

Hi, Denis!

denis_berthier wrote:Just out of curiosity, what's the procedure for finding a DP from a strongly minimal UA (given in the same standard(?) form as:
.................................................................1..2.34..3..4.21 ( 8)
Does one have to test all the possible minimal permutations?

One should find all possible permutations first.
To find all UA permutations, starting from given permutation, one should complete given permutation to valid solution grid in some way. For example, by considering given permutation as pseudo puzzle. Then one should "invert" found solution grid, treating the cells of given permutation as empty cells and treating remaining cells as clue cells. Solving such "inverted" puzzle gives all UA permutations. If we are dealing with strongly minimal UA, we must get 2 permutations exactly. Greater number of permutations implies that UA isn't minimal or is weakly minimal (both cases are not suitable for DP construction).

Then one should check both permutations for minimality - permutations must differ in every UA cells. Both permutations' digits are candidates for DP cell.

Denis, if you want to generate high order UA, I can propose you to use two-row UA sets, having even orders (from U4 to U18), or more complicated two-row two-column UAs, having even orders from U6 to U34.

Serg

Website · by **denis_berthier** » Sat Jan 11, 2025 12:37 pm

Serg wrote:
denis_berthier wrote:Just out of curiosity, what's the procedure for finding a DP from a strongly minimal UA (given in the same standard(?) form as:
.................................................................1..2.34..3..4.21 ( 8)
Does one have to test all the possible minimal permutations?

One should find all possible permutations first.
To find all UA permutations, starting from given permutation, one should complete given permutation to valid solution grid in some way. For example, by considering given permutation as pseudo puzzle. Then one should "invert" found solution grid, treating the cells of given permutation as empty cells and treating remaining cells as clue cells. Solving such "inverted" puzzle gives all UA permutations. If we are dealing with strongly minimal UA, we must get 2 permutations exactly. Greater number of permutations implies that UA isn't minimal or is weakly minimal (both cases are not suitable for DP construction).
Then one should check both permutations for minimality - permutations must differ in every UA cells. Both permutations' digits are candidates for DP cell.

OK, I understand. When I first said systematic, I thought of something simpler (some easy symbol manipulation of the UA representation). I now see it's more complex than I thought. I don't have the software to do this; I've concentrated on solving puzzles.

Serg wrote:Denis, if you want to generate high order UA, I can propose you to use two-row UA sets, having even orders (from U4 to U18), or more complicated two-row two-column UAs, having even orders from U6 to U34.

Not sure what your proposal is. Do you have the software to do this?
After my first quick tests upto DP9, I'm more or less convinced that larger DPs are not (or very rarely) useable, not only by a manual solver but also by software. It would be marginally interesting to check this and I'll do it for all the DPs I can get a hand on (maybe someone has already done it somewhere). But I don't think it worth to invest time in generating such DPs if it requires writing new software.
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by **Serg** » Sat Jan 11, 2025 2:16 pm

denis_berthier wrote:Not sure what your proposal is. Do you have the software to do this?

I can describe an algorithm to generate strongly minimal two-row UAs. I have no ready program to do it. Maybe coloin has a program to generate UAs.

Serg

by **blue** » Sat Jan 11, 2025 9:33 pm

Below, is the list of deadly patterns that can be produced from the (strongly) minimal UA sets with size <= 12 -- 2 characters per cell.
(For size <= 12, the minimal UA sets ... 525 of them ... are all "strongly minimal", with valency=2).

There are only 408 "essentially distinct" deadly patterns.
These are the minlex forms.

For the ones with "(size,1)" at the end of the line, the two solutions are isomorhpic ... they have the same minlex form.
For the "(size,2)" cases, that isn't the case. Each of those, accounts for two (essentially) distinct UA sets.
There are 291 "(size,1)", and 117 "(size,2)" cases ... 291 + 2 * 117 = 525.

Hidden Text: Show

Website · by **denis_berthier** » Sun Jan 12, 2025 8:49 am

Hi Blue
Thanks for the list. It's exactly what I needed.
I'm busy today, but I'll work on it tomorrow.
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by **eleven** » Sun Jan 12, 2025 6:26 pm

For a (manual) solver MUG's are more interesting, because they are not that rare / have less extra candidates as some multi-cell DP's with 2 candidates.
E.g. you can look for this MUG

Code: Select all: 123 123 123 . . . . . . ------------ 123 123 123 . . . . . .

instead of that DP

Code: Select all: 12 23 13 . . . . . . ------------ 13 12 13 . . . . . .

or this one

Code: Select all: . . . | . . . . . . | . . . . . . | . 12 12 -------------------- . . 134 | . . 134 . . 134 | . 134 . . . 234 | . 234 234

instead of that

Code: Select all: . . . | . . . . . . | . . . . . . | . 12 12 -------------------- . . 13 | . . 13 . . 14 | . 14 . . . 34 | . 24 23

Website · by **denis_berthier** » Mon Jan 13, 2025 3:48 am

blue wrote:For the ones with "(size,1)" at the end of the line, the two solutions are isomorhpic ... they have the same minlex form.
For the "(size,2)" cases, that isn't the case. Each of those, accounts for two (essentially) distinct UA sets.

