The New Sudoku Players' Forum

by **champagne** » Sun Oct 26, 2008 10:50 pm

Hi Allan,

Here a selection in my list of hard puzzle of some puzzle giving something different

Code: Select all: 100000005020400060003000700040006000000049080002800000000050100060900020007000003 col803# 98781

Code: Select all: 1 789 46 |2367 236789 2378 |23489 349 5 5789 2 589 |4 13789 13578 |389 6 189 46 589 3 |1256 12689 1258 |7 149 12489 -------------------------------------------------------- 35789 4 1589 |12357 1237 6 |2359 13579 1279 3567 1357 156 |12357 4 9 |2356 8 1267 35679 13579 2 |8 137 1357 |34569 134579 14679 -------------------------------------------------------- 23489 389 489 |2367 5 23478 |1 479 46789 3458 6 1458 |9 1378 13478 |458 2 478 24589 1589 7 |126 1268 1248 |45689 459 3

floors1357 permutations =85

Code: Select all: N:.....................................X...........XX.............................. R:.XXXXX.XX.........XX.XXXXX...........XXXXX.XX.........XX.XXXXX................... C:.XXXXX.XX.........XX.XXXXX..........XXXX.XXX..........XX.XXX.XX.................. B:.XXXXXXX...........XXXXXXX..........XX.XXXX.X.........XX.XXX.XX.................. 1 2 3 4 5 6 7 8 9 HC.x.xxxxx.x.x.xxx.x.x.xxx.xxx.xxx.xxxx.xx..x.xxx....xxxxx.x.x.xxx.x.xxx.xxx.xxxxx. NE..................................x....x......................................... 1: r3c9 3: r4c5

Nothing really special, just a mix not to rich candidates and nodes

Code: Select all: 100000005020400060003000700040809000000046080000000200007001000080900020500000300 col807# 95104

Code: Select all: 1 679 4689 |2367 236789 2378 |489 349 5 789 2 589 |4 135789 3578 |189 6 1389 4689 569 3 |156 15689 58 |7 149 2 ---------------------------------------------------------- 2367 4 1256 |8 12357 9 |156 1357 1367 2379 13579 1259 |12357 4 6 |159 8 1379 36789 135679 15689 |1357 1357 357 |2 134579 134679 ---------------------------------------------------------- 23469 369 7 |2356 23568 1 |45689 459 4689 346 8 146 |9 3567 3457 |1456 2 1467 5 169 12469 |267 2678 2478 |3 1479 146789

Code: Select all: 4: r8c9r9c89 floors4 permutations =8 actifs R:...........................X.X..XXXX............................................. C:...........................X.X..XXXX............................................. B:...........................X.X..XXXX............................................. 1 2 3 4 5 6 7 8 9

An example where the start of my solver is three turbots

Code: Select all: 000100030000000065003060800008090006070002000000400000009080050020001000400700900 col080502

Code: Select all: 256789 45689 24567 |1 2457 45789 |247 3 2479 12789 1489 1247 |238 2347 34789 |1247 6 5 12579 1459 3 |25 6 4579 |8 12479 12479 ------------------------------------------------------- 1235 1345 8 |35 9 357 |123457 1247 6 13569 7 1456 |68 135 2 |1345 1489 13489 123569 13569 1256 |4 1357 68 |12357 12789 123789 ------------------------------------------------------- 1367 136 9 |236 8 346 |123467 5 12347 35678 2 567 |9 345 1 |3467 478 3478 4 13568 156 |7 235 356 |9 128 1238

floors156 permutations =4745

N:..........................................................................X......
R:.XXXXXX.X...........................X.XXXX.XXX...XXXXX...........................
C:XXX.X.XXX...........................XXXXXXX..XXXX.XX.............................
B:X.XXXXX.X...........................XX.XXXXX.X..XX.XXX...........................
1 2 3 4 5 6 7 8 9
total =61 sets actifs
HCxxx.xx...xxx...x..xx.x.x.xxxx.x.xxx.x.xxx.xxxxxx.xxxxxxx.x.xx.xx.x.x.x...x..xx.xx
assigned 6: r5c4
eliminations
6: r5c13r6c6r7c4
NE.......................................x.........................................

