The New Sudoku Players' Forum

by **Mike Barker** » Fri Mar 03, 2006 2:55 pm

I was going to post the number of solved puzzles and forgot and should have posted the solving order. I will also combine box/line and box/box results in the future. As far as the number of puzzles, you are right, only 92.3% of the puzzles were actually solved, but I did include the results from unsolved puzzles in the statistics. The solving order is as follows:

The initial clues for one of the jellyfish was:
..24...............91.56....3....6.9...6.1..41.6.35..2........1..92...3.38.....47
which proceeded to:
..24....3..3..2....91356.2853..2461992.6.1354146935..22.45.3..1.1924..3.385169247
with candidates (* are the jellyfish, x are the deletions):

Code: Select all: +-------------+----------+--------------+ | 678* 56 2 | 4 19 78*| 1579* 679* 3 | |4678x 567 3 | 78 19 2 |14579x 679x 56| | 47* 9 1 | 3 5 6 | 47* 2 8 | +-------------+----------+--------------+ | 5 3 78 | 78 2 4 | 6 1 9 | | 9 2 78 | 6 78 1 | 3 5 4 | | 1 4 6 | 9 3 5 | 78* 78* 2 | +-------------+----------+--------------+ | 2 67 4 | 5 78 3 | 89 689 1 | | 67* 1 9 | 2 4 78*| 58 3 56 | | 3 8 5 | 1 6 9 | 2 4 7 | +-------------+----------+--------------+

For the finned squirmbag:
........82.713..6.46...7.1..7.....42....64...8..........3.....9..53..1....25..8.7
........82.7138.6.468..7.1..768...42....64.8.8.4........3..2.59..53..12...25..837

Code: Select all: +---------------+---------------+---------------+ | 1359 1359 19 | 46 2459x 569x| 2579 79 8 | | 2 59* 7 | 1 3 8 | 459* 6 45 | | 4 6 8 | 29* 259* 7 | 2359* 1 35 | +---------------+---------------+---------------+ | 1359* 7 6 | 8 159* 1359*| 359* 4 2 | | 1359 12359 19 | 279 6 4 | 3579 8 135 | | 8 12359 4 | 279 1259 1359 | 35679 79 1356 | +---------------+---------------+---------------+ | 17 18 3 | 46 78 2 | 46 5 9 | | 679* 489* 5 | 3 78 69*| 1 2 46 | | 69* 49* 2 | 5 149* 169*| 8 3 7 | +---------------+---------------+---------------+

This one actually contained 2 7-node Grouped Turbot Chains (p-group elements, g-guards) with a broken wing
.5.....6.2..1..........3519...7...95...6.....7....2..3.9.27.1.4.........53....2..
.5.9.7.622.91563......23519...7...959.563.7217..592..3.9.275134...3..95.53...92..

Code: Select all: +---------------+-------------+-------------+ | 13 5 13 | 9 48 7 | 48 6 2 | | 2 48* 9 | 1 5 6 | 3 478 78 | | 468p 67 4678p| 48* 2 3 | 5 1 9 | +---------------+-------------+-------------+ | 3468 26 2348 | 7 148x 148g| 68 9 5 | | 9 48x 5 | 6 3 48x| 7 2 1 | | 7 16 168 | 5 9 2 | 468 48 3 | +---------------+-------------+-------------+ | 68 9 68 | 2 7 5 | 1 3 4 | | 14 127 1247 | 3 168 148x| 9 5 678 | | 5 3 147 |48* 1468g 9 | 2 78 678 | +---------------+-------------+-------------+

There are 24997 more. I'd be happy to share them all as well as my solver if you need it

by **Mike Barker** » Fri Mar 03, 2006 3:24 pm

Just noticed that the last two puzzles weren't completely solved. Here's a 7-node Grouped Turbot Fish for a solved puzzle:

..35.82...1.6..3...59.3...6.........4...6.82..6..41..3...7.....728....5...4......
6435.82.781762.3.5259.37.8638..7....47..6.82.962841573..67.....728....5...4...7..

Code: Select all: +----------+-------------+---------------+ | 6 4 3 | 5 19* 8 | 2 19 7 | | 8 1 7 | 6 2 49 | 3 49 5 | | 2 5 9 | 14* 3 7 | 14* 8 6 | +----------+-------------+---------------+ | 3 8 15g| 29 7 259 |1469x 146g 149p| | 4 7 15 | 39 6 359 | 8 2 19p| | 9 6 2 | 8 4 1 | 5 7 3 | +----------+-------------+---------------+ | 15 39 6 | 7 58 249 | 149g 134 28 | | 7 2 8 | 134g 19*346 | 469 5 149*| | 15 39 4 | 129 58 26 | 7 136 28 | +----------+-------------+---------------+

And for the finned squirmbag:
..1..2....5...7.4.....9..7.......8.....94.6..49..5....5.......23..2.15...7....9..
7.14.2359953.1724...439.17.1.572.894..794.61549.15.72351..794323492.15.7.725349.1

Code: Select all: +------------+----------+---------+ | 7 68* 1 | 4 68 2 | 3 5 9 | | 9 5 3 | 68* 1 7 | 2 4 68*| |268x 268* 4 | 3 9 5 | 1 7 68*| +------------+----------+---------+ | 1 36* 5 | 7 2 36*| 8 9 4 | | 28 238 7 | 9 4 38 | 6 1 5 | | 4 9 68*| 1 5 68*| 7 2 3 | +------------+----------+---------+ | 5 1 68*| 68* 7 9 | 4 3 2 | | 3 4 9 | 2 68 1 | 5 68 7 | | 68 7 2 | 5 3 4 | 9 68 1 | +------------+----------+---------+

I'll go ahead and modify my solver only to count completed puzzles and rerun (should take a day or so).

by **tarek** » Fri Mar 03, 2006 3:43 pm

hi there mike,

Thanx for the interesting puzzles.......

I just went through the first 3, interesting remarks:

#1: Now I'm not sure if you use the same Finned-fish technique which I'm using, but as you emply finned x-wing prior to jellyfish:
There is a finned x-wing as follows before the Jellyfish.

Code: Select all: *-----------------------------------------------------------------* |#678 56 2 | 4 19 78 | 1579 679 3 | |*4678 -567 3 | 78 19 2 | 14579 679 *56 | | 47 9 1 | 3 5 6 | 47 2 8 | |---------------------+---------------------+---------------------| | 5 3 78 | 78 2 4 | 6 1 9 | | 9 2 78 | 6 78 1 | 3 5 4 | | 1 4 6 | 9 3 5 | 78 78 2 | |---------------------+---------------------+---------------------| | 2 67 4 | 5 78 3 | 89 689 1 | |*67 1 9 | 2 4 78 | 58 3 *56 | | 3 8 5 | 1 6 9 | 2 4 7 | *-----------------------------------------------------------------* Eliminating 6 From r2c2 (Finned XWing in Columns 19) *-----------------------------------------------------------------* | 678 56 2 | 4 19 78 | 1579 679 3 | | 4678 57 3 | 78 19 2 | 14579 679 56 | | 47 9 1 | 3 5 6 | 47 2 8 | |---------------------+---------------------+---------------------| | 5 3 78 | 78 2 4 | 6 1 9 | | 9 2 78 | 6 78 1 | 3 5 4 | | 1 4 6 | 9 3 5 | 78 78 2 | |---------------------+---------------------+---------------------| | 2 67 4 | 5 78 3 | 89 689 1 | | 67 1 9 | 2 4 78 | 58 3 56 | | 3 8 5 | 1 6 9 | 2 4 7 | *-----------------------------------------------------------------* Eliminating 7 From r2c1 (2x2x2x2 Jellyfish in Columns 2345) Eliminating 7 From r2c7 (2x2x2x2 Jellyfish in Columns 2345) Eliminating 7 From r2c8 (2x2x2x2 Jellyfish in Columns 2345)

#2: The same here, but after the double finned x-wing, there is a finned swordfish

Code: Select all: *-----------------------------------------------------------------* | 1359 1359 *19 | 46 2459 569 | 2579 *79 8 | | 2 59 7 | 1 3 8 | 459 6 45 | | 4 6 8 | 29 259 7 | 2359 1 35 | |---------------------+---------------------+---------------------| | 1359 7 6 | 8 159 1359 | 359 4 2 | | 1359 12359#*19 | 279 6 4 |-3579 *8 135 | | 8 -12359 *4 | 279 1259 1359 | 35679#*79 1356 | |---------------------+---------------------+---------------------| | 17 18 3 | 46 78 2 | 46 5 9 | | 679 489 5 | 3 78 69 | 1 2 46 | | 69 49 2 | 5 149 169 | 8 3 7 | *-----------------------------------------------------------------* Eliminating 9 From r6c2 (Finned XWing in Columns 38) Eliminating 9 From r5c7 (Finned XWing in Columns 38) *-----------------------------------------------------------------* | 1359 1359 *19 |*46 -2459 -569 | 2579 *79 8 | | 2 59 7 | 1 3 8 | 459 6 45 | | 4 6 8 |#29 259 7 | 2359 1 35 | |---------------------+---------------------+---------------------| | 1359 7 6 | 8 159 1359 | 359 4 2 | | 1359 12359 *19 |*279 6 4 | 357 8 135 | | 8 1235 4 |*279 1259 1359 | 35679 *79 1356 | |---------------------+---------------------+---------------------| | 17 18 3 | 46 78 2 | 46 5 9 | | 679 489 5 | 3 78 69 | 1 2 46 | | 69 49 2 | 5 149 169 | 8 3 7 | *-----------------------------------------------------------------* Eliminating 9 From r1c5 (Finned Swordfish in Columns 348) Eliminating 9 From r1c6 (Finned Swordfish in Columns 348)

which means that the above eliminations can be achieved by the same finned swordfish

#3: This was a nice surprise, a finned jellyfish

Code: Select all: *--------------------------------------------------------* | 13 5 13 | 9 48 7 | 48 6 2 | | 2 48 9 | 1 5 6 | 3 478 78 | |*468 67 *4678 |*48 2 3 | 5 1 9 | |------------------+------------------+------------------| |*3468 26 *2348 | 7 -148 *148 | 68 9 5 | | 9 48 5 | 6 3 #48 | 7 2 1 | | 7 16 168 | 5 9 2 | 468 48 3 | |------------------+------------------+------------------| | 68 9 68 | 2 7 5 | 1 3 4 | |*14 127 *1247 | 3 168 *148 | 9 5 678 | | 5 3 *147 |*48 1468 9 | 2 78 678 | *--------------------------------------------------------* Eliminating 4 From r4c5 (Finned Jellyfish in Columns 1346)

I will have a look at the next 2........

Tarek

by **tarek** » Fri Mar 03, 2006 4:01 pm

To continue:

#4: My solver couldn't spot the grouped turbot

#5: Again there is simpler fish:

Code: Select all: *-----------------------------------------------* | 7 68 1 | 4 68 2 | 3 5 9 | | 9 5 3 |*68 1 7 | 2 4 *68 | |*268 268 4 | 3 9 5 | 1 7 *68 | |---------------+---------------+---------------| | 1 36 5 | 7 2 36 | 8 9 4 | | 28 238 7 | 9 4 38 | 6 1 5 | | 4 9 68 | 1 5 68 | 7 2 3 | |---------------+---------------+---------------| |*5 1 -68 |*68 7 9 | 4 3 2 | | 3 4 9 | 2 68 1 | 5 68 7 | |#68 7 2 | 5 3 4 | 9 68 1 | *-----------------------------------------------* Eliminating 6 From r7c3 (Finned Swordfish in Columns 149)

I'm not sure if that means that there is a difference in our perspective to seeing things or is it just a programming issue.

Tarek

by **Mike Barker** » Fri Mar 03, 2006 4:13 pm

Thanks for the feedback. Looking at the results, my solver is missing the sashimi fillets. I'll fix that. Not, sure about the Turbot fish. Can you send me the steps your solver takes and I'll look at the differences.

by **ronk** » Fri Mar 03, 2006 4:38 pm

Mike Barker wrote:I went ahead and reran my solver with 25000 random puzzles first moving colors after grouped turbot fish (so there are now no color eliminations) and changing it so it records the number of times a technique is used not just the number of puzzles it is used in.

Are those 25000 random puzzles available to others in any forum? If "yes", where?

If "no", I suggest using Gordon Royle's library of 36,628 puzzles available at http://www.csse.uwa.edu.au/~gordon/sudoku17. Then others can run the same puzzles through their solvers and compare results.

Ron

by **Havard** » Fri Mar 03, 2006 5:55 pm

Hi Mike! Thanks for providing those puzzles!

As you know, I will now do anything I can to try and prove that you don't need such complicated techniques to solve them!

Nothing personal!

Lets start with the jellyfish:
..24...............91.56....3....6.9...6.1..41.6.35..2........1..92...3.38.....47

Now, first I am a bit puzzled that your turbot fish did not already kill off this one:

and then to take out the other two, you can add one more strong link to that pattern:

No need to involve 10 7's when 6 does the job!

Ok, onto the finned squirmbag:
..1..2....5...7.4.....9..7.......8.....94.6..49..5....5.......23..2.15...7....9..

Again that elimination can be done with three strong links:

and just for fun, look at the patterns of the 6's... A completly identical pattern... I have never seen anything like this before!

this reduction also solves the puzzle! (the one in the 8's don't)

Now for the grouped Turbot with 7 nodes:
..35.82...1.6..3...59.3...6.........4...6.82..6..41..3...7.....728....5...4......

If I understand your list correctly, you are allowed to apply ALS xz for up to 4 cells before you use the Turbot 7.

Now if you first identify this one:
(suprise, suprise... three strong links!

)

and now this als:

Code: Select all: +----------+-------------+---------------+ | 6 4 3 | 5 19 8 | 2 19 7 | | 8 1 7 | 6 2 49+| 3 49 5 | | 2 5 9 | 14 3 7 | 14 8 6 | +----------+-------------+---------------+ | 3 8 15#| 29 7 259+|1469 16# 149 | | 4 7 15 | 39 6 359 | 8 2 19 | | 9 6 2 | 8 4 1 | 5 7 3 | +----------+-------------+---------------+ | 15 39 6 | 7 58 249+| 149 134 28 | | 7 2 8 | 134 19 346 | 469 5 149 | | 15 39 4 | 129 58 26+| 7 136* 28 | +----------+-------------+---------------+ x=5, z=6 # marks one set, + the other * cell to eliminate 6 from

and then you can use this little one:

Agreed it is on the line of what is "simpler" but maybe a little...?

Summed up, I think the power of three strong links is not something one should underestimate! They can be hard to find, but only using 6 cells, they are by definition easier to find than anything that requires more cells... (like the 11 of a finned squirmbag...)

(and they are really easy to program too... I don't even want to think about how to program finned squirmbags or grouped turbot fishes...)

please keep those puzzles coming!

havard

edit: did not comment on the right elimination...

by **Mike Barker** » Thu Jun 08, 2006 1:55 am

[Edit: updated to include advanced BUG techniques and longer XY-chains]

I thought it might be worthwhile to update my list of solving techniques and their relative frequency. In this case, I've used a set of 10000 randomly generated puzzles (using suexg). My solver has been expanded to include most of the non-advanced techniques listed in the Collection of Solving Techniques including locked sets (except for remote pairs which get picked up in XY-chains), Fishy cycles (including the latest Frakenfish), X-cycles (which I implement by finding disjoint strong links and grouped strong links rather than Turbot Fish, etc), ALS techniques, all of the latest UR techniques, BUG-lite techniques including strong link varieties, as well as simple and grouped nice loops (without AUR and almost-X-cycles). I never implemented a full BUG. For processing time reasons I've limited ALS to no more than 6 cells (fewer when part of grouped nice loops) and nice loops to no more than 9 bivalued cells or strong links. BUG-lites are also limited in size. I've chosen the following solving order working from easier to harder, but keeping similar techniques together:

Below is summarized the number of times a technique is used in solving puzzles. Only the results from successful solutions are included (9953 out of 10000). Compared to the last listing the biggest change is the introduction of simple nice loops prior to most ALS techniques. The new UR techniques also show up fairly often as well (especially when compared to the original Types 1-4). After looking at a number of XYZ-wings where the ALS was not confined to a box, I decided to require the mYZ-wings be limited to be in a box otherwise the patterns could spread too far over the board. This explains the reduction in these types of eliminations and an increase in ALS. Empty rectangles show up much more frequently since I moved them prior to fish. Note, because almost all technique lists treat locked line/box and locked box/box eliminations as separate (although complementary) techniques, I've gone ahead and included them separately. If you prefer to treat them as one technique then simply sum the two corresponding values.

What does all this mean? Not surprisingly the first message is to search out locked sets (singles, pairs, and candidates) and empty rectangles. Based on these results, the next thing I'd look for are small nice loops (combinations of bivalued cells and strong links with make up a small continuous or discontinuous loop), followed by fish and small ALS (combinations of bivalued cells and an ALS with at least one restricted common candidate). In reality since finding a UR is easier, I might try to locate UR's in conjunction with strong links or ALS prior to the small nice loops and ALS, but the payoff is smaller. After maybe some bigger fish other techniques are less likely to result in advancing the puzzle. Of course these priorities change if the puzzle is of a know pedigree.

Given the relative frequency of small nice loops, has anyone looked at classifying the types of reductions that can occur with these and their relative frequency? It might make another nice step between beginning and intermediate techniques.

Also I still can't seem to find a Type 5 UR. Does anyone have an example or an explanation of why they are so rare?

by **doduff** » Fri Jun 09, 2006 8:31 pm

It seems that one concern here is the order to apply the given techniques.

Why doesn't anyone look at the state of the puzzle and look at all possible reductions given all available techniques and then apply all of the resulting eliminations and count that as one step in the puzzle solution? This way no step will destroy any other valid step and maybe this will lead to a quicker solution.

Using an 'eliminated candidate' from one technique in an application of another technique should be perfectly valid, in my intuition that is.

Any thoughts?

by **Mike Barker** » Sun Jun 25, 2006 9:21 pm

Doduff - I agree in principle that applying all techniques to the puzzle and then performing the eliminations will reduce the dependance on order. It will not eliminate the problem since an elimination may not be possible given the current state of the puzzle, but some current elimination will prevent a future elimination. For UR's this is addressed somewhat by dealing with missing candidates. I know when I am hand solving, my tendancy is to use my latest elimination as a starting point for determining the next step which is contrary to waiting until all eliminations are determined.

On a different subject Havard once asked what the order of techniques would be based on the highest order technique required to solve the puzzles. I used the same data set as my previous post. Obviously order here will also be important, but for the order used the results are listed below. Probably the result I found most striking was how seldom most of the UR techniques (with the exception of Type 1) actually crack a puzzle. A more advanced study would look at how elimination of some of these techniques increases the requirement for even more advanced techniques. As in the previous results simple nice loops with 3 or 4 strong links or bivalue cells show up high on the list. The numbers in parentheses are the number of times that a technique was the highest required for sucessfully completed puzzles out of 10000 randomly generated puzzles.

Code: Select all: 1 (4472) L_HIDDEN1 2 (1243) L_LOCKED1 'include line/box and box/box eliminations 3 ( 630) L_XWING 'includes basic, finned, big fin, and franken 4 ( 496) L_XY 'XY-wing 5 ( 434) L_NAKED2 6 ( 347) L_NICE4 '4 strong links/bivalue cells 7 ( 239) L_XYCHAIN6 '6-node XY-chain 8 ( 237) L_NICE3 '3 strong links/bivalue cells 9 ( 203) L_NAKED3 10 ( 192) L_XYCHAIN5 '5-node XY-chain 11 ( 176) L_ALS1xz 'xz rule (set A is a bivalue cell) 12 ( 157) L_WXYZ 'generalized (allows 2-4 candidate pilots) 13 ( 153) L_NAKED1 14 ( 113) L_XYCHAIN7 '7-node XY-chain 15 ( 104) L_NICE5 '5 strong links/bivalue cells 16 ( 72) L_SWORDFISH 'includes basic, finned, big fin, and franken 17 ( 68) L_XYZ 'generalized (allows 2-3 candidate pilots) 18 ( 60) L_VWXYZ 'generalized (allows 2-5 candidate pilots) 19 ( 55) L_XYCHAIN8 '8-node XY-chain 20 ( 52) L_HIDDEN2 21 ( 44) L_UNIQUE1 'UR+1 (type 1) 22 ( 30) L_UVWXYZ 'generalized (allows 2-6 candidate pilots) 23 ( 26) L_BUG2 '2 rows or columns (all types including advanced) 24 ( 26) L_BUG3 '3 rows or columns (all types including advanced) 25 ( 26) L_NICE6 '6 strong links/bivalue cells 26 ( 26) L_ALS2xz 'xz rule (A=2 cell ALS) 27 ( 21) L_XYRING5 '5-node XY-ring 28 ( 21) L_NICE3G '3 grouped strong links/ALS 29 ( 19) L_XYCHAIN9 '9-node XY-chain 30 ( 16) L_NICE4G '4 grouped strong links/ALS 31 ( 15) L_XYRING6 '6-node XY-ring 32 ( 14) L_ALS3xz 'xz rule (A=3 cell ALS) 33 ( 14) L_ALS2xy 'xy rule (B=2 cell ALS) 34 ( 13) L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL 35 ( 13) L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D) 36 ( 13) L_ALS1xy 'xy rule (B=1 cell ALS) 37 ( 12) L_UNIQUE9 'UR+2k(x,d) 38 ( 11) L_UNIQUE6 'UR+2r(x,d) 39 ( 11) L_ALS3xy 'xy rule (B=3 cell ALS) 40 ( 10) L_JELLYFISH 'includes basic, finned, big fin, and franken 41 ( 10) L_XYRING4 '4-node XY-ring 42 ( 10) L_UNIQUE3 'UR+2X (types 3/3B) 43 ( 10) L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...) 44 ( 10) L_BUG4 '4 rows or columns (all types including advanced) 45 ( 10) L_ALS4xy 'xy rule (B=4 cell ALS) 46 ( 9) L_XYRING7 '7-node XY-ring 47 ( 8) L_UNIQUE2 'UR+2x (types 2/2B) 48 ( 7) L_HIDDEN3 49 ( 6) L_TUVWXYZ 'generalized (allows 2-7 candidate pilots) 50 ( 6) L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL 51 ( 5) L_XYRING8 '8-node XY-ring 52 ( 4) L_STRONG3 'three strong links (basic and grouped) 53 ( 4) L_ALS4xz 'xz rule (A=4 cell ALS) 54 ( 3) L_UNIQUE8 'UR+4(X,C)/3SL 55 ( 3) L_NICE5G '5 grouped strong links/ALS 56 ( 2) L_STRONG2 'two strong links (basic and grouped) 57 ( 2) L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL 58 ( 2) L_NICE8 '8 strong links/bivalue cells 59 ( 2) L_NICE6G '6 grouped strong links/ALS 60 ( 1) L_HIDDEN4 61 ( 1) L_SQUIRMBAG 'includes basic, finned, big fin, and franken 62 ( 1) L_NICE7 '7 strong links/bivalue cells 63 ( 0) L_NAKED4 64 ( 0) L_EMPTY 'empty rectangle 65 ( 0) L_STRONG4 'four strong links (basic and grouped) 66 ( 0) L_SUEDECOQ 'SueDeCoq 67 ( 0) L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...) 68 ( 0) L_BUG5 '5 rows or columns (all types including advanced) 69 ( 0) L_NICE2 '2 strong links/bivalue cells 70 ( 0) L_NICE9 '9 strong links/bivalue cells 71 ( 0) L_ALS5xz 'xz rule (A=5 cell ALS) 72 ( 0) L_ALS6xz 'xz rule (A=6 cell ALS) 73 ( 0) L_ALS5xy 'xy rule (B=5 cell ALS) 74 ( 0) L_ALS6xy 'xy rule (B=6 cell ALS) 75 ( 0) L_NICE2G '2 grouped strong links/ALS

by **daj95376** » Tue Jun 27, 2006 10:41 pm

Mike,

If you get a spare moment, may I ask that you test your 10,000 puzzles using the following hierarchy and give me a count/ordering on frequency of use for all techniques. There are so many techniques and I'd like to implement new ones based on this information as a starting point. TIA!!!!!!!!!

Code: Select all: L_NAKED1 Naked Single L_HIDDEN1 Hidden Single L_NAKED2 Naked Pair L_HIDDEN2 Hidden Pair L_NAKED3 Naked Triple L_HIDDEN3 Hidden Triple L_NAKED4 Naked Quad L_HIDDEN4 Hidden Quad L_LOCKED1 'include line/box and box/box eliminations L_XY 'XY-wing L_SWORDFISH 'includes basic, finned, big fin, and franken L_JELLYFISH 'includes basic, finned, big fin, and franken L_SQUIRMBAG 'includes basic, finned, big fin, and franken ??? XYZ-Wing L_UNIQUE1 'UR+1 (type 1) ??? Colors ??? Multi-Colors any order you'd prefer for the remaining techniques

by **algernon** » Sat Jul 01, 2006 9:22 am

I am thinking about an ordering of strategies, which does not depend on
taste or matching order.

This is not so trivial, as a strategy like "hidden quad" alone does not normally solve a puzzle on its own.

So we have to look at combinations. If there is a particular set of n
"helper strategies" {S_1, ... S_n}, you can compare two other strategies T and U "modulo" these strategies {S_1, ... S_n}:

If any puzzle which can be solved using {S1, ... S_n, T} can
also be solved by using {S1, ... S_n, U} we will say that
"U is greater than T (modulo {S_1, ... S_n})".

It is obvious that this would allow that:
"U greater than T" as well as "T greater than U", even modulo the same
helper strategies.
This is especially true if e.g. S_1 = "Full Backtracking", so S_1 alone
would solve any puzzle.
At least the ordering is transitive and reflexive.

But for limited helper strategies {S_1, ... S_n} perhaps some definite
results could be achieved.

I suspect that "simple coloring" is greater than "remote pairs" modulo
any set of helper strategies. Independency from the helper strategies
is not so easy to achieve, as some puzzles may need only one last step
to solve, so the "greater" strategie must be able to make the very same
eliminations, and the helper set might be empty!

Even if the dependency on "helper strategies" might seem ugly,
I think this reasoning shows the limits of hierarchies independant
from personal taste.

Would you consider this a legitimate approach?
Do you know more examples of strategies which could be ordered
this way, preferably independent from the helper strategies, or
with a "simple enough" helper set (singles only or such)?
Hat "helper set" would you find most appropriate to mimic human
perception of a good ordering?

by **Mike Barker** » Sun Jul 02, 2006 1:06 pm

Algernon, I'm not sure it will be simple to do what you propose. Although there is some hierarchy (nice loops include advanced coloring(?) includes X-cycles includes X-wings) comparison of different types of techniques (X-wings vs XY-wings) may not be as easy. I will have to think about it more, but I wanted to get DAJ his results.

DAJ, here are the results. Since I don't have a multi-color algorithm, I modified my nice loop algorithm to implement a form of advanced colors - nice loops with only strong links. My coloring algorithm is a little dusty, but I believe is correct. One reason I don't use it is that coloring seems to be a subset of many other techniques (my solver only used grouped coloring Type 1 12 times given its location in the hierarchy).

The solving order (I almost feel bad for having one - the inputs on reducing dependence on hierarchy are valid):

The results based on frequency of total occurances is:

Here's the ordering based on the highest order technique used to complete a puzzle:

Code: Select all: 1 (4467) L_HIDDEN1 'hidden single 2 ( 967) L_NAKED2 'naked pair 3 ( 713) L_ADVANCED4 'advanced coloring 4-links (basic) 4 ( 656) L_XWING 'X-wing (basic, finned, big fin, and franken) 5 ( 487) L_XY 'XY-wing 6 ( 426) L_LOCKED1 'include line/box and box/box eliminations 7 ( 406) L_ADVANCED3 'advanced coloring 3-links (basic) 8 ( 397) L_HIDDEN2 'hidden pair 9 ( 168) L_NAKED1 'naked single 10 ( 167) L_NICE4 '4 strong links/bivalue cells 11 ( 105) L_NAKED3 'naked triple 12 ( 94) L_NICE5 '5 strong links/bivalue cells 13 ( 88) L_ALS1xz 'xz rule (set A is a bivalue cell) 14 ( 87) L_UNIQUE1 'UR+1 (type 1) 15 ( 65) L_XYZ 'generalized XYZ-wing (2-3 candidate pilots) 16 ( 58) L_SWORDFISH 'swordfish (basic, finned, big fin, and franken) 17 ( 54) L_NICE3 '3 strong links/bivalue cells 18 ( 47) L_XYCHAIN6 '6-node XY-chain 19 ( 46) L_WXYZ 'generalized WXYZ-wing (2-4 candidate pilots) 20 ( 38) L_ADVANCED4G 'advanced coloring 4-links (grouped) 21 ( 29) L_XYCHAIN7 '7-node XY-chain 22 ( 29) L_NICE4G '4 grouped strong links/ALS 23 ( 27) L_UNIQUE6 'UR+2r(x,d) 24 ( 26) L_XYCHAIN5 '5-node XY-chain 25 ( 25) L_VWXYZ 'generalized VWXYZ-wing (2-5 candidate pilots) 26 ( 25) L_NICE6 '6 strong links/bivalue cells 27 ( 20) L_ALS2xz 'xz rule (A=2 cell ALS) 28 ( 17) L_ADVANCED3G 'advanced coloring 3-links (grouped) 29 ( 16) L_ALS1xy 'xy rule (B=1 cell ALS) 30 ( 15) L_HIDDEN3 'hidden triple 31 ( 15) L_NICE3G '3 grouped strong links/ALS 32 ( 13) L_SUEDECOQ 'SueDeCoq 33 ( 13) L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL 34 ( 12) L_UNIQUE3 'UR+2X (types 3/3B) 35 ( 12) L_UNIQUE9 'UR+2k(x,d) 36 ( 12) L_XYRING4 '4-node XY-ring 37 ( 12) L_UVWXYZ 'generalized UVWXYZ-wing (2-6 candidate pilots) 38 ( 11) L_BUGLITE2 '2 line BUG-lite (all types including advanced) 39 ( 10) L_ALS2xy 'xy rule (B=2 cell ALS) 40 ( 9) L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...) 41 ( 9) L_BUGLITE3 '3 line BUG-lite (all types including advanced) 42 ( 9) L_ALS3xy 'xy rule (B=3 cell ALS) 43 ( 8) L_XYCHAIN8 '8-node XY-chain 44 ( 8) L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D) 45 ( 8) L_ALS3xz 'xz rule (A=3 cell ALS) 46 ( 8) L_ALS4xy 'xy rule (B=4 cell ALS) 47 ( 7) L_UNIQUE2 'UR+2x (types 2/2B) 48 ( 6) L_NICE5G '5 grouped strong links/ALS 49 ( 5) L_BUG1 'basic BUG eliminations (+1, +nx, +nX) 50 ( 5) L_STRONG3 'three strong links (basic and grouped) 51 ( 5) L_XYRING6 '6-node XY-ring 52 ( 5) L_XYCHAIN9 '9-node XY-chain 53 ( 4) L_JELLYFISH 'jellyfish (basic, finned, big fin, and franken) 54 ( 4) L_XYRING5 '5-node XY-ring 55 ( 4) L_XYRING7 '7-node XY-ring 56 ( 4) L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL 57 ( 4) L_NICE7 '7 strong links/bivalue cells 58 ( 3) L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL 59 ( 2) L_COLOR1 'coloring type 1 (basic and grouped) 60 ( 2) L_NICE8 '8 strong links/bivalue cells 61 ( 1) L_NAKED4 'naked quadruple 62 ( 1) L_SQUIRMBAG 'squirmbag (basic, finned, big fin, and franken) 63 ( 1) L_UNIQUE8 'UR+4(X,C)/3SL 64 ( 1) L_ALS4xz 'xz rule (A=4 cell ALS) 65 ( 1) L_ALS5xy 'xy rule (B=5 cell ALS) 66 ( 1) L_NICE6G '6 grouped strong links/ALS 67 ( 0) L_HIDDEN4 'hidden quadruple 68 ( 0) L_COLOR2 'coloring type 2 (basic and grouped) 69 ( 0) L_COLOR3 'coloring type 3 (basic and grouped) 70 ( 0) L_ADVANCED2 'advanced coloring 2-links (basic) 71 ( 0) L_EMPTY 'empty rectangle 72 ( 0) L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...) 73 ( 0) L_BUG2 'strong link BUG eliminations 74 ( 0) L_BUG3 'advanced BUG eliminations 75 ( 0) L_TURBOT4 '4-node X-cycle (locked candidates) 76 ( 0) L_STRONG2 'two strong links (basic and grouped) 77 ( 0) L_ADVANCED2G 'advanced coloring 2-links (grouped) 78 ( 0) L_TURBOT5 'turbot fish (basic, grouped, and backwing) 79 ( 0) L_TURBOT6 '6-node X-cycle (basic, finned, and grouped) 80 ( 0) L_TURBOT7 'turbot chain (basic, grouped, and backwing) 81 ( 0) L_TUVWXYZ 'generalized TUVWXYZ-wing (2-7 candidate pilots) 82 ( 0) L_STRONG4 'four strong links (basic and grouped) 83 ( 0) L_XYRING8 '8-node XY-ring 84 ( 0) L_BUGLITE4 '4 line BUG-lite (all types including advanced) 85 ( 0) L_BUGLITE5 '5 line BUG-lite (all types including advanced) 86 ( 0) L_NICE2 '2 strong links/bivalue cells 87 ( 0) L_NICE9 '9 strong links/bivalue cells 88 ( 0) L_ALS5xz 'xz rule (A=5 cell ALS) 89 ( 0) L_ALS6xz 'xz rule (A=6 cell ALS) 90 ( 0) L_ALS6xy 'xy rule (B=6 cell ALS) 91 ( 0) L_NICE2G '2 grouped strong links/ALS

by **daj95376** » Sun Jul 02, 2006 4:17 pm

Wow Mike !!!!!!!!!!

Your results are way more than I'd hoped to get!!!

Thank You Very Much!!!!!!!

Now, I need to read the forum closer and learn more about the techniques you listed that produce fruitful results.

by **Mike Barker** » Mon May 07, 2007 3:55 am

There have been several changes since the last time I updated my method hierarchy results. Mutant fish, endo fins, Obi-Wahn's improvement to broken wings, RW convinced me that uniqueness and BUG tests should be relatively early in the solving order, BUG eliminations, and overlapping ALS and nice loops. I've added Kraken techniques which occur last in my solver. Note that with these added my solver solves approximately 9998 out of 10000 randomly generated puzzles (prior it was closer to 9940-9960). Of course there are other ways to achieve this result including using larger ALS and "nice networks", but this is the one I chose (of course I'm biased). Although 99.98% seems like a pretty big number, there are still .133*10^19 puzzles that my solver can't solve which means there is still lots of room for improvement!

Here is the order of solving techniques I used. The biggest difference (besides addition of new techniques) was moving shorter nice loops and advanced coloring earlier. This made sense because of their effectiveness. Similarly locked candidates were also moved up. This reflects the way I solve puzzles in which locked candidates are often easy to identify without knowing pencil marks. ALS have been moved later given the concensus that finding ALS is tough. As before techniques are broken down by the size of the chains and/or the size of the ALS involved with the idea that shorter or smaller is better.

Code: Select all: 0 L_NAKED1 'naked single 1 L_HIDDEN1 'hidden single 2 L_LOCKED1 'include line/box and box/box eliminations 3 L_NAKED2 'naked pair 4 L_NAKED3 'naked triple 5 L_HIDDEN2 'hidden pair 6 L_HIDDEN3 'hidden triple 7 L_NAKED4 'naked quadruple 8 L_HIDDEN4 'hidden quadruple 9 L_XWING 'X-wing (basic and finned) 10 L_FRANK2 'Franken X-wing 11 L_XY 'XY-wing 12 L_XYZ 'generalized XYZ-wing (2-3 candidate pilots) 13 L_EMPTY 'empty rectangle 14 L_BUG1 'BUG+1 eliminations 15 L_UNIQUE1 'UR+1 (type 1) 16 L_UNIQUE2 'UR+2x (types 2/2B) 17 L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...) 18 L_UNIQUE3 'UR+2X (types 3/3B) 19 L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...) 20 L_UNIQUE6 'UR+2r(x,d) 21 L_UNIQUE9 'UR+2k(x,d) 22 L_BUG2 'BUG+n(x,X) eliminations 23 L_BUG3 'strong link BUG eliminations 24 L_BUGLITE2 'basic 2-line BUG-lite 25 L_BUGLITE3 'basic 3-line BUG-lite 26 L_STRONG2 'two strong links (basic and grouped) 27 L_MUTANT2 'finless & finned mutant x-wing 28 L_SWORDFISH 'swordfish (basic and finned) 29 L_FRANK3 'Franken Swordfish 30 L_XYRING4 '4-node XY-ring 31 L_WXYZ 'generalized WXYZ-wing (2-4 candidate pilots) 32 L_ADVANCED2 '2-link advanced coloring 33 L_NICE2 '2-element nice loop (strong links/bivalue cells) 34 L_XYCHAIN5 '5-node XY-chain 35 L_XYRING5 '5-node XY-ring 36 L_VWXYZ 'generalized VWXYZ-wing (2-5 candidate pilots) 37 L_STRONG3 'three strong links (basic and grouped) 38 L_MUTANT3 'finless & finned mutant swordfish 39 L_JELLYFISH 'jellyfish (basic and finned) 40 L_FRANK4 'Franken Jellyfish 41 L_XYCHAIN6 '6-node XY-chain 42 L_XYRING6 '6-node XY-ring 43 L_UVWXYZ 'generalized UVWXYZ-wing (2-6 candidate pilots) 44 L_ADVANCED3 '3-link advanced coloring 45 L_NICE3 '3-element nice loop (strong links/bivalue cells) 47 L_ALS1xz 'A=1 cell ALS xz-rule 46 L_SUEDECOQ 'SueDeCoq 48 L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL 49 L_XYCHAIN7 '7-node XY-chain 50 L_XYRING7 '7-node XY-ring 51 L_TUVWXYZ 'generalized TUVWXYZ-wing (2-7 candidate pilots) 52 L_STRONG4 'four strong links (basic and grouped) 53 L_MUTANT4 'finless & finned mutant jellyfish 54 L_SQUIRMBAG 'squirmbag (basic and finned) 55 L_FRANK5 'Franken Squirmbag 56 L_XYCHAIN8 '8-node XY-chain 57 L_XYRING8 '8-node XY-ring 58 L_ADVANCED4 '4-link advanced coloring 59 L_NICE4 '4-element nice loop (strong links/bivalue cells) 60 L_TURBOT4 '4-node X-cycle (locked candidates) 61 L_XYCHAIN9 '9-node XY-chain 62 L_XYRING9 '9-node XY-ring 63 L_MUTANT5 'finless & finned mutant squirmbag 64 L_XYCHAIN10 '10-node XY-chain 65 L_XYRING10 '10-node XY-ring 66 L_ADVANCED5 '5-link advanced coloring 67 L_NICE5 '5-element nice loop (strong links/bivalue cells) 68 L_TURBOT5 'turbot fish (basic, grouped, and backwing) 69 L_XYCHAIN11 '11-node XY-chain 70 L_COLOR1 'coloring type 1 (basic and grouped) 71 L_COLOR2 'coloring type 2 (basic and grouped) 72 L_COLOR3 'coloring type 3 (basic and grouped) 73 L_MUTANT6 'finless & finned mutant whale 74 L_ADVANCED6 '6-link advanced coloring 75 L_NICE6 '6-element nice loop (strong links/bivalue cells) 76 L_TURBOT6 '6-node X-cycle (basic, finned, and grouped) 77 L_ADVANCED7 '7-link advanced coloring 78 L_TURBOT7 'turbot chain (basic, grouped, and backwing) 79 L_NICE7 '7-element nice loop (strong links/bivalue cells) 80 L_NICE8 '8-element nice loop (strong links/bivalue cells) 81 L_NICE9 '9-element nice loop (strong links/bivalue cells) 82 L_UNIQUE8 'UR+4(X,C)/3SL 83 L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL 84 L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D) 85 L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL 86 L_BUGLITE4 'basic 4-line BUG-lite 87 L_BUGLITE2A 'advanced 2-line BUG-lite 88 L_BUGLITE3A 'advanced 3-line BUG-lite 89 L_BUGLITE4A 'advanced 4-line BUG-lite 90 L_BUG4 'advanced BUG eliminations 91 L_BUGLITE5 'basic 5-line BUG-lite 92 L_BUGLITE5A 'advanced 5-line BUG-lite 93 L_ALS1xy 'B=1 cell ALS xy-rule 94 L_ALS2xz 'A=2 cell ALS xz-rule 95 L_ALS2xy 'B=2 cell ALS xy-rule 96 L_ALS3xz 'A=3 cell ALS xz-rule 97 L_ALS3xy 'B=3 cell ALS xy-rule 98 L_ALS4xz 'A=4 cell ALS xz-rule 99 L_ALS4xy 'B=4 cell ALS xy-rule 100 L_ALS5xz 'A=5 cell ALS xz-rule 101 L_ALS5xy 'B=5 cell ALS xy-rule 102 L_ALS6xz 'A=6 cell ALS xz-rule 103 L_ALS6xy 'B=6 cell ALS xy-rule 104 L_ADVANCED2G '2-link grouped advanced coloring 105 L_NICE2G '2-element grouped nice loop (GSL/ALS) 106 L_ADVANCED3G '3-link grouped advanced coloring 107 L_NICE3G '3-element grouped nice loop (GSL/ALS) 108 L_ADVANCED4G '4-link grouped advanced coloring 109 L_NICE4G '4-element grouped nice loop (GSL/ALS) 110 L_ADVANCED5G '5-link grouped advanced coloring 111 L_NICE5G '5-element grouped nice loop (GSL/ALS) 112 L_ADVANCED6G '6-link grouped advanced coloring 113 L_NICE6G '6-element grouped nice loop (GSL/ALS) 114 L_ADVANCED7G '7-link grouped advanced coloring 115 L_NICE7G '7-element grouped nice loop (GSL/ALS) 116 L_SUMCELL2 'bivalued/1-link kraken blossom 117 L_SUMUNIT2 'bivalued/1-link kraken unit 118 L_SUMCELL3 '3-valued/1-link kraken blossom 119 L_SUMUNIT3 '3-valued/1-link kraken unit 120 L_SUMCELL4 '4-valued/1-link kraken blossom 121 L_SUMUNIT4 '4-valued/1-link kraken unit 122 L_SUMCELL5 '5-valued/1-link kraken blossom 123 L_SUMUNIT5 '5-valued/1-link kraken unit 124 L_SUM2CELL2 'bivalued/2-link kraken blossom 125 L_SUM2UNIT2 'bivalued/2-link kraken unit 126 L_SUM2CELL3 '3-valued/2-link kraken blossom 127 L_SUM2UNIT3 '3-valued/2-link kraken unit 128 L_SUM2CELL4 '4-valued/2-link kraken blossom 129 L_SUM2UNIT4 '4-valued/2-link kraken unit 130 L_SUM2CELL5 '5-valued/2-link kraken blossom 131 L_SUM2UNIT5 '5-valued/2-link kraken unit 132 L_SUMALS '1-link kraken ALS 133 L_SUM2ALS '2-link kraken ALS 134 L_SUMXWING '1-link kraken X-wing 135 L_SUMSWORD '1-link kraken swordfish 136 L_SUMJELLY '1-link kraken jellyfish 137 L_SUMSQUIRM '1-link kraken squirmbag 138 L_SUM2XWING '2-link kraken x-wing 139 L_SUM2SWORD '2-link kraken swordfish 140 L_SUM2JELLY '2-link kraken jellyfish 141 L_SUM2SQUIRM '2-link kraken squirmbag 142 L_SUMURB 'bivalued/1-link kraken UR 143 L_SUMUR '1-link kraken UR 144 L_SUM2UR '2-link kraken UR 145 L_SUMBUG2 '2-line/1-link kraken BUG-lite 146 L_SUMBUG3 '3-line/1-link kraken BUG-lite 147 L_SUM2BUG2 '2-line/2-link kraken BUG-lite 148 L_SUM2BUG3 '3-line/2-link kraken BUG-lite 149 L_SUMAALS2 '2-cell/1-link kraken Almost ALS 150 L_SUMAALS3 '3-cell/1-link kraken Almost ALS 151 L_SUM2AALS2 '2-cell/2-link kraken Almost ALS 152 L_SUM2AALS3 '3-cell/2-link kraken Almost ALS 153 L_MUTANT21 '1-link kraken mutant x-wing 154 L_MUTANT31 '1-link kraken mutant swordfish 155 L_MUTANT41 '1-link kraken mutant jellyfish 156 L_MUTANT51 '1-link kraken mutant squirmbag 157 L_MUTANT22 '2-link kraken mutant x-wing 158 L_MUTANT32 '2-link kraken mutant swordfish 159 L_MUTANT42 '2-link kraken mutant jellyfish 160 L_MUTANT52 '2-link kraken mutant squirmbag

The following summarizes the total number of times a technique is used for all successfully solved puzzles. A notable difference from previous results is the higher frequency of occurence of UR+2/1SL techniques which resulted from moving them before UR+2k and UR+2r eliminations which makes sense from a complexity viewpoint. Note that, just as before, even though there are many occurences of URs they "crack" a dispropotionately small number of puzzles (except for UR+1). Most Kraken techniques are not even used which is not surprising since they are a method of last resort in my solver. Kraken Blossom and Kraken Unit are actually quite common.

Code: Select all: 1) Naked Single (436922) 2) Hidden Single (134411) 3) Locked Line/Box (17810) 4) Locked Box/Box (4370) 5) Finned X-wing (3682) 6) Naked Pair (3488) 7) Naked Triple (1986) 8) UR+2(X,D,B)/1SL (Type 4,...) (1692) 9) XY-wing (1676) 10) Nice Loops with 3 Strong Links/Bivalue Cells (1481) 11) Advanced Colouring with 3 Links (992) 12) 5-node XY-chain (985) 13) Generalized WXYZ-wing (904) 14) Nice Loops with 4 Strong Links/Bivalue Cells (862) 15) Hidden Pair (796) 16) Advanced Colouring with 4 Links (789) 17) 6-node XY-chain (786) 18) Generalized XYZ-wing (670) 19) X-wing (602) 20) Empty Rectangle (594) 21) Generalized VWXYZ-wing (412) 22) UR+3(X,C,N,U,E)/2SL (382) 23) A=1 cell ALS-xz rule (352) 24) Nice Loops with 5 Strong Links/Bivalue Cells (347) 25) UR+1 (Type 1) (303) 26) Finned Swordfish (282) 27) B=1 cell ALS-xy rule (235) 28) Advanced Colouring with 5 Links (199) 29) 7-node XY-chain (181) 30) Hidden Triple (175) 31) BUG+1 (169) 32) Grouped Nice Loops with 3 GSL/ALS (141) 33) Generalized UVWXYZ-wing (136) 34) 5-node XY-ring (107) 35) X-cycle with 3 Grouped Strong Links (106) 36) UR+2X (Type 3) (102) 37) 4-node XY-ring (100) 38) Grouped Nice Loops with 4 GSL/ALS (99) 39) 8-node XY-chain (93) 40) Swordfish (91) 41) X-cycle with 2 Grouped Strong Links (91) 42) Nice Loops with 6 Strong Links/Bivalue Cells (91) 43) B=2 cell ALS-xy rule (78) 44) UR+2k(x,d) (74) 45) UR+4(x,X)/2SL, UR+4(x,X)/1SL (73) 46) X-cycle with 3 Strong Links (71) 47) UR+2K(X,D),UR+3K(X,D) (69) 48) 6-node XY-ring (62) 49) Basic BUG-Lite with 2 lines (62) 50) UR+2x (Type 2) (58) 51) Mutant Swordfish (56) 52) SueDeCoq (51) 53) B=3 cell ALS-xy rule (50) 54) A=2 cell ALS-xz rule (42) 55) Mutant Jellyfish (41) 56) Basic BUG-Lite with 3 lines (41) 57) X-cycle with 2 Strong Links (40) 58) Advanced BUG-Lite with 2 lines (39) 59) Franken JellyFish (36) 60) A=3 cell ALS-xz rule (36) 61) B=4 cell ALS-xy rule (36) 62) UR+4(X,C)/3SL (33) 63) Advanced Colouring with 6 Links (33) 64) Franken SwordFish (29) 65) BUG+n(x,X) (26) 66) Nice Loops with 7 Strong Links/Bivalue Cells (26) 67) UR+2r(x,d) (24) 68) Grouped Nice Loops with 5 GSL/ALS (21) 69) B=5 cell ALS-xy rule (19) 70) Naked Quadruple (17) 71) Advanced BUG-Lite with 3 lines (17) 72) 3-valued/2-link Kraken Blossom (17) 73) 7-node XY-ring (16) 74) Strong Link BUG Eliminations (16) 75) 4-valued/2-link Kraken Blossom (14) 76) Bivalued/2-link Kraken Unit (14) 77) 5-valued/2-link Kraken Blossom (11) 78) 3-valued/2-link Kraken Unit (11) 79) Bivalued/2-link Kraken Blossom (10) 80) A=4 cell ALS-xz rule (9) 81) B=6 cell ALS-xy rule (8) 82) X-cycle with 4 Grouped Strong Links (7) 83) 9-node XY-chain (7) 84) UR+2D,UR+3(x,X)/1SL (7) 85) 5-valued/1-link Kraken Blossom (7) 86) 4-valued/2-link Kraken Unit (7) 87) Mutant Squirmbag (5) 88) 4-valued/1-link Kraken Blossom (5) 89) Finned Jellyfish (3) 90) Franken Squirmbag (3) 91) 8-node XY-ring (3) 92) Grouped Advanced Colouring with 4 Links (3) 93) Nice Loops with 8 Strong Links/Bivalue Cells (3) 94) Nice Loops with 9 Strong Links/Bivalue Cells (3) 95) 3-valued/1-link Kraken Blossom (3) 96) 5-valued/2-link Kraken Unit (3) 97) 2-link Kraken ALS (3) 98) 10-node XY-chain (2) 99) Advanced BUG-Lite with 4 lines (2) 100) Advanced Colouring with 7 Links (2) 101) Grouped Nice Loops with 2 GSL/ALS (2) 102) Grouped Nice Loops with 6 GSL/ALS (2) 103) Jellyfish (1) 104) Broken Wing (1) 105) 11-node XY-chain (1) 106) UR+2d,UR+3x (Type 5,...) (1) 107) Grouped Advanced Colouring with 3 Links (1) 108) A=5 cell ALS-xz rule (1) 109) 3-valued/1-link Kraken Unit (1) 110) 4-valued/1-link Kraken Unit (1) 111) 5-valued/1-link Kraken Unit (1) 112) 2-link Kraken X-wing (1) 113) Hidden Quadruple (0) 114) Squirmbag (0) 115) Finned Squirmbag (0) 116) Franken X-wing (0) 117) Mutant X-wing (0) 118) Mutant Whale (0) 119) 4-node X-cycle = X-wing (0) 120) Turbot Fish (0) 121) 6-node X-cycle (0) 122) 7-node Turbot Chain (0) 123) Grouped 4-node X-cycle = Locked box/box (0) 124) Grouped Turbot Fish (0) 125) Grouped 6-node X-cycle (0) 126) Grouped 7-node Turbot Chain (0) 127) 7-node Broken Wing (0) 128) Grouped Broken Wing (0) 129) Grouped 7-node Broken Wing (0) 130) X-cycle with 4 Strong Links (0) 131) Grouped Empty Rectangle (0) 132) Generalized TUVWXYZ-wing (0) 133) 9-node XY-ring (0) 134) 10-node XY-ring (0) 135) Basic BUG-Lite with 4 lines (0) 136) Basic BUG-Lite with 5 lines (0) 137) Advanced BUG-Lite with 5 lines (0) 138) Advanced BUG Eliminations (0) 139) Simple Colouring Type 1 (0) 140) Simple Colouring Type 2 (0) 141) Simple Colouring Type 3 (0) 142) Grouped Simple Colouring Type 1 (0) 143) Grouped Simple Colouring Type 2 (0) 144) Grouped Simple Colouring Type 3 (0) 145) Advanced Colouring with 2 Links (0) 146) Grouped Advanced Colouring with 2 Links (0) 147) Grouped Advanced Colouring with 5 Links (0) 148) Grouped Advanced Colouring with 6 Links (0) 149) Grouped Advanced Colouring with 7 Links (0) 150) Nice Loops with 2 Strong Links/Bivalue Cells (0) 151) Grouped Nice Loops with 7 GSL/ALS (0) 152) A=6 cell ALS-xz rule (0) 153) Bivalued/1-link Kraken Blossom (0) 154) Bivalued/1-link Kraken Unit (0) 155) 1-link Kraken ALS (0) 156) 2-cell/1-link Kraken Almost ALS (0) 157) 3-cell/1-link Kraken Almost ALS (0) 158) 2-cell/2-link Kraken Almost ALS (0) 159) 3-cell/2-link Kraken Almost ALS (0) 160) Bivalued/1-link Kraken UR (0) 161) 1-link Kraken UR (0) 162) 2-link Kraken UR (0) 163) 2-line/1-link Kraken BUG-Lite (0) 164) 3-line/1-link Kraken BUG-Lite (0) 165) 2-line/2-link Kraken BUG-Lite (0) 166) 3-line/2-link Kraken BUG-Lite (0) 167) 1-link Kraken X-wing (0) 168) 1-link Kraken Swordfish (0) 169) 1-link Kraken Jellyfish (0) 170) 1-link Kraken Squirmbag (0) 171) 2-link Kraken Swordfish (0) 172) 2-link Kraken Jellyfish (0) 173) 2-link Kraken Squirmbag (0) 174) 1-link Mutant X-wing (0) 175) 1-link Mutant Swordfish (0) 176) 1-link Mutant Jellyfish (0) 177) 1-link Mutant Squirmbag (0) 178) 2-link Mutant X-wing (0) 179) 2-link Mutant Swordfish (0) 180) 2-link Mutant Jellyfish (0) 181) 2-link Mutant Squirmbag (0)

This is probably the more interesting result which shows how many times out of 10000 runs a specific technique was the highest order techniques used to solve a puzzle. Based on previous results these results are not too surprising with basic/intermediate techniques followed by short XY chains, advanced coloring and nice loops. Again UR+1 (Type 1) and BUG+1 are the most useful forms of these techniques. mYZ-wings, for example WXYZ wings, (which in my solver are limited to a bivalue cell and an ALS limited to a box) are also fairly high up. As before, moving nice loops higher in the solving order would eliminate occurences of many of the techniques in this list, but I think I'd prefer looking for an X-wing before a nice loop.

Code: Select all: 1 (4471) L_HIDDEN1 'hidden single 2 (1257) L_LOCKED1 'includes line/box and box/box eliminations 3 ( 663) L_XWING 'X-wing (basic and finned) 4 ( 431) L_XY 'XY-wing 5 ( 366) L_NAKED2 'naked pair 6 ( 255) L_XYCHAIN5 '5-node XY-chain 7 ( 208) L_XYCHAIN6 '6-node XY-chain 8 ( 202) L_NICE3 '3-element nice loop (strong links/bivalue cells) 9 ( 184) L_NAKED3 'naked triple 10 ( 174) L_ADVANCED4 '4-link advanced coloring 11 ( 163) L_NICE4 '4-element nice loop (strong links/bivalue cells) 12 ( 159) L_WXYZ 'generalized WXYZ-wing (2-4 candidate pilots) 13 ( 150) L_ADVANCED3 '3-link advanced coloring 14 ( 110) L_NAKED1 'naked single 15 ( 105) L_UNIQUE1 'UR+1 (type 1) 16 ( 74) L_XYZ 'generalized XYZ-wing (2-3 candidate pilots) 17 ( 69) L_NICE5 '5-element nice loop (strong links/bivalue cells) 18 ( 61) L_VWXYZ 'generalized VWXYZ-wing (2-5 candidate pilots) 19 ( 61) L_XYCHAIN7 '7-node XY-chain 20 ( 57) L_BUG1 'BUG+1 eliminations 21 ( 57) L_UNIQUE4 'UR+2(X,D,B)/1SL (types 4/4B,...) 22 ( 50) L_HIDDEN2 'hidden pair 23 ( 49) L_ADVANCED5 '5-link advanced coloring 24 ( 48) L_ALS1xz 'A=1 cell ALS xz-rule 25 ( 43) L_ALS1xy 'B=1 cell ALS xy-rule 26 ( 36) L_SWORDFISH 'swordfish (basic and finned) 27 ( 33) L_EMPTY 'empty rectangle 28 ( 31) L_XYCHAIN8 '8-node XY-chain 29 ( 29) L_NICE3G '3-element grouped nice loop (GSL/ALS) 30 ( 21) L_NICE6 '6-element nice loop (strong links/bivalue cells) 31 ( 20) L_STRONG2 'two strong links (basic and grouped) 32 ( 19) L_UNIQUE3 'UR+2X (types 3/3B) 33 ( 19) L_UVWXYZ 'generalized UVWXYZ-wing (2-6 candidate pilots) 34 ( 18) L_XYRING5 '5-node XY-ring 35 ( 17) L_ALS2xy 'B=2 cell ALS xy-rule 36 ( 17) L_NICE4G '4-element grouped nice loop (GSL/ALS) 37 ( 16) L_UNIQUE2 'UR+2x (types 2/2B) 38 ( 16) L_BUGLITE3 'basic 3-line BUG-lite 39 ( 16) L_XYRING6 '6-node XY-ring 40 ( 15) L_STRONG3 'three strong links (basic and grouped) 41 ( 14) L_ALS3xy 'B=3 cell ALS xy-rule 42 ( 12) L_BUGLITE2 'basic 2-line BUG-lite 43 ( 12) L_ALS2xz 'A=2 cell ALS xz-rule 44 ( 12) L_ALS3xz 'A=3 cell ALS xz-rule 45 ( 11) L_ALS4xy 'B=4 cell ALS xy-rule 46 ( 10) L_SUM2UNIT2 'bivalued/2-link kraken unit 47 ( 9) L_BUG2 'BUG+n(x,X) eliminations 48 ( 9) L_XYRING4 '4-node XY-ring 49 ( 9) L_UNIQUE7 'UR+3(X,C,N,U,E)/2SL 50 ( 9) L_ADVANCED6 '6-link advanced coloring 51 ( 8) L_SUEDECOQ 'SueDeCoq 52 ( 7) L_HIDDEN3 'hidden triple 53 ( 6) L_NICE5G '5-element grouped nice loop (GSL/ALS) 54 ( 6) L_SUM2CELL4 '4-valued/2-link kraken blossom 55 ( 5) L_BUG3 'strong link BUG eliminations 56 ( 5) L_FRANK3 'Franken Swordfish 57 ( 5) L_XYRING7 '7-node XY-ring 58 ( 5) L_SUM2CELL5 '5-valued/2-link kraken blossom 59 ( 4) L_XYCHAIN9 '9-node XY-chain 60 ( 4) L_BUGLITE3A 'advanced 3-line BUG-lite 61 ( 4) L_SUM2UNIT3 '3-valued/2-link kraken unit 62 ( 3) L_UNIQUE9 'UR+2k(x,d) 63 ( 3) L_SUMCELL5 '5-valued/1-link kraken blossom 64 ( 2) L_NAKED4 'naked quadruple 65 ( 2) L_MUTANT3 'finless & finned mutant swordfish 66 ( 2) L_MUTANT4 'finless & finned mutant jellyfish 67 ( 2) L_UNIQUE10 'UR+2K(X,D), UR+3K(X,D) 68 ( 2) L_BUGLITE2A 'advanced 2-line BUG-lite 69 ( 2) L_ALS4xz 'A=4 cell ALS xz-rule 70 ( 2) L_SUMCELL3 '3-valued/1-link kraken blossom 71 ( 2) L_SUMCELL4 '4-valued/1-link kraken blossom 72 ( 2) L_SUM2CELL2 'bivalued/2-link kraken blossom 73 ( 2) L_SUM2UNIT4 '4-valued/2-link kraken unit 74 ( 2) L_SUM2UNIT5 '5-valued/2-link kraken unit 75 ( 2) L_SUM2ALS '2-link kraken ALS 76 ( 1) L_FRANK4 'Franken Jellyfish 77 ( 1) L_STRONG4 'four strong links (basic and grouped) 78 ( 1) L_XYRING8 '8-node XY-ring 79 ( 1) L_ADVANCED7 '7-link advanced coloring 80 ( 1) L_NICE7 '7-element nice loop (strong links/bivalue cells) 81 ( 1) L_UNIQUE11 'UR+2D, UR+3(x,X)/1SL 82 ( 1) L_NICE2G '2-element grouped nice loop (GSL/ALS) 83 ( 1) L_NICE6G '6-element grouped nice loop (GSL/ALS) 84 ( 1) L_SUMUNIT3 '3-valued/1-link kraken unit 85 ( 1) L_SUMUNIT4 '4-valued/1-link kraken unit 86 ( 1) L_SUM2CELL3 '3-valued/2-link kraken blossom 87 ( 1) L_SUM2XWING '2-link kraken x-wing 88 ( 0) L_HIDDEN4 'hidden quadruple 89 ( 0) L_FRANK2 'Franken X-wing 90 ( 0) L_UNIQUE5 'UR+2d, UR+3x (types 5/5B,...) 91 ( 0) L_UNIQUE6 'UR+2r(x,d) 92 ( 0) L_MUTANT2 'finless & finned mutant x-wing 93 ( 0) L_ADVANCED2 '2-link advanced coloring 94 ( 0) L_NICE2 '2-element nice loop (strong links/bivalue cells) 95 ( 0) L_JELLYFISH 'jellyfish (basic and finned) 96 ( 0) L_TUVWXYZ 'generalized TUVWXYZ-wing (2-7 candidate pilots) 97 ( 0) L_SQUIRMBAG 'squirmbag (basic and finned) 98 ( 0) L_FRANK5 'Franken Squirmbag 99 ( 0) L_TURBOT4 '4-node X-cycle (locked candidates) 100 ( 0) L_XYRING9 '9-node XY-ring 101 ( 0) L_MUTANT5 'finless & finned mutant squirmbag 102 ( 0) L_XYCHAIN10 '10-node XY-chain 103 ( 0) L_XYRING10 '10-node XY-ring 104 ( 0) L_TURBOT5 'turbot fish (basic, grouped, and backwing) 105 ( 0) L_XYCHAIN11 '11-node XY-chain 106 ( 0) L_COLOR1 'coloring type 1 (basic and grouped) 107 ( 0) L_COLOR2 'coloring type 2 (basic and grouped) 108 ( 0) L_COLOR3 'coloring type 3 (basic and grouped) 109 ( 0) L_MUTANT6 'finless & finned mutant whale 110 ( 0) L_TURBOT6 '6-node X-cycle (basic, finned, and grouped) 111 ( 0) L_TURBOT7 'turbot chain (basic, grouped, and backwing) 112 ( 0) L_NICE8 '8-element nice loop (strong links/bivalue cells) 113 ( 0) L_NICE9 '9-element nice loop (strong links/bivalue cells) 114 ( 0) L_UNIQUE8 'UR+4(X,C)/3SL 115 ( 0) L_UNIQUE12 'UR+4(x,X)/2SL, UR+4(x,X)/1SL 116 ( 0) L_BUGLITE4 'basic 4-line BUG-lite 117 ( 0) L_BUGLITE4A 'advanced 4-line BUG-lite 118 ( 0) L_BUG4 'advanced BUG eliminations 119 ( 0) L_BUGLITE5 'basic 5-line BUG-lite 120 ( 0) L_BUGLITE5A 'advanced 5-line BUG-lite 121 ( 0) L_ALS5xz 'A=5 cell ALS xz-rule 122 ( 0) L_ALS5xy 'B=5 cell ALS xy-rule 123 ( 0) L_ALS6xz 'A=6 cell ALS xz-rule 124 ( 0) L_ALS6xy 'B=6 cell ALS xy-rule 125 ( 0) L_ADVANCED2G '2-link grouped advanced coloring 126 ( 0) L_ADVANCED3G '3-link grouped advanced coloring 127 ( 0) L_ADVANCED4G '4-link grouped advanced coloring 128 ( 0) L_ADVANCED5G '5-link grouped advanced coloring 129 ( 0) L_ADVANCED6G '6-link grouped advanced coloring 130 ( 0) L_ADVANCED7G '7-link grouped advanced coloring 131 ( 0) L_NICE7G '7-element grouped nice loop (GSL/ALS) 132 ( 0) L_SUMCELL2 'bivalued/1-link kraken blossom 133 ( 0) L_SUMUNIT2 'bivalued/1-link kraken unit 134 ( 0) L_SUMUNIT5 '5-valued/1-link kraken unit 135 ( 0) L_SUMALS '1-link kraken ALS 136 ( 0) L_SUMXWING '1-link kraken X-wing 137 ( 0) L_SUMSWORD '1-link kraken swordfish 138 ( 0) L_SUMJELLY '1-link kraken jellyfish 139 ( 0) L_SUMSQUIRM '1-link kraken squirmbag 140 ( 0) L_SUM2SWORD '2-link kraken swordfish 141 ( 0) L_SUM2JELLY '2-link kraken jellyfish 142 ( 0) L_SUM2SQUIRM '2-link kraken squirmbag 143 ( 0) L_SUMURB 'bivalued/1-link kraken UR 144 ( 0) L_SUMUR '1-link kraken UR 145 ( 0) L_SUM2UR '2-link kraken UR 146 ( 0) L_SUMBUG2 '2-line/1-link kraken BUG-lite 147 ( 0) L_SUMBUG3 '3-line/1-link kraken BUG-lite 148 ( 0) L_SUM2BUG2 '2-line/2-link kraken BUG-lite 149 ( 0) L_SUM2BUG3 '3-line/2-link kraken BUG-lite 150 ( 0) L_SUMAALS2 '2-cell/1-link kraken Almost ALS 151 ( 0) L_SUMAALS3 '3-cell/1-link kraken Almost ALS 152 ( 0) L_SUM2AALS2 '2-cell/2-link kraken Almost ALS 153 ( 0) L_SUM2AALS3 '3-cell/2-link kraken Almost ALS 154 ( 0) L_MUTANT21 '1-link kraken mutant x-wing 155 ( 0) L_MUTANT31 '1-link kraken mutant swordfish 156 ( 0) L_MUTANT41 '1-link kraken mutant jellyfish 157 ( 0) L_MUTANT51 '1-link kraken mutant squirmbag 158 ( 0) L_MUTANT22 '2-link kraken mutant x-wing 159 ( 0) L_MUTANT32 '2-link kraken mutant swordfish 160 ( 0) L_MUTANT42 '2-link kraken mutant jellyfish 161 ( 0) L_MUTANT52 '2-link kraken mutant squirmbag

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