Tarek,
In addition to information supplied via PM, in general the file games_sample can be used for such purposes.
Regards,
Mike
Revision of SE ratings and resolution rules
Re: Revision of SE ratings and resolution rules
by m_b_metcalf » Sat Sep 07, 2019 9:22 am
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m_b_metcalf - 2017 Supporter
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Re: Revision of SE ratings and resolution rules
by tarek » Sat Sep 07, 2019 10:21 am
Thanks Mike,
I'm going now through some batch rating puzzles in the BUG zone (5.6-6.1) to test lksudoku's BUG bug fixes
I'm also doing another rating to test his Chain sorting bug fix too (Testing puzzles in the 8.0-10.0 range).
I do think that the Sukaku explainer future release would be useful addition for the Patterns game. It has the added dimension of the "Technique name" as another way to trump a previous entry with same ER/EP/ED for those puzzles in the rating overlap area.
The bug fixes would have an improved and more accurate rating
If it is going to be a new game. Then a change in the rating hierarchy for the lower ratings <5.6 can be introduced without too much fuss along the lines mentioned in previous posts.
tarek
I'm going now through some batch rating puzzles in the BUG zone (5.6-6.1) to test lksudoku's BUG bug fixes
I'm also doing another rating to test his Chain sorting bug fix too (Testing puzzles in the 8.0-10.0 range).
I do think that the Sukaku explainer future release would be useful addition for the Patterns game. It has the added dimension of the "Technique name" as another way to trump a previous entry with same ER/EP/ED for those puzzles in the rating overlap area.
The bug fixes would have an improved and more accurate rating
If it is going to be a new game. Then a change in the rating hierarchy for the lower ratings <5.6 can be introduced without too much fuss along the lines mentioned in previous posts.
tarek
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tarek - Posts: 3762
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Re: Revision of SE ratings and resolution rules
by creint » Sat Sep 07, 2019 12:06 pm
Is there an small file (~200 puzzles) which only contains rating 7.5-10.5 sorted on rating, so I can compare solve speed my solver vs SE? I doubt if SE is fast at the lower range forcing chains.
We cannot test SE for variants but my solver is a bit faster than WinSAT at solving those 206 puzzles:
http://forum.enjoysudoku.com/sudoku16-minimal-puzzles-t35780-15.html#p275765
We cannot test SE for variants but my solver is a bit faster than WinSAT at solving those 206 puzzles:
http://forum.enjoysudoku.com/sudoku16-minimal-puzzles-t35780-15.html#p275765
- creint
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Re: Revision of SE ratings and resolution rules
by m_b_metcalf » Sat Sep 07, 2019 12:23 pm
creint wrote:Is there an small file (~200 puzzles) which only contains rating 7.5-10.5 sorted on rating, so I can compare solve speed my solver vs SE?
There is a file of 1000 puzzles, unsorted, here, that probably contains most of what you want.
Regards,
Mike
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Re: Revision of SE ratings and resolution rules
by tarek » Sat Sep 07, 2019 6:58 pm
Good news about lksudoku's bug fixes for BUG & UR/UL Type 3. The group of BUG Puzzles from Patterns game were all rated the same or downgraded.
Bad news about the chaining sorting .... Although the majority were rated the same or downgraded, there were also some that were rated higher after the fix
after the fix it became:
Therefore this part of lksudoku's bug fixes will not be merged with the Sukaku explainer at this stage
tarek
Bad news about the chaining sorting .... Although the majority were rated the same or downgraded, there were also some that were rated higher after the fix
- Code: Select all
100200003040000050003006700002000008030070040900000100008400600050000020600003009 9.7/9.7/9.4 Patrice
after the fix it became:
- Code: Select all
100200003040000050003006700002000008030070040900000100008400600050000020600003009 9.7/9.7/9.5 DDFC+/DDFC+/DCFC
Therefore this part of lksudoku's bug fixes will not be merged with the Sukaku explainer at this stage
tarek
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Re: Sukaku Explainer v1.3.0.2
by tarek » Sun Sep 08, 2019 7:42 am
Sukaku Explainer v1.3.0.2 release is available
We've included the backward compatible "SukakuExplainer.jar" and another modified version "SukakuExplainer_NewRatings13021.jar" with proposed new ratings. The modified version will show that clearly in the GUI and would have version 1.3.0.2.1.
Using either binary for the patterns game is similar to what has been done before but you can now add the options %S/%T/%U to get the short names of corresponding techniques for %r/%p/%d
The command line parameters are available on the wiki page
https://github.com/SudokuMonster/SukakuExplainer/wiki/Batch-mode-command-line-parameters
With the helpful puzzles from the patterns game pointed out and supplied by Mike, I also looked at most puzzles rated 4.5-5.1 (Except 5.0) for re-rating. Some of the interesting results:
tarek
We've included the backward compatible "SukakuExplainer.jar" and another modified version "SukakuExplainer_NewRatings13021.jar" with proposed new ratings. The modified version will show that clearly in the GUI and would have version 1.3.0.2.1.
Using either binary for the patterns game is similar to what has been done before but you can now add the options %S/%T/%U to get the short names of corresponding techniques for %r/%p/%d
The command line parameters are available on the wiki page
https://github.com/SudokuMonster/SukakuExplainer/wiki/Batch-mode-command-line-parameters
New rating Patterns game 0359: Show
With the helpful puzzles from the patterns game pointed out and supplied by Mike, I also looked at most puzzles rated 4.5-5.1 (Except 5.0) for re-rating. Some of the interesting results:
- Code: Select all
+-------------------+-------------------+-------------------+
| 35689 367 389 | 467 467 1 | 57 89 2 |
| 5689 267 289 | 267 3 89 | 57 4 1 |
| 4 127 12 | 5 27 89 | 3 6 89 |
+-------------------+-------------------+-------------------+
| 69 26 5 | 289 28 3 | 1 7 4 |
| 39 8 379 | 179 17 4 | 2 5 6 |
| 1 4 27 | 267 5 67 | 89 89 3 |
+-------------------+-------------------+-------------------+
| 38 13 6 | 18 9 5 | 4 2 7 |
| 2 5 4 | 3 67 67 | 89 1 89 |
| 7 9 18 | 148 148 2 | 6 3 5 |
+-------------------+-------------------+-------------------+
10 cells Unique Loop type 3 (with Hidden Triplet)
5.1/1.2/1.2 champagne becomes 5.0/1.2/1.2 UL103/HS/HS
+-------------+-------------+-------------+
| 57 1 6 | 4 3 2 | 789 58 59 |
| 3 89 57 | 1 6 89 | 27 257 4 |
| 2 4 89 | 7 5 89 | 1 6 3 |
+-------------+-------------+-------------+
| 1 6 57 | 2 89 3 | 789 4 59 |
| 57 89 2 | 6 89 4 | 3 57 1 |
| 89 3 4 | 5 1 7 | 289 28 6 |
+-------------+-------------+-------------+
| 6 5 3 | 8 7 1 | 4 9 2 |
| 4 7 1 | 9 2 6 | 5 3 8 |
| 89 2 89 | 3 4 5 | 6 1 7 |
+-------------+-------------+-------------+
12 cells Unique Loop type 3 (with Naked Pair)
5.1/1.2/1.2 champagne becomes 5.0/1.2/1.2 UL123/HS/HS
tarek
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tarek - Posts: 3762
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Re: Revision of SE ratings and resolution rules
by tarek » Sun Sep 15, 2019 8:14 am
I haven't got much feedback about rating changes especially after 999_Springs post. No feedback about what I said regarding Patterns game either.
Rating Quads in general higher than UR/UL when a UL + Quad would rank lower is silly.
The only way to bring Quads any further down would risk having a quad ranked easier than a simple UR1.
The way that Explainer currently ranks methods would guarantee that a Turbot fish at ER=6.6 will always be ranked higher than any 12 cell Unique loop Type 3 with a quad or any type of BUG. A 4x3x3x3 Jellyfish will always be ranked less than a turbot fish despite an obvious disparity.
The next releases of Sukaku Explainer will allow the command line solver to toggle between old and the proposed new ratings. It should allow also 2 different ways of batch solving one of them is lksudoku's enhancement in his FIxed14 release. I can discuss that in the thread the deals with Sukaku explainer improvements if needed.
Rating Quads in general higher than UR/UL when a UL + Quad would rank lower is silly.
The only way to bring Quads any further down would risk having a quad ranked easier than a simple UR1.
The way that Explainer currently ranks methods would guarantee that a Turbot fish at ER=6.6 will always be ranked higher than any 12 cell Unique loop Type 3 with a quad or any type of BUG. A 4x3x3x3 Jellyfish will always be ranked less than a turbot fish despite an obvious disparity.
The next releases of Sukaku Explainer will allow the command line solver to toggle between old and the proposed new ratings. It should allow also 2 different ways of batch solving one of them is lksudoku's enhancement in his FIxed14 release. I can discuss that in the thread the deals with Sukaku explainer improvements if needed.
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tarek - Posts: 3762
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Re: Revision of SE ratings and resolution rules
by tarek » Mon Sep 16, 2019 10:00 am
Having now integrated lksudoku's fixes and enhancements into the project, some of you may like the fact that in the future release you can control (form the command line) what techniques to use or omit. The solving and rating can therefore be done in a variety of ways!
The ability to use the suggested new rating can be done also from the command line via an option in addition to using 2 optional batch solving modes.
These modifications have made Sukaku explainer more versatile but the main driving force behind the project was to improve functionality / Speed / rating especially in the very difficult area of the ratings with very difficult Sukakus. That would be the main focus of the next phase of improvements if there is going to be more work done
let me know if there are still any suggestions feedback regarding old/new ratings.
tarek
The ability to use the suggested new rating can be done also from the command line via an option in addition to using 2 optional batch solving modes.
These modifications have made Sukaku explainer more versatile but the main driving force behind the project was to improve functionality / Speed / rating especially in the very difficult area of the ratings with very difficult Sukakus. That would be the main focus of the next phase of improvements if there is going to be more work done
let me know if there are still any suggestions feedback regarding old/new ratings.
tarek
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tarek - Posts: 3762
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Re: Rating of WXYZ wing
by tarek » Tue Oct 08, 2019 5:09 pm
This is the proposed rating mechanism for #wxyz wing which will be followed by similar rating techniques for larger wings.
Base rate: A fixed number (5.5 for WXYZ wing)
Total candidate number difficulty: Added to Base rate. (Total candidates in Larger ALS / 2 - number of cells in larger ALS) * 0.1
Largest cell size difficulty:Added to Base rate. (Total number of cells in the wing - number of candidates in largest cell )* 0.1
[This post is no longer valid as the rating has been revised and changed]
Base rate: A fixed number (5.5 for WXYZ wing)
Total candidate number difficulty: Added to Base rate. (Total candidates in Larger ALS / 2 - number of cells in larger ALS) * 0.1
Largest cell size difficulty:Added to Base rate. (Total number of cells in the wing - number of candidates in largest cell )* 0.1
- Code: Select all
WXYZ wing ratings
ALS 6 7 8 9 10 11 12
Cand#
LC
2 5.7 5.7 5.8 5.8 5.9 5.9 6.0
3 5.6 5.6 5.7 5.7 5.8 5.8 5.9
4 5.5 5.5 5.6 5.6 5.7 5.7 5.8
[This post is no longer valid as the rating has been revised and changed]
Last edited by tarek on Wed Oct 09, 2019 6:21 am, edited 1 time in total.
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Re: Revision of SE ratings and resolution rules
by tarek » Tue Oct 08, 2019 9:59 pm
I decided to abandon the WXYZ wing rating idea above and change to a simpler (sort of) method.
Base rate remains at 5.5.
Added difficulty depends on size of largest cell. I decided to consider it easier if the largest cell is bigger or smaller than the average of Possible largest cell sizes
This means that if the largest cell size is 3 then it is more difficult. The largest cell of size 4 or of size 2 would be considered easier. 0 for 2 1 for 3 and 0 for 4.
So in short the final rating would always be 5.5 unless the largest cell has 3 candidates. this would have a rating of 5.6
Base rate remains at 5.5.
Added difficulty depends on size of largest cell. I decided to consider it easier if the largest cell is bigger or smaller than the average of Possible largest cell sizes
This means that if the largest cell size is 3 then it is more difficult. The largest cell of size 4 or of size 2 would be considered easier. 0 for 2 1 for 3 and 0 for 4.
So in short the final rating would always be 5.5 unless the largest cell has 3 candidates. this would have a rating of 5.6
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Re: Sukaku explainer new techniques ratings
by tarek » Thu Jul 16, 2020 8:42 am
This is just a recap on how Sukaku Explainer rates the aditional techniques that were not in Sudoku v1.2.1
dobrichev last year tabulated the difficulty rating for each technique which are represented by a positive
number rounded to the tenths digit. Rating is formed by:
2 strong links techniques:
Skyscraper in rows or columns conjugate pair: 4.0
2-string kite in rows or column conjugate pair: 4.1
Turbot Fish with block conjugate pair: 4.2
Any variant region or Grouped strong links 4.3
3 strong links: 5.4 - 5.7
4 strong links: 5.8 - 6.1
5 strong links: 6.2 - 6.5
6 strong links: 6.6 - 6.9
WXYZ - TUVWXYZ:
Each wing will have a fixed base rating. for WXYZ & VWXYZ wings there is a complexity
modifier based on size of largest wing cell. Extremities of size incur less complexity rating
while the average size will incur maximum complexity rating. UVWXYZ & TUVWXYZ will
have a fixed base rate only.
WXYZ: Base rating 5.5 Complexity Rating 0 - 0.1 Rating 5.5 - 5.6
VWXYZ: Base rating 6.2 Complexity Rating 0 - 0.2 Rating 6.2 - 6.4
UVWXYZ: Rating 6.6
TUVWXYZ: Rating 7.5
Non Consecutive techniques:
Forcing Cell Non consecutive: 2.4
Forcing Cell Ferz Non consecutive: 2.4
Locked Non consecutive: 2.5
Locked Ferz Non consecutive: 2.5
Generalized intersections: 2.9
Sukaku Explainer still uses the flawed UR/UL ratings which we discussed previously.
Current UR/UL ratings (4.5 - 5.3):
Suggested UR/UL new ratings (From New rating/order option 4.3 - 5.4):
The resolution rules order shows the ratings overlap (modified from 999_Springs):
dobrichev last year tabulated the difficulty rating for each technique which are represented by a positive
number rounded to the tenths digit. Rating is formed by:
- 1. Base difficulty for the used technique.
2. Complexity modifier accounting for details within the used technique.
3. Preceding technique modifier accounting for relationship between currently used
technique and the technique from the preceding step.
4. In addition to the rating number, a rating ordering attribute is used to distinguish
the preferred technique within the possible techniques that evaluate to the exactly
same rating number.
2 strong links techniques:
Skyscraper in rows or columns conjugate pair: 4.0
2-string kite in rows or column conjugate pair: 4.1
Turbot Fish with block conjugate pair: 4.2
Any variant region or Grouped strong links 4.3
3 strong links: 5.4 - 5.7
4 strong links: 5.8 - 6.1
5 strong links: 6.2 - 6.5
6 strong links: 6.6 - 6.9
WXYZ - TUVWXYZ:
Each wing will have a fixed base rating. for WXYZ & VWXYZ wings there is a complexity
modifier based on size of largest wing cell. Extremities of size incur less complexity rating
while the average size will incur maximum complexity rating. UVWXYZ & TUVWXYZ will
have a fixed base rate only.
WXYZ: Base rating 5.5 Complexity Rating 0 - 0.1 Rating 5.5 - 5.6
VWXYZ: Base rating 6.2 Complexity Rating 0 - 0.2 Rating 6.2 - 6.4
UVWXYZ: Rating 6.6
TUVWXYZ: Rating 7.5
Non Consecutive techniques:
Forcing Cell Non consecutive: 2.4
Forcing Cell Ferz Non consecutive: 2.4
Locked Non consecutive: 2.5
Locked Ferz Non consecutive: 2.5
Generalized intersections: 2.9
Sukaku Explainer still uses the flawed UR/UL ratings which we discussed previously.
Current UR/UL ratings (4.5 - 5.3):
- Code: Select all
4 4.5 4.5 4.5 4.6 4.7 4.8 4.5
6 4.6 4.6 4.6 4.7 4.8 4.9 4.5
8 4.7 4.7 4.7 4.8 4.9 5.0 4.5
10 5.0 5.0 5.0 5.1 5.2 5.3 5.0
12 5.0 5.0 5.0 5.1 5.2 5.3 5.0
14 5.0 5.0 5.0 5.1 5.2 5.3 5.0
16 5.0 5.0 5.0 5.1 5.2 5.3 5.0
Suggested UR/UL new ratings (From New rating/order option 4.3 - 5.4):
- Code: Select all
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
The resolution rules order shows the ratings overlap (modified from 999_Springs):
- Code: Select all
1.0: Last value in block, row or column
1.2: Hidden Single in block
1.5: Hidden Single in row or column
1.7: Direct Pointing
1.9: Direct Claiming
2.0: Direct Hidden Pair
2.3: Naked Single
2.4: Forcing Cell (NC & FNC only)
2.5: Locked Cells (NC & FNC only)
2.5: Direct Hidden Triplet
2.6: Pointing
2.8: Claiming
2.9: Generalized Intersections
3.0, 3.2, 3.4: Naked Pair, X-Wing, Hidden Pair
3.6, 3.8, 4.0: Naked Triplet, Swordfish, Hidden Triplet
4.0-4.3: Skyscraper, 2-String Kite, Turbot Crane
4.2, 4.4: XY-Wing, XYZ-Wing
4.5-5.3: Unique rectangles and loops
5.0, 5.2, 5.4: Naked Quad, Jellyfish, Hidden Quad
5.4-5.7: 3 Strong links techniques (includes rings)
5.6: Generalized Naked Quintuple
5.5-5.6: WXYZ Wing (including double linked)
5.6-6.0: Bivalue Universal Graves
5.8-6.1: 4 Strong links techniques (includes rings)
6.2-6.4: VWXYZ Wing (including double linked)
6.2: Aligned Pair Exclusion
6.2-6.5: 5 Strong links techniques (includes rings)
5.6: Generalized Naked Sextuple
6.6: UVWXYZ Wing (including double linked)
6.6-6.9: 6 Strong links techniques (includes rings)
6.5-6.9: X-chains/X-cycles (common 6.5-6.8; rare 6.9)
6.6-7.0: Y-cycles (common 6.6-6.8; rare 6.9-7.0)
7.0-8.0: Bidirectional Cycles (common 7.0-7.2; rare 7.3+)
7.1-7.5: Forcing Chains (common 7.1-7.3; rare 7.4-7.5)
7.5: TUVWXYZ Wing (including double linked)
7.5: Aligned Triplet Exclusion
7.6-8.1: Nishio (common 7.6 and 7.8; semi-rare 7.7 and 7.9; rare 8.0-8.1)
8.2-8.7: Cell/Region Forcing Chains (common 8.2-8.5 (8.2 only for region); rare 8.6-8.7)
8.8-9.6: Dynamic Forcing Chains (common 8.8-9.4; rare 8.7 and 9.5(9.6?))
9.1-10.1: Dynamic Forcing Chains(+) (comon 9.4-10.1; rare 9.3 and 10.2; ?9.1-9.2)
9.9-10.9: Dynamic Forcing Chains(+Forcing Chains) (common 10.2-10.7;
rare 10.1 and 10.8(10.9?); ultra rare 9.9-10.0)
10.8-11.5?: Dynamic Forcing Chains(+Multiple Forcing Chains)
11.4-11.9: Dynamic Forcing Chains(+Dynamic Forcing Chains) 12.0-12.7(Pencilmarks)
Last edited by tarek on Sun Jul 19, 2020 11:16 am, edited 1 time in total.
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Re: Revision of SE ratings and resolution rules
by Hajime » Fri Jul 17, 2020 8:15 am
Very impressive list of methods.
Q1: The Almost Locked Sets and AALS are not present. Why is that?
Q2: in topic http://forum.enjoysudoku.com/windoku-and-xy-chain-t37966.html an intersection of 3 houses needs to be used to solve the Windoku puzzle. It has a rating 2.9, only 0.1 more than pointing/claiming of just 2 houses?
Q1: The Almost Locked Sets and AALS are not present. Why is that?
Q2: in topic http://forum.enjoysudoku.com/windoku-and-xy-chain-t37966.html an intersection of 3 houses needs to be used to solve the Windoku puzzle. It has a rating 2.9, only 0.1 more than pointing/claiming of just 2 houses?
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Re: Revision of SE ratings and resolution rules
by tarek » Fri Jul 17, 2020 10:36 am
Hajime wrote:Very impressive list of methods.
Thanks. It is a collaborative effort. I added a few methods to an already big list from the original
Hajime wrote:Q1: The Almost Locked Sets and AALS are not present. Why is that?
It wasn't originally added. There are the XY - TUVWXYZ wings which are an ALS XZ with 1 bivalue cell but I agree that it should be extended. The collaborative part was mainly focused on enhancement of the current code, improve rating efficiency specifically targeting extremely difficult Sukaku puzzles. Very little was done on the Resolution rules addition. visit the wiki page to see the difference between v1.2.1 methods & the current v1.17.7
Hajime wrote:Q2: in topic http://forum.enjoysudoku.com/windoku-and-xy-chain-t37966.html an intersection of 3 houses needs to be used to solve the Windoku puzzle. It has a rating 2.9, only 0.1 more than pointing/claiming of just 2 houses?
In this generalized method you may want to look at at all intersections with all the candidates in Block 1.
All candidates in Block 1 are obviously locked into that 1 single house (so one house) 1r5c3 can see all of those candidates in Block 1 through c3 & through Windoku Group 5. So you are correct in that it is an intersection of 3 houses but the essential part is that we are talking about 1 value candidates locked in 1 house here. You will see examples with more intersecting houses but the essence is that all the 1 value candidates from 1 single house can see each elimination cell.
You will see this concept of generalization adopted in Generalized Naked sets which is also in Sukaku Explainer and has the same rating of the Non-Generalized Naked sets.
The other issue from that question is "is 0.1 difference justified? (or in the case of the generalized naked sets there is no difference!)." I decided based on what I mentioned above that it is but the idea of mentioning this here is to discuss and if needed change if appropriate!
thanks again
Tarek
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tarek - Posts: 3762
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Re: Revision of SE ratings and resolution rules
by tarek » Tue Jul 21, 2020 9:13 am
Within the next 2 weeks I'll be looking at adding w-wing to the SE resolution rules ...
As it includes a strong link in the core structure ... I may be able to extend the power of the technique similar to what I've done with the strong links algorithm.
In the ideal world I would look at including the grouped strong links as well
Any idea what the ratings should be?
So the the basic structure of the w-wing is as follows
If I have the time to include the extension of strong links as I did with Turbot fishes then we would have:
VLV: W-Wing, VLLV: Extended W-Wing (2 strong links) , VLLLV (3 strong links), VLLLV (4 Strong links) (So still 2 digits in total but an increasing number of strengths in location and a fixed number of strong cells at 2)
What I need is a base rating for W-wing (And the extended forms) & possibly a complexity rating depending on the complexity of the strong links (conjugate pair v grouped strong link)!
Any help would be appreciated as these will go eventually into the program that we all love for everybody to use!!
Tarek
As it includes a strong link in the core structure ... I may be able to extend the power of the technique similar to what I've done with the strong links algorithm.
In the ideal world I would look at including the grouped strong links as well
Any idea what the ratings should be?
So the the basic structure of the w-wing is as follows
SpAce wrote:2 strong cells, 1 strength in location (house), 2 total digits : W-Wing : VLV
If I have the time to include the extension of strong links as I did with Turbot fishes then we would have:
VLV: W-Wing, VLLV: Extended W-Wing (2 strong links) , VLLLV (3 strong links), VLLLV (4 Strong links) (So still 2 digits in total but an increasing number of strengths in location and a fixed number of strong cells at 2)
What I need is a base rating for W-wing (And the extended forms) & possibly a complexity rating depending on the complexity of the strong links (conjugate pair v grouped strong link)!
Any help would be appreciated as these will go eventually into the program that we all love for everybody to use!!
Tarek
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tarek - Posts: 3762
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Re: Revision of SE ratings and resolution rules
by tarek » Fri Jul 24, 2020 6:56 am
The old SE supported Forcing X-chain & Bi-Directional X-Cycle are subsumed within the newer Strong links algorithms (Turbot Fishes, 3 - 5 Strong links). So you will not find these creatures anymore if the new techniques are enabled.
They are not equivalent, however, because the grouped strong links will require most likely Nishio forcing chains to catch ...
tarek
They are not equivalent, however, because the grouped strong links will require most likely Nishio forcing chains to catch ...
tarek
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tarek - Posts: 3762
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