## Commonness of various techniques

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

### Commonness of various techniques

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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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.
Mike Barker

Posts: 458
Joined: 22 January 2006

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: 11Turbot fish: 5Naked pair: 3Hidden pair: 3Singles forcing chain: 3Swordfish: 2XY-wing: 2X-wing: 13 strong links: 1Finned X-wing: 1Locked candidates type 2: 0Hidden triple: 0Naked quad: 0Hidden quad: 0Jellyfish: 04 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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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.)
wapati
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Location: Brampton, Ontario, Canada

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

I don't know what they are. Could you please explain?
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

I did some more puzzles. Here is an update:
Code: Select all
`Locked candidates type 1: 30 Naked pair: 7Turbot fish: 6Hidden pair: 6X-wing: 4Singles forcing chain: 3 Swordfish: 2 XY-wing: 2 3 strong links: 2Finned X-wing: 2 Locked candidates type 2: 2Naked triple: 1Y-wing: 1Nishio: 1Hidden 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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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 )

~ Pat

Pat

Posts: 3880
Joined: 18 July 2005

update:
Code: Select all
`Locked candidates type 1: 60 Hidden pair: 13Naked pair: 12 Turbot fish: 8X-wing: 5Locked candidates type 2: 4Singles forcing chain: 3 Swordfish: 3 XY-wing: 2 3 strong links: 2 Finned X-wing: 2 Naked triple: 1 Naked quad: 1Y-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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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......259.843..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....2.3.7.4.64.6..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...74...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..941......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`
daj95376
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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: 6Singles 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: 1Hidden quad: 0 Jellyfish: 0 4 strong links, finned swordfish, ALS xz, xyz-wing, Sue de Coq, etc...... and everything else: ZERO!!!`
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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  |+-------------------+----------------+-------------+`
Mike Barker

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Joined: 22 January 2006

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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

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Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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.
Mike Barker

Posts: 458
Joined: 22 January 2006

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.`
daj95376
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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: 24Turbot fish: 23 Naked pair: 21  X-wing: 13 Locked candidates type 2: 10 3 strong links: 6 Singles forcing chain: 4XY-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.
Once upon a time I was a teenager who was active on here 2007-2011
ocean and eleven should have paired up to make a sudoku-solving duo called Ocean's Eleven
999_Springs

Posts: 487
Joined: 27 January 2007
Location: In the toilet, flushing down springs, one by one.

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