here a mix with the three cases : asigment, eliminations of candidates and node to clear

and the same results using floors 236

Code: Select all: N:.........................................................X....................... R:.........XXXX.XX.X.X.XXXXXX..................X...XXXXX........................... C:.........X.XXX.XXXXX.XXXX.X..................XXXX.XX............................. B:.........XXXX.X.XX.X.XXXXXX..................X..XX.XXX........................... 1 2 3 4 5 6 7 8 9 total =61 sets actifs HCxxx.x.x.xx.xxxxx..x..x...xxxx.x.xxx.x.xxx.x.xxxx.xxxxxxx...xx.xx.x.x.x.x.xx.xx.xx

and with floors 567

Code: Select all: N:.................................................................X............... R:....................................X.XXXX.XXX...XXXXXXXXX.XXX................... C:....................................XXXXXXX..XXXX.XX..X.X.XXXXX.................. B:....................................XX.XXXXX.X..XX.XXXXXX.XXX.X.................. 1 2 3 4 5 6 7 8 9 total =61 sets actifs HCxxx.xxx.xx.x.xxx..xx.x.x.xxxx.x.xxx.x.xxx.x..xxx.xxxxxxx.x.xx.xx...x.xxx.xx.xx...

using floors 357, only the clearing of another node appears
éliminations trouvées

Code: Select all: NE...................................................................x............. floors357 permutations =6525 N:..............................X.X................................................ R:...................X.XXXXXX.........X.XXXX.XX.........XXXX.XXX................... C:..................XX.XXXX.X.........XXXXXXX...........X.X.XXXXX.................. B:...................X.XXXXXX.........XX.XXXXX..........XXX.XXX.X.................. 1 2 3 4 5 6 7 8 9 total =65 sets actifs HCxxx.xxx.xx.xxxxx..xx.x.x.xxxx....xx.x.x.x.x.xxxx.x.xxxxx.x.xx.xx.x.x.xxx.xx.xx..x

Code: Select all: 000010005020400090003000700040006000000049080000800002007000100060900020500000003 col810# 95384

Code: Select all: 46789 789 4689 |367 1 378 |2 346 5 1678 2 1568 |4 35678 3578 |368 9 168 1468 158 3 |256 9 258 |7 146 1468 --------------------------------------------------------- 123789 4 12589 |12357 2357 6 |359 1357 179 12367 1357 1256 |12357 4 9 |356 8 167 13679 13579 1569 |8 357 1357 |34569 134567 2 --------------------------------------------------------- 23489 389 7 |2356 23568 23458 |1 456 4689 1348 6 148 |9 3578 134578 |458 2 478 5 189 12489 |1267 2678 12478 |4689 467 3

I'll come back with an edit for that one.
The solver did not find any possibility combining up to four floors.
I added a possibility to combine five floors and I will check it to day.

Code: Select all: 000001009000000085009050060008030006070002000100400000003080050400700000020000300 col401# 98353

Code: Select all: 235678 34568 24567 |2368 2467 1 |247 2347 9 2367 1346 12467 |2369 24679 4679 |1247 8 5 2378 1348 9 |238 5 478 |1247 6 12347 --------------------------------------------------------- 259 459 8 |159 3 579 |124579 12479 6 3569 7 456 |15689 169 2 |14589 1349 1348 1 3569 256 |4 679 56789 |25789 2379 2378 --------------------------------------------------------- 679 169 3 |1269 8 469 |124679 5 1247 4 15689 156 |7 1269 3 |12689 129 128 6789 2 167 |1569 1469 4569 |3 1479 1478

A second example with two possibilities to combine 4 floors

The best one
floors1247 permutations =9

Code: Select all: N:......X........X........X.....................................X.................. R:.XXXX.XXXXXXX.XXX..........XXXXX.X.X..................XXXX.XX.X.................. C:.XXXX.XXXX.XXX.XXX..........XX.XXXXX..................X.X.XXXXX.................. B:X.X.XXXXXXXXX.X.XX.........XXXX.X.XX..................XXX.XXX.X.................. 1 2 3 4 5 6 7 8 9 HCxxxxx..x.xxxxxx...xx.x.x..xxx.x.xxx...xxx.xxx..x.xxxxxxx.x.xx...xx.x.xxxx.xxxx.xx 1: r4c8r5c47r7c7r8c279r9c49 2: r1c148r2c4r678c7 4: r1c28r2c36r57c7r9c6 7: r1c18r2c67r3c1r4c7r6c67r7c9r9c1 NE..x.x......x.x............x.......x......................x.....................x.

and a very limted effect (one node to clear) using
floors1678 permutations =16150
actifs