Is this distinction related to the type of permutation inside the UA?

About guardians. I think we can use the same name as in impossible patterns: in one case they guard against contradiction, here they guard against non-uniqueness.
As I understand the notation, in a pattern such as ... . . . 12 23 34 . . . ...
- any digit other than 1 and 2 in cell "12" is a guardian
- any digit other than 2 and 3 in cell "23" is a guardian
...

I've finally had time yesterday evening to adapt your list to the format I used in the rule generators I've written a few days ago.
I takes SudoRules 3s on my Mac to generate the 4x408 ORk-detection rules derivable from it.
The factor 4 is decomposed as:
- 2 for row-column symmetry. as those are not generic rules, I need to explicitly use rows, columns, blocks... and therefore
- 2 for activation + detection

First decision was to choose a cutoff for the number of guardians allowed. I chose 8.
I tried a first run with all the rules loaded but it quickly led to very long computation time and to memory saturation for some puzzles (even with 64 GB).
Therefore, I restricted my computations to DPs with 11 or fewer cells. Computations are still slow, but they are manageable.
After running during the night, it appears that:
- many DPs must exist with more than 8 guardians
- very few DPs with ≤ 8 guardians and ≥ 8 cells exist
- based on the 1st 8,000 puzzles in cbg-000, there not a single example where the W + DP9-O6W and W + DP11-ORW would be different

I've found only one instance of a DP11 (but it's useless in the puzzle):

Code: Select all: Puzzle cbg-000 #5600 +-------+-------+-------+ ! . 2 . ! 4 5 . ! . . . ! ! . 5 . ! 1 . 9 ! 2 . . ! ! 6 8 . ! . . . ! 1 . 4 ! +-------+-------+-------+ ! 2 . . ! 7 . 8 ! . . . ! ! 7 . 6 ! . 4 5 ! . . . ! ! . . . ! . 9 . ! . . . ! +-------+-------+-------+ ! . . . ! . 7 . ! 9 . . ! ! 5 . 4 ! . . . ! . 6 . ! ! . . . ! 5 . 3 ! . . . ! +-------+-------+-------+ .2.45.....5.1.92..68....1.42..7.8...7.6.45.......9........7.9..5.4....6....5.3... 98622

Code: Select all: Resolution state after Singles and whips[1]: +-------------------+-------------------+-------------------+ ! 13 2 137 ! 4 5 6 ! 378 3789 3789 ! ! 4 5 37 ! 1 8 9 ! 2 37 6 ! ! 6 8 9 ! 23 23 7 ! 1 5 4 ! +-------------------+-------------------+-------------------+ ! 2 1349 5 ! 7 13 8 ! 6 1349 139 ! ! 7 139 6 ! 23 4 5 ! 38 12389 12389 ! ! 8 134 13 ! 6 9 12 ! 5 12347 1237 ! +-------------------+-------------------+-------------------+ ! 13 6 2 ! 8 7 4 ! 9 13 5 ! ! 5 37 4 ! 9 12 12 ! 378 6 378 ! ! 9 17 8 ! 5 6 3 ! 4 127 127 ! +-------------------+-------------------+-------------------+ 94 candidates.

Code: Select all: DP4-2-1s-OR7-relation in cells (marked #): (r9c9 r9c8 r6c9 r6c8) with 7 guardians (in cells marked @) : n7r9c9 n7r9c8 n3r6c9 n7r6c9 n3r6c8 n4r6c8 n7r6c8 +-------------------------+-------------------------+-------------------------+ ! 13 2 137 ! 4 5 6 ! 378 3789 3789 ! ! 4 5 37 ! 1 8 9 ! 2 37 6 ! ! 6 8 9 ! 23 23 7 ! 1 5 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 1349 5 ! 7 13 8 ! 6 1349 139 ! ! 7 139 6 ! 23 4 5 ! 38 12389 12389 ! ! 8 134 13 ! 6 9 12 ! 5 12347#@ 1237#@ ! +-------------------------+-------------------------+-------------------------+ ! 13 6 2 ! 8 7 4 ! 9 13 5 ! ! 5 37 4 ! 9 12 12 ! 378 6 378 ! ! 9 17 8 ! 5 6 3 ! 4 127#@ 127#@ ! +-------------------------+-------------------------+-------------------------+

Code: Select all: DP4-2-1s-OR8-relation in cells (marked #): (r9c9 r9c8 r5c9 r5c8) with 8 guardians (in cells marked @) : n7r9c9 n7r9c8 n3r5c9 n8r5c9 n9r5c9 n3r5c8 n8r5c8 n9r5c8 +-------------------------+-------------------------+-------------------------+ ! 13 2 137 ! 4 5 6 ! 378 3789 3789 ! ! 4 5 37 ! 1 8 9 ! 2 37 6 ! ! 6 8 9 ! 23 23 7 ! 1 5 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 1349 5 ! 7 13 8 ! 6 1349 139 ! ! 7 139 6 ! 23 4 5 ! 38 12389#@ 12389#@ ! ! 8 134 13 ! 6 9 12 ! 5 12347 1237 ! +-------------------------+-------------------------+-------------------------+ ! 13 6 2 ! 8 7 4 ! 9 13 5 ! ! 5 37 4 ! 9 12 12 ! 378 6 378 ! ! 9 17 8 ! 5 6 3 ! 4 127#@ 127#@ ! +-------------------------+-------------------------+-------------------------+

Code: Select all: DP11-3-31s-OR8-relation in cells (marked #): (r3c4 r3c5 r8c6 r8c5 r4c2 r4c5 r6c9 r6c6 r5c9 r5c2 r5c4) with 8 guardians (in cells marked @) : n4r4c2 n9r4c2 n3r6c9 n7r6c9 n3r5c9 n8r5c9 n9r5c9 n9r5c2 +-------------------------+-------------------------+-------------------------+ ! 13 2 137 ! 4 5 6 ! 378 3789 3789 ! ! 4 5 37 ! 1 8 9 ! 2 37 6 ! ! 6 8 9 ! 23# 23# 7 ! 1 5 4 ! +-------------------------+-------------------------+-------------------------+ ! 2 1349#@ 5 ! 7 13# 8 ! 6 1349 139 ! ! 7 139#@ 6 ! 23# 4 5 ! 38 12389 12389#@ ! ! 8 134 13 ! 6 9 12# ! 5 12347 1237#@ ! +-------------------------+-------------------------+-------------------------+ ! 13 6 2 ! 8 7 4 ! 9 13 5 ! ! 5 37 4 ! 9 12# 12# ! 378 6 378 ! ! 9 17 8 ! 5 6 3 ! 4 127 127 ! +-------------------------+-------------------------+-------------------------+

solution in W2

Website · by **denis_berthier** » Mon Jan 13, 2025 3:51 am

eleven wrote:For a (manual) solver MUG's are more interesting, because they are not that rare / have less extra candidates as some multi-cell DP's with 2 candidates.
E.g. you can look for this MUG
Code: Select all
123 123 123 . . . . . . ------------ 123 123 123 . . . . . .

instead of that DP
Code: Select all
12 23 13 . . . . . . ------------ 13 12 13 . . . . . .

OK, but if you define the pattern as in the above MUG, how do you know what the guardians are?
Or do you mean that you look only for DPs whose guardians are the candidates in the MUG but not in the DP?

[Edit]: on second thoughts, I think defining a MUG as a DP that has only guardians from the digits in the DP would make an alternative way of restricting the number of guardians in DP. I don't know if this is (or is equivalent to) the standard definition of a MUG (if such a thing exists).
For me, it would require to write a slightly different version of my DP detection rules, but it'd be easy to do.
However, I doubt that the final results about the resolution power would be much more positive.
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by **eleven** » Mon Jan 13, 2025 1:45 pm

MUG's are deadly uniqueness patterns, complete or not. The bigger they are, the more rare they seem to be. In hard puzzles very seldom a DP is really useful because of the many extra candidates (maybe with the exception of tridagon puzzles with their special structure), but sometimes they can be integrated in chains.
This simple pattern has been used several times in the puzzle thread, in what you would call easy puzzles.
For the other one i posted i could not find a good application so far, just this one to get an "elegant" solution in an (also manual) easy puzzle:

Hidden Text: Show

The New Sudoku Players' Forum

Unavoidable sets vs deadly patterns.

Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

Re: Unavoidable sets vs deadly patterns.

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