## full tagging level 4 examples

Advanced methods and approaches for solving Sudoku puzzles

### full tagging level 4 examples

Full tagging is my sample file of hardest puzzles.
First shown here, the solutions of these puzzles have been transferred on my web site, which gives more flexibility.

New versions (end of April 2008) of these puzzles are coming slowly.

The last status of the new file can be found starting here

http://pagesperso-orange.fr/gpenet/UX/UX.htm

The sample file includes five puzzles (extended to 7 in the web site)

The first one is a “coloin” puzzle ranked as 02805 in gsf’s list. This puzzle has exactly the same loop as the Easter Monster but is much easier to solve.

Next one is the well known Easter Monster

The third one is DML 155, one of the toughest puzzles with no symmetry. This is my sample file for tests.

Next one is at the top of JF list m_b_metcalf.

The last one is golden Nugget, the second puzzle with no symmetry in that group.

Code: Select all
`600000002090400050001000700050943000000105000000800040007000600030009080200000001 coloin 02805 100000002090400050006000700050903000000070000000850040700000600030009080002000001  Easter Monster100900000020050030004006000600000100030080020007000004000300700000020050080004009 dml 500000009020100070008000300040600000000050000000207010003000800060004020900000005 # m_b_metcalf 000000039000001005003050800008090006070002000100400000009080050020000600400700000 Golden Nugget `

I open the five posts immediately. Puzzles having the start thru a loop can be considered finalized and will be detailed quickly.

Remarks:

The appropