Commonness of various techniques

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Commonness of various techniques

Postby 999_Springs » Sun May 06, 2007 7:24 pm

I have read the thread "Method hierarchy" in "Advanced solving techniques" and there are some techniques which it seems Mike Barker's frequency analysis finds much, much more than I do when I solve my puzzles.

Is there any reason why?

These are the techniques:
Locked candidates type 2
Finned swordfish
Hidden triple
ALS xz-rule
XY-wing
Sue de Coq (although this one is fairly high on my hierarchy of techniques)

And there is one technique which I find a lot more than Mike Barker suggests which is the ordinary turbot fish.
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Postby Mike Barker » Sun May 06, 2007 11:39 pm

There are a number of explanations for the differences. I show no Turbot fish mostly because I use Havard's strong link approach rather than searching for Turbot fish. Even then a skyscraper is also a Sashimi X-wing and my solver will pick it up as a finned fish. My solver doesn't distinguish between the other two types (a kite or a turbot fish), but treats them as X-cycles (two strong links). This makes the approach to two strong links equivalent to three or more strong links where we definitely don't have names for all of the possibilities.

The rest of the differences could be because I made a mistake. Another possibility is because of differences in our random puzzle generators. I use suexg to generate random puzzles. I don't know if anyone has tested it to see if it is unbiased (there was lots of discussion about this earlier this year). If your generator is creating puzzles of a specific level, then there could be a bias which would explain some of the differences. Note too that the results are based on only 10000 runs so there will be some variation in the results.

Another big issue is the order of solving techniques. doduff correctly suggested looking for all possible eliminations first and then performing the eliminations. This is a great idea for counting occurrences of techniques, but would be a major rewrite of my solver. Also I think its more human to make eliminations one at a time. This probably is most obvious in the occurrences of swordfish. Back then they were very high in my solving hierarchy (since then I've moved them down). ALS xz-rule was also pretty high given the complexity of finding an ALS. Sue de Coq is high because I had placed it before ALS xz-rule. Following this technique the occurrences are much lower. It doesn't surprise me that locked candidates and XY-wings are relatively high in occurrence.

I ran an update to the hierarchy a while ago, but never posted it. I'll go ahead and do so now. My results are in no way authoritative. I'd love to see your results as well.
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Postby 999_Springs » Tue May 15, 2007 7:42 pm

I tend to use my brain when solving puzzles rather than a solver. That probably is one of the reasons but I can't compare how my brain works to how a computer program works so I don't know.

When I search for X-wings I look for 2 strong links. This always results in turbot fish. I can't find any other way to look for X-wings. Could this be a possible reason why I find a lot of them?

Mike Barker wrote:Sue de Coq is high because I had placed it before ALS xz-rule.

So do I but I never find either!

Mike Barker wrote:I'd love to see your results as well.

I tried to do some Su-Dokus over the weekend (using my brain rather than a solver so I didn't do very many) and these are the results for the relative occurrence of techniques except for singles:
Code: Select all
Locked candidates type 1: 11

Turbot fish: 5

Naked pair: 3
Hidden pair: 3
Singles forcing chain: 3

Swordfish: 2
XY-wing: 2

X-wing: 1
3 strong links: 1
Finned X-wing: 1

Locked candidates type 2: 0
Hidden triple: 0
Naked quad: 0
Hidden quad: 0
Jellyfish: 0
4 strong links, finned swordfish, ALS xz, xy-chain, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!


I don't know why there are 2 XY-wings there. I have only ever found 3 and here are 2 of them.
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Postby wapati » Tue May 15, 2007 10:06 pm

Just because I am curious, can you break down the Turbots you found into the three types?

Classic (fish shaped), two-string kite and skyscraper.

Paper solving I find skyscrapers and finned-x in nearly all puzzles.
(BTW, the skyscraper is a sashimi-x so I mentally include it in finned-x wings.)
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Postby 999_Springs » Thu May 17, 2007 7:17 pm

wapati wrote:Classic (fish shaped), two-string kite and skyscraper.


I don't know what they are. Could you please explain?
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Postby 999_Springs » Sun May 20, 2007 6:20 pm

I did some more puzzles. Here is an update:
Code: Select all
Locked candidates type 1: 30


Naked pair: 7

Turbot fish: 6
Hidden pair: 6

X-wing: 4

Singles forcing chain: 3

Swordfish: 2
XY-wing: 2
3 strong links: 2
Finned X-wing: 2
Locked candidates type 2: 2

Naked triple: 1
Y-wing: 1
Nishio: 1

Hidden triple: 0
Naked quad: 0
Hidden quad: 0
Jellyfish: 0
4 strong links, finned swordfish, ALS xz, xy-chain, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!


Turbot fish seem to have calmed down a bit. I will update these every week or two or so.
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Postby Pat » Mon May 21, 2007 11:20 am

999_Springs wrote:
wapati wrote:Classic (fish shaped), two-string kite and skyscraper.

I don't know what they are. Could you please explain?


see: two "new" techniques, Skyscraper and 2-string Kite

( or try the SuDoPedia, or Mike Barker )

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Postby 999_Springs » Thu Jun 07, 2007 7:57 pm

update:
Code: Select all
Locked candidates type 1: 60

Hidden pair: 13

Naked pair: 12

Turbot fish: 8

X-wing: 5

Locked candidates type 2: 4

Singles forcing chain: 3
Swordfish: 3

XY-wing: 2
3 strong links: 2
Finned X-wing: 2

Naked triple: 1
Naked quad: 1
Y-wing: 1
Nishio: 1

Hidden triple: 0

Hidden quad: 0
Jellyfish: 0
4 strong links, finned swordfish, ALS xz, xy-chain, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!


I have been doing the first 3 of the top95, hence hidden pairs have gone up and locked candidates also but not much else.

As for the types of turbot fish: I find roughly equal numbers of all three types but skyscraper is slightly higher as I look for X-wings before turbots and this results in many sets of 2 parallel strong links.
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Postby daj95376 » Thu Jun 07, 2007 9:05 pm

Try these from wapati and see what technique distribution you get.

Code: Select all
...2..39.....7.4.1.....6.276...135...8.6.5.3...578...446.3.....8.3.5.....52..4...
...6.3.5..9.8...1...8.....6.67.9...28..7.2..99...8.74.7.....6...2...8.9..8.3.4...
..39..6.5..97.....27...3....1.43......6...4......75.2....5...13.....89..3.1..95..
52......91....4.....621.5..39..........6.1..........82..9.651.....3....48......25
9.843..2...2..8.36..39.....8...6....4..8.5..2....4...3.....93..25.3..4...9..542.7
...1..84...45.76......8...29.6.5..1...37.89...5..1.3.43...7......56.34...68..1...
.9...8...148....3..6..4.2......27..3..49.35..3..45......9.7..5..2....164...5...9.
...41..5.3....8..1...5..89.5.7....3..3.....2..1....4.9.93..1...2..9....6.5..76...
......47...175..628.7...5.9....81...5..4.9..1...52....2.4...1.617..349...98......
5...8...2..69.23....................3.5...6.98.95.72.46.42.17.8....5....2.3.7.4.6
4.6..2........4....5.3..1...8.1..93........2..2.9..85..3.8..5.......7...7.1..9...
6..21...7...839....2.....9.1.7...5.3.4.....8.9.5...7.6.1.....5....456...5..32...9
...3...5.....6.7.9.....146.5..73.8...4.6.2.3...2.18..6.741.....3.9.2.....2...7...
..492..57....4.9.19..1...4.3.1......65.....18......5.4.8...1..55.2.8....17..524..
5..12..94..9.....2.1...9...8...1.5..4..8.6..3..2.5...1...2...6.1.....2..32..64..7
..49.5.1.5.8...3..7......56....6..9.2..5.3..1.4..2....12......5..7...1.3.6.7.19..
...9..54.....18....6.3.....84.....569..6.5..365.....18.....9.3....24.....78..3...
..9.1...28.....96.2..8..3.1....41....6.7.8.1....96....7.3..5..9.92.....76...7.8..
17.4.5.39...8.1.....4...2.....5.6....2..3..6...3.4.5...1.....7.74.....92..9.8.4..
4....3..6...8..4....61.4.9.6.4..8.7.........38.3..6.1...89.5.3....4..1..7....1..5
.9.4.3.....7..8.691........76.8....58..719..39....6.18........154.3..9.....6.7.5.
............841....64...53...27.36..7.......5.9..2..7...1...3...4..7..6.9...8...7
4...2...5.964...8.85..........5.17...7..9..6...47.6..........46.6...532.2...7...1
....8.54....9.7..2......3.7.3.6.4.2.1.......4.8.5.3.1.2.1......3..1.5....45.7....
3.....84..582..9.1.9..7......91.753.....2......76.342..2..1.....813..7.27.....31.
.......2.15....3...6.3...197..53..4....1.7....3..69..749...5.6...6....91.1.......
..8..3..4...6..29.59...4..38...4......3..9.126...3....91...8..7...9..48...5..7..9
41......6..9.16.....6....2.2...9.6.1.4.5.1.9.7.1.2...5.5....8.....46.9..9......52
....1.8.47.4..2....5..3.2..63...5....452.836....3...58..3.2..8....7..4.34.7.5....
....3...9.928.6....3...462......9..3.2.3.5.4.5..7......846...3....9.248.2...8....
.651.....4...657......9.1..8..7....2..6...4..9....1..3..3.2......851...9.....481.
8..2....9.7..6...2.3....67....6...9...94.73...1...5....48....1.7...8..2.6....3..7
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Postby 999_Springs » Fri Jun 22, 2007 7:55 pm

The second of wapati's puzzles was flooded with strong links of ones and fives hence the surge in turbot fish.

Code: Select all
Locked candidates type 1: 82

Turbot fish: 18
Naked pair: 18
Hidden pair: 18

X-wing: 10

Locked candidates type 2: 7

3 strong links: 6

Singles forcing chain: 3
Swordfish: 3
XY-wing: 3
Naked triple: 3 

Finned X-wing: 2

Naked quad: 1
Y-wing: 1
Nishio: 1
Hidden triple: 1
XY-chain: 1

Hidden quad: 0
Jellyfish: 0
4 strong links, finned swordfish, ALS xz, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!
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Postby Mike Barker » Sat Jun 23, 2007 1:09 am

Thanks for posting your results. It would be really interesting if you could post all of the puzzles (81 digit line format) you've used so far and I could compare directly with what you have. How many of the Turbot fish you've found are not a skyscraper since we already know that will be counted as a sashimi X-wing or a "turbot fish" since that will show up as an empty rectangle? This should leave only kites as discussed here.

For Wapati's second puzzle I get 6 finned X-wings, 2 empty rectangles, 1 kite, and a 5-node XY-chain. Note I didn't try to see the minimum number that could be used. Here's an example of an X-wing, empty rectangle, and the kite:
Code: Select all
Row Finned X-Wing (skyscraper): r2c15|r4c16 => r3c6<>5
+-------------------+-----------------+-------------+
|   124    7    14  |  6   124     3  |   9  5   8  |
|  2345*   9     6  |  8   245*    7  | 234  1  34  |
| 12345  145     8  | 29  1245  19-5  | 234  7   6  |
+-------------------+-----------------+-------------+
|    15*   6     7  |  4     9    15* |   8  3   2  |
|     8  145   145  |  7     3     2  |  15  6   9  |
|     9    3     2  | 15     8     6  |   7  4  15  |
+-------------------+-----------------+-------------+
|     7  145  1345  | 29   125   159  |   6  8  34  |
|   145    2  1345  | 15     6     8  |  34  9   7  |
|     6    8     9  |  3     7     4  |  15  2  15  |
+-------------------+-----------------+-------------+

Empty Row Rectangle (grouped turbot fish): b4|r59c7 => r9c1<>1
+--------------------+----------------+----------------+
|   124    7     14  |  6   124    3  |   9  5      8  |
| 23456    9   3456  |  8   245    7  | 234  1     34  |
| 12345  145      8  | 29  1245  159  | 234  7      6  |
+--------------------+----------------+----------------+
|    15*   6      7  |  4     9   15  |   8  3      2  |
|     8  145*   145* |  7     3    2  |  15* 6      9  |
|     9    3      2  | 15     8    6  |   7  4     15  |
+--------------------+----------------+----------------+
|     7  145   1345  | 29   125  159  |   6  8   1345  |
| 13456    2  13456  | 15    67    8  |  34  9  13457  |
|  56-1    8      9  |  3    67    4  |  15* 2    157  |
+--------------------+----------------+----------------+

Two Strong Links (kite): r4c1=1=r4c6-1-r6c4=1=r8c4~1~ => r8c1<>1
+-------------------+----------------+-------------+
|   124    7    14  |  6   124    3  |   9  5   8  |
|  2345    9     6  |  8   245    7  | 234  1  34  |
| 12345  145     8  | 29  1245   19  | 234  7   6  |
+-------------------+----------------+-------------+
|    15*   6     7  |  4     9   15* |   8  3   2  |
|     8  145   145  |  7     3    2  |  15  6   9  |
|     9    3     2  | 15*    8    6  |   7  4  15  |
+-------------------+----------------+-------------+
|     7  145  1345  | 29    12  159  |   6  8  34  |
|   4-1    2  1345  | 15*    6    8  |  34  9   7  |
|     6    8     9  |  3     7    4  |  15  2  15  |
+-------------------+----------------+-------------+
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Postby 999_Springs » Sat Jun 23, 2007 6:08 pm

Mike Barker wrote:It would be really interesting if you could post all of the puzzles (81 digit line format) you've used so far and I could compare directly with what you have.


I don't have most of them. The puzzles that I have been doing are: the first 3 from the top95; the first 2 from wapati's list; lots of super fiendish Times puzzles; and sometimes the odd nice-looking puzzle which happens to bump into me. I will try to recover some of the Times puzzles.

All your finned X-wings made from 2 strong links are turbot fish if you ask me.

The very moment I started all this in the first place, all the triples decided to run away. Can there be any reason why? Naked triples used to be rather common.
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Postby Mike Barker » Sat Jun 23, 2007 6:51 pm

In your original post the issue you raised was why you seem to have many more turbot fish than I report. I think we've found the answer: I report them as finned fish and empty rectangles. No argument that they are also turbot fish, I guess I just prefer the strong link approach.
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Postby daj95376 » Sun Jun 24, 2007 12:04 am

999_Springs wrote:The very moment I started all this in the first place, all the triples decided to run away. Can there be any reason why? Naked triples used to be rather common.

I don't know why this occurs in your case, but seeing the high count for Locked Candidate 1 gives me a good idea. Many Naked Triples coincide with Locked Candidate 1 patterns. My solver finds a Naked Triple when Simple Sudoku may pop out a stream of Locked Candidate 1 patterns. Hierarchy of techniques is everything sometimes!!!

Try this example from Mike Barker's contribution to the zoo. Three Locked Candidate 1 patterns ... or one Locked Naked Triple.

Code: Select all
 9.......1.5...23.....534........94..7...2...8.....5.7..19.....3......2..3.291..8.
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Postby 999_Springs » Sun Jul 15, 2007 7:39 pm

I have not had much time recently as I have been away for a week and I have also had exams, but here is an update:

Code: Select all
Locked candidates type 1: 103

Hidden pair: 24

Turbot fish: 23

Naked pair: 21
 
X-wing: 13

Locked candidates type 2: 10

3 strong links: 6

Singles forcing chain: 4
XY-chain: 4 

Swordfish: 3
XY-wing: 3
Naked triple: 3 

Finned X-wing: 2

Naked quad: 1
Y-wing: 1
Nishio: 1
Hidden triple: 1
ALS xz: 1!!! Finally!

Hidden quad: 0
Jellyfish: 0
4 strong links, finned swordfish, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!


The ALS xz was not in the puzzles which were posted in the "How do you find almost-locked set eliminations" thread, but in wapati's 4th puzzle. I now think that it would be better not to look for ALS in puzzles but only notice when they jump out at me.

(I'm also not very fast at finding empty rectangles.)

daj95376 wrote:Many Naked Triples coincide with Locked Candidate 1 patterns.

I see. But both types seem to be disappearing now to be replaced with something like hundreds of hidden pairs.
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