Code: Select all: N:..........................................................................X...... R:.XXXX.XXX....................................XX..XXXXXXXXX.XX.XX.X.XX.XX......... C:.XXXX.XXX....................................XXXXXXX..X.X.XXXXXXX.X.XX.X......... B:X.X.XXXXX....................................XX.XX.XXXXXX.XXX.XXX..XXX.X......... 1 2 3 4 5 6 7 8 9 HCxxxxx.xx.xxxxxxx..xx.x.xx.x...x.xxx.x.xxx.xxx.xx.xxxxxxx.x.xx.x.xx.x.xxxx..xxx.xx NE........................................................................x........

by **champagne** » Sun Oct 26, 2008 11:10 pm

Hi again,

Some days, you are lucky. It seems that extension to 5 floors worked immediatly.
My first idea was to edit the previous post, having several results, I find better to show it individually

Code: Select all: 000010005020400090003000700040006000000049080000800002007000100060900020500000003 col810# 95384

Code: Select all: 46789 789 4689 |367 1 378 |2 346 5 1678 2 1568 |4 35678 3578 |368 9 168 1468 158 3 |256 9 258 |7 146 1468 --------------------------------------------------------- 123789 4 12589 |12357 2357 6 |359 1357 179 12367 1357 1256 |12357 4 9 |356 8 167 13679 13579 1569 |8 357 1357 |34569 134567 2 --------------------------------------------------------- 23489 389 7 |2356 23568 23458 |1 456 4689 1348 6 148 |9 3578 134578 |458 2 478 5 189 12489 |1267 2678 12478 |4689 467 3

No outlet found by the solver combining up to four floors.
We know that increasing the number of floors we must find possibilites (taking all floors, we have in once all false candidates elimnated).

What I don't know is whether this is still feasible to extract sets/linksets patterns, but Allan will tell us.
We have seven possibilties to combine succesfully floors. I give all of them.

floors12357 permutations =43 (may be the best)

Code: Select all: N:..............................XX..X..X.X.........XX.............................. R:.XXXXX.XX..XXX.X.XXX.XXXXX...........XXXXXXX..........XX.XXX.XX.................. C:XXXX.X.XXX.XXXX...XX.XXXXX...........XXXXXXX..........XX.XXX.XX.................. B:X.XXXXXX..X.XX.XX..XXXXXXX..........XX.XXX.XX.........XX.XXX.XX.................. 1 2 3 4 5 6 7 8 9 HCxx.x.x.x.x.x.xxx.xxx.x.x.xxx.x...x.xx.x...x.xxxx...xx.xx.xxx.x.x.x.xxx.x.xxxxx.x. 1: r6c1 3: r7c56 5: r6c37 NE....................................x.x.............................x............

floors13457 permutations =89

Code: Select all: N:..................................X..X...........XX.............................. R:.XXXXX.XX.........XX.XXXXX.X.X..XXXX.XXXXXXX..........XX.XXX.XX.................. C:XXXX.X.XX.........XX.XXXXX.X.X..XXXX.XXXXXXX..........XX.XXX.XX.................. B:X.XXXXXX...........XXXXXXX.X.X..XXXXXX.XXX.XX.........XX.XXX.XX.................. 1 2 3 4 5 6 7 8 9 HCxxxx.x.x.x.x.xxx.xxx.x.x.xxx.xxx.x.xx.xx..x.xxxx...xx.xx.xxx.xxx.x.xxx.x.xxxxxxx. 3: r7c5 5: r6c7 NE...................................................................xx............

floors13567 permutations =112

Code: Select all: N:...X..............................X..X....X.X....XX.............................. R:.XXXXX.XX.........XX.XXXXX...........XXXXXXX.XXX.XXX.XXX.XXX.XX.................. C:XXXX.X.XX.........XX.XXXXX...........XXXXXXX.X.XXX.XXXXX.XXX.XX.................. B:X.XXXXXX...........XXXXXXX..........XX.XXX.XXXXXX.X.XXXX.XXX.XX.................. 1 2 3 4 5 6 7 8 9 HCxxx..x.x.x.x.xxx.xxx.x.x.xxx.xxx.x.xx.xx.....xxx...xx.xx.xxx.xxx.x.xxx.x.xxxxxxx. 1: r6c3 3: r7c5 5: r6c7 6: r5c13r6c78

floors13578 permutations =125

Code: Select all: N:.....X........X....X..............X..X...........XX................X............. R:.XXXXX.XX.........XX.XXXXX...........XXXXXXX..........XX.XXX.XXXXXX..XXX......... C:XXXX.X.XX.........XX.XXXXX...........XXXXXXX..........XX.XXX.XXXXX.XXX.X......... B:X.XXXXXX...........XXXXXXX..........XX.XXX.XX.........XX.XXX.XXXXXX..XXX......... 1 2 3 4 5 6 7 8 9 HCxxxx...x.x.x.x.x.xx..x.x.xxx.xxx.x.xx.xx..x.xxxx...xx.xx.xxx.xxx.x..xx.x.xxxxxxx. 8: r2c3r89c6

floors13579 permutations =135

Code: Select all: N:.................................XXX.X........X..XX.............................. R:.XXXXX.XX.........XX.XXXXX...........XXXXXXX..........XX.XXX.XX.........X..X.XX.X C:XXXX.X.XX.........XX.XXXXX...........XXXXXXX..........XX.XXX.XX.........XXX...X.X B:X.XXXXXX...........XXXXXXX..........XX.XXX.XX.........XX.XXX.XX.........X..X.XX.X 1 2 3 4 5 6 7 8 9 HCxxxx.x.x.x.x.xxx.xxx.x.x.xxx.xxx....x.xx..x.xx.x...xx.xx.xxx.xxx.x.xxx.x.xxxxxxx. 1: r6c3

floors23567 permutations =1130

Code: Select all: N:...X.................X.........X..........X......X.......X....................... R:...........XXX.X.XXX.XXXXX...........XXXXXXX.XXX.XXX.XXX.XXX.XX.................. C:.........X.XXXX...XX.XXXXX...........XXXXXXX.X.XXX.XXXXX.XXX.XX.................. B:..........X.XX.XX..XXXXXXX..........XX.XXX.XXXXXX.X.XXXX.XXX.XX.................. 1 2 3 4 5 6 7 8 9 HCxxx..x.x.x.x.xxx.xxx...x.xxx.xx..xxxxxxx....xxxx..xxx.xx..xx.xxx...xxx.x..xxxxxx. 6: r9c4

floors24689 permutations =1079

Code: Select all: N:..X...........................................................X...............X.. R:...........XXX.X.X.........X.X..XXXX.........XXX.XXX.X.........XXXX..XXXX..X.XX.X C:.........X.XXXX............X.X..XXXX.........X.XXX.XXX.........XXX.XXX.XXXX...X.X B:..........X.XX.XX..........X.X..XXXX.........XXXX.X.XX.........XXXX..XXXX..X.XX.X 1 2 3 4 5 6 7 8 9 HCxx.x.x.x.x.x.xxx.xxx.x.x.xxx.xxx.x.xx.xx..x.xxxx...xx.xx.xxx.x.x.x.xxx.x.xxxxx.x. 8: r8c6

by **ronk** » Mon Oct 27, 2008 3:17 am

Allan, a couple of questions: For a given puzzle state (pencilmarks), is your program capable of ...

finding the smallest rank0 constraint set(s) for any elimination(s)
exhaustively searching for all different rank0 constraint sets that result in an identical set of elimination(s)

[edit: Constraint sets with identical strong sets but different weak sets would also be considered "different" in my POV.]

by **Allan Barker** » Mon Oct 27, 2008 6:48 am

Champagne,

Champagne wrote:Here, what tells me the solver for the three puzzles at the top of my list of hardest (including Golden Nugget, number 3)

Just some initial feedback. So we can talk about your logic, here is some notation:

U = set of all occupied sets in a puzzle (usually about 300)
P = group all candidates in some logic
S = set of all sets in some logic (every node is in the logic)
L = set of all linksets in some logic (some or all nodes in logic)
X = all sets *not* in some logic

Right now, your logic is all S, no linksets yet. After slimfast you would have S + L.

I looked at the first three puzzles. SP, col809# 92145 (COL) and GN,

In my analyzer, there are no eliminations from X(SP), X(COL), or X(GN)

1) GN. If I add one more set/linkset to cell N79 (a cell set), I get the elimination r7c9<>3, which is correct.
2) SP. If I add one linkset to cell N48 *or* N52, no eliminations. If I add linksets to both N48 and N52, then I get the correct two eliminations, N48<>2 N52<>8.

I think you are missing some of the required constraints.

I have found the loop in SP for N48<>2 N52<>8, it uses 15 sets, maybe this can help. (It may not be the same as a loop you find, but close.

I see what you mean about Silver Platter, it is worse than Golden Nugget. I have one more loop before this one, eliminates
one candidate.

Code: Select all: set 5R4: 548===========================546A=549==541==546A | 544 | | | | | | | | 5R2: | | | 521==526==525 | | | | | | 5R5: | 552==554==559==551 | | | | | | | | 5R8: | | | 589=======586==585 1C8: 148=======138==168==178 | | | | | | | | | | | | 1C4: | 144==134 | | | | | | | 154 | | | | | | 1C2: | | 162==172==152 | | | | | | | | | | 6N6: | | | | 566G===========566G==|===766H===========766H=366F=366F | | | | | | | | | | 6N5: | 165B======165B=======|===565D================565D=765E===========765E=365C=365C | | | | | | 3C4: | | | | | 344==394==314 | | | | | 354 | | | | | | | | | 7C4: | | | 734==774==744 | | | | | | | | 754 | | | 7C2: | 752===========================762==732 | | | | | | | | | | | 7C8: 748=======================|============================768=======778 | | | | | | | | 3C2: | 352===============================================362=======392 | | | | 3C8: 348========================================================================368============318 All notation is NCR format '=' strong set | | } '|' weak set 165B======165B= } same candidate in 2 sets

by **ttt** » Mon Oct 27, 2008 7:08 am

Hi Allan & champagne,

For Silver Plate, I took long… long times to study it. It seems SK loop with [(13) & (57)] but 1’s at r8c79, then I try to study as a “Almost SK loop” : if r8c7=1 or r8c9=1 => …nothing the same as SK loop deductions when r8c79<>1… Must be more time for this

ttt

by **champagne** » Mon Oct 27, 2008 7:50 am

Allan Barker wrote:I think you are missing some of the required constraints.

In my turn a quick feedback before I analyze your post.

What I did is just to apply a "focusing step" to select groups of floors leading to "eliminations/assignments".

There is no slimfast program applied here. All sets belonging to the selected floors contribute to the permutation process. I only made a restriction on nodes to reduce the number of permutations. Only nodes having no extra candidates (not belonging to the floors) contribute to the permutations till the final step.

What I forecast is that you should find a sets/linksets organization giving the same results (maybe partial) using only sets belonging to the group selected.

I can be wrong.

What is for sure is that what I have shown as "eliminated" is not allowed in permutations (subject to no bug in the program) valid for that group.

champagne

by **champagne** » Mon Oct 27, 2008 7:59 am

ttt wrote:Hi Allan & champagne,

For Silver Plate, I took long… long times to study it. It seems SK loop with [(13) & (57)] but 1’s at r8c79, then I try to study as a “Almost SK loop” : if r8c7=1 or r8c9=1 => …nothing the same as SK loop deductions when r8c79<>1… Must be more time for this

ttt

I have a long and boring solution (20% longer than GN ) I never published. I must confess I never digged in it.

I had the feeling nobody would be interested by the result and GN was enough..

Another reason is that I hope, thru work in progress to come to something easier to digest.

I can try to summarize the way the solver cracks it if you want.

champagne

by **Allan Barker** » Mon Oct 27, 2008 8:51 am

Ronk wrote:Allan, a couple of questions: For a given puzzle state (pencilmarks), is your program capable of ...
finding the smallest rank0 constraint set(s) for any elimination(s)
exhaustively searching for all different rank0 constraint sets that result in an identical set of elimination(s)
[edit: Constraint sets with identical strong sets but different weak sets would be considered "different" in my POV.]

Ronk, I think you question is clear, let me try for a clear answer.

The software has a small solver and a large solver integrated to an editor/analyzer. Some things will be done by a solver and some can done in the E/A after eliminations are found. The small solver does exhaustive search and is comfortable up to 6-10 sets or about 20 to 25 candidates. The big solver (one used for monsters) is not exhaustive but can go to almost any size.

The answer for the small solver is yes to both. You can include higher ranks or choose a particular rank like 1. It may also find different groups of strong sets that eliminate the same candidate, say a fish and a chain. The E/A can also find different (weak) constraint sets. I.e., it will fill in the weak sets for a given set of constraints.

The big solver will not guarantee the smallest elimination but often comes close. It will often provide a number of examples but may miss some configurations.

by **champagne** » Mon Oct 27, 2008 9:11 am

Hi Allan,

I now make quick comments to your post.

Right now, your logic is all S, no linksets yet. After slimfast you would have S + L.
In my analyzer, there are no eliminations from X(SP), X(COL), or X(GN)

I am not sure I catch your point here.

. my logic is analysing permutatons in a group of floors and linking Cells/Nodes in that "focusing step";
. the definition for 'X' is not clear to me.

but it does not affect the rest.

1) GN. If I add one more set/linkset to cell N79 (a cell set), I get the elimination r7c9<>3, which is correct.
2) SP. If I add one linkset to cell N48 *or* N52, no eliminations.
If I add linksets to both N48 and N52, then I get the correct two eliminations, N48<>2 N52<>8.

. difficult to figure out what you mean precisely, especially after I analyzed your loop. In SP loop, I did not see any addition to the group of sets I printed. May be you want to say that you can not find the loop if you start a growing program only with the target?
. for me nothing estonishing if you need both N48 and N52 to build a sets/linksets structure

I have found the loop in SP for N48<>2 N52<>8, it uses 15 sets, maybe this can help.
(It may not be the same as a loop you find, but close.
I see what you mean about Silver Platter, it is worse than Golden Nugget. I have one more loop before this one, eliminates
one candidate.

. unhappily, I am not yet in a position to find sets/linksets groups and I had no time to work recently on that topic.
. You say you have another loop, I am interested to know if it uses more than four floors.
My program says it is not possible to find other clearings with only four floors, but I did not reduce the number of permutations using nodes with extra candidates, so I can miss some eliminations.

And now your sets/linksets diagram.

This is exactly what I was expecting.
All sets and linksets are in the group I used.

Now I have just to find:

The appropriate slimfast program,
The rank calculation.

Code: Select all: I see we have here 15 sets and 19 linkset -> rank 4. If I am right, 8 triple points, all linkset form. and we must conclude N48 N52 are rank 0.

still some work for me.

Champagne

by **Allan Barker** » Mon Oct 27, 2008 5:22 pm

champagne wrote:
Allan wrote:Right now, your logic is all S, no linksets yet. After slimfast you would have S + L.
In my analyzer, there are no eliminations from X(SP), X(COL), or X(GN)

Uh-oh, super dylsexia, I mean that set groups
S(Silver P), S(Coloin's puzzle), or S(Golden N) produce no eliminations by themselves, I must add some more linksets

Srooy, Allan

by **Allan Barker** » Sat Nov 15, 2008 9:59 pm

Destruction of a Mild Monster, Top1465 #2

Following 999_Springs lead here , I took a look at this ER = 9.5 puzzle to see if I could understand it's hardness level. The results provide a little more insight into nature of initial SK-type loops, so I thought to post it here.

What I found was a relatively small 13 set SK-like loop with no apparent symmetry and no way to morph the puzzle to a symmetrical form (that I could find). Otherwise, it shares all the logical qualities of other SK loops, i.e., it is rank 0 (like a swordfish) with equal numbers of sets and cover sets. It eliminates all external candidates in its 13 cover sets. It can be described as a single cell set in r4c5 connecred to 4 ALS each with 3 sets, for a total of 13 sets. The 4 ALS's are in a row, a row, a column , and a cell otherwise the logic looks fairlysymetrical.

The other point of interest is the loop virtually blasts the puzzle into singles. It does this by eliminating 31 candidates, after wihci there is very little left except perhaps a hidden pair. Below are details and a thumb.

Code: Select all: EPRC 36 Nodes, Raw Rank = 0 (linksets - sets) 13 Sets = {578r2 269r5 578c2 4n5 7n157} 13 Links = {12r7 5c5 7c7 2n89 5n236 6n2 9n2 9b5 8b7} (5c5) => r1c5<>5, (2n8) => r2c8<>4, (2n8) => r2c8<>6, (2n9) => r2c9<>9, (9b5) => r4c4<>9, (9b5) => r4c6<>9, (7c7) => r4c7<>7, (5n2) => r5c2<>1, (5n3) => r5c3<>1, (5n3) => r5c3<>7, (5n6) => r5c6<>4, (5n6) => r5c6<>7, r5c6<>9, (7c7) => r5c7<>7, (6n2) => r6c2<>2, (6n2) => r6c2<>6, (5c5) => r6c5<>5, (7c7) => r6c7<>7, (1r7) => r7c3<>1, (2r7) => r7c3<>2, (2r7) => r7c6<>2, (1r7) => r7c8<>1, (8b7) => r8c1<>8, (8b7) => r9c1<>8, (9n2) => r9c2<>1, (9n2) => r9c2<>2, (9n2) => r9c2<>3, (9n2) => r9c2<>6, r9c2<>8, (5c5) => r9c5<>5, (7c7) => r9c7<>7

Code: Select all: +--------------------------------------------------------------------------------------+ | 7 126 8 | 459 4569 4569 | 3 1456 1259 | | 469 36 3469 | 2 3469(5) 1 | 469(7) 46(578) 9(578) | | 5 1236 123469 | 78 3469 78 | 12469 146 129 | +--------------------------------------------------------------------------------------+ | 189 4 1579 | 3579 (59) 3579 | 178 2 6 | | 3 1(267) 17(269) | 47(9) 8 47(269) | 147 1457 157 | | 268 26(578) 2567 | 1 2456 24567 | 478 9 3 | +--------------------------------------------------------------------------------------+ | (128) 9 12357 | 6 (125) 2358 | (127) 1378 4 | | 12468 1236(8) 12346 | 3489 7 23489 | 5 1368 1289 | | 12468 1236(578) 1234567 | 34589 12459 234589 | 12679 13678 12789 | +--------------------------------------------------------------------------------------+

Code: Select all: 5c5 2n8 2n9 7c7 1r7 2r7 8b7 9n2 6n2 5n2 5n3 5n6 9b5 7N5: 575=================175==275 | | | 5R2: 525==528==529 | | | | | | | 8R2: | 828==829 | | | | | | | 7R2: | 728==729==727 | | | | | | 7N7: | 777==177==277 | | | 7N1: | 171==271==871 | | 8C2: | 892B=892B=862 | 882 | | | | | 5C2: | 592==562 | | | 7C2: | 792==762==752 | | 6R5: | 652==653==656 | | | | 2R5: | 252==253==256 | | | 9R5: | 953==956A=956A | 954 | | 4N5: 545=========================================================945 Note: 956A=956A, and similar, same candidate sits in 2 cover sets

Thumb 2D grid drawing with set logic in the green heads up display.

by **champagne** » Sun Nov 16, 2008 12:01 am

Hi Allan,

Your top1465 _2 is an interesting example.
At the point where you started, you could have found a very simple SLG in floor 2 eliminating 2r9c2.
But I guess this was not your goal. This locks, for the time being, my search for more complex SLGs

Your SLG is not very big, but it is using six different digits: 256789.
It seems to me that such a solution can only come if you are exploring all possible paths to find a kind of "One shot" solution.

Using classical AIC's and AIC's nets, it is a "medium difficulty" puzzle.
If I apply a strategy to speed up the process, i find two AIC's:
. one using digits 5 and 9 eliminating 9r2c79
. one using digits 5,7,9 eliminating 7t5c236

For sure, you can find corresponding SLG's, but both are using AHS/ACs and I don't know yet how it is translated in SLGs

champagne

Website · by **denis_berthier** » Sun Nov 16, 2008 12:03 am

Allan Barker wrote:Following 999_Springs lead here , I took a look at this ER = 9.5 puzzle to see if I could understand it's hardness level. The results provide a little more insight into nature of initial SK-type loops, so I thought to post it here.
What I found was a relatively small 13 set SK-like loop with no apparent symmetry and no way to morph the puzzle to a symmetrical form (that I could find). Otherwise, it shares all the logical qualities of other SK loops, i.e., it is rank 0 (like a swordfish) with equal numbers of sets and cover sets. It eliminates all external candidates in its 13 cover sets. It can be described as a single cell set in r4c5 connecred to 4 ALS each with 3 sets, for a total of 13 sets. The 4 ALS's are in a row, a row, a column , and a cell otherwise the logic looks fairlysymetrical.

Two questions.

1) Could you define more precisely what you call an "SK-like loop", especially if there is no symmetry in the pattern. Your description evokes less a loop than some central cell with petals.

I gave two different interpretations of the "SK-loop", here: http://forum.enjoysudoku.com/viewtopic.php?t=5894
When I activate any of them, I can't find any belt, even after the following whip eliminations (starting from your PM):
nrczt-whip-cn[4] n2{r9c1 r6c1} - n2{r6c3 r3c3} - n2{r3c7 r7c7} - {n2r7c5 .} ==> r9c2 <> 2
nrczt-whip-cn[4] n8{r2c9 r2c8} - n5{r2c8 r2c5} - {n5 n9}r4c5 - {n9r4c1 .} ==> r2c9 <> 9
nrczt-whip-rn[6] n7{r9c3 r9c2} - n7{r9c9 r2c9} - n8{r2c9 r2c8} - n5{r2c8 r2c5} - {n5 n9}r4c5 - {n9r5c6 .} ==> r5c3 <> 7
nrczt-whip-rc[10] n2{r9c1 r6c1} - n2{r6c5 r9c5} - n1{r9c5 r7c5} - {n1 n8}r7c1 - n8{r4c1 r4c7} - n8{r6c7 r6c2} - n5{r6c2 r9c2} - n7{r9c2 r5c2} - n7{r5c9 r6c7} - {n7r7c7 .} ==> r7c3 <> 2
nrczt-whip[21] n5{r6c2 r9c2} - n5{r9c4 r1c4} - n5{r2c5 r7c5} - {n5 n9}r4c5 - n9{r4c1 r2c1} - n9{r2c5 r1c6} - n6{r1c6 r5c6} - n9{r5c6 r5c3} - n2{r5c3 r5c2} - n7{r5c2 r6c2} - {n7 n6}r6c3 - {n6 n8}r6c1 - {n8 n1}r4c1 - {n1 n2}r7c1 - n2{r9c3 r3c3} - n2{r3c7 r9c7} - n9{r9c7 r3c7} - n6{r3c7 r2c7} - {n6 n3}r2c2 - {n3 n4}r2c5 - {n4r2c3 .} ==> r6c6 <> 5

after which there's no nrczt-whip (more complex whips are not - not yet? - in SudoRules).
Notice that the whip[21], although very long, is rather easy to find because there are not many whips.

If I have time, I'll try to see what I get with braids, but, as they are not programmed in SudoRules, I have to do this manually and you know I'm a little lazy for manual solving of hard puzzles.

Anyway, if there appears to be an interpretation of the "SK-loop" more general than mine, whatever it is, I'm interested if it can be described in terms of factual patterns.

2) Second question. ttt gave another, apparently much simpler, solution in the "abominable T&E" thread. What do you think of it? And, if it is really simpler, do you know why your solver didn't find it?

by **ronk** » Sun Nov 16, 2008 3:15 am

denis_berthier wrote:1) Could you [edit: Allan Barker] define more precisely what you call an "SK-like loop", especially if there is no symmetry in the pattern. Your description evokes less a loop than some central cell with petals.

A "best symmetry" isomorph of the top1465 #2 is ...

Code: Select all: 7 . 8 | . . . | 3 . . . . . | 2 . 1 | . . . 5 . . | . . . | . . . -------+-------+------- . 4 . | . . . | . 2 6 3 . . | . 8 . | . . . . . . | 1 . . | . 9 . -------+-------+------- . 9 . | 6 . . | . . 4 . . . | . 7 . | 5 . . . . . | . . . | . . . top1465 #2 . . . | . . . | . . . . 7 . | . . . | . . 5 . . 6 | . . 9 | . 4 . -------+-------+------- . . . | . 5 . | . . . . . . | 8 7 . | . . 3 1 . 2 | . . . | . . . -------+-------+------- . . . | . . 4 | 2 6 . . . 1 | . . . | 9 . . . 8 . | . 3 . | . . . top1465 #2 isomorph permutation: -pr(159)(268)(347)c(1526)(34)(798)

Allan, I would like to see the 2-D grid drawing for your "SK-like loop" deduction in this isomorph. Assuming you have the time, thanks in advance.

by **Allan Barker** » Sun Nov 16, 2008 5:11 am

champagne wrote:At the point where you started, you could have found a very simple SLG in floor 2 eliminating 2r9c2.But I guess this was not your goal. This locks, for the time being, my search for more complex SLGs

I do see several shorter eliminations but found this one after searching around a bit. I was quite surprised to see 31 eliminations, so I focused on this elimination

By "lock" you mean that the simpler solutions prevent the solver from finding more complex eliminations, right? I often see this, too.

champagne wrote:Your SLG is not very big, but it is using six different digits: 256789. It seems to me that such a solution can only come if you are exploring all possible paths to find a kind of "One shot" solution.

Yes, I am looking for any path, as opposed to starting with floors. To the solver, multiple digits in a row/column are the same as one digit in several rows/columns. Of course, any is not the same as every.

champagne wrote:For sure, you can find corresponding SLG's, but both are using AHS/ACs and I don't know yet how it is translated in SLGs

This is an interesting point. In principle, there must be a (constraint) set description for any elimination path. However, a rule may embody this in various ways. Compared to computer languages, a rule might be C language and the 324 constraints would be assembly language. (?)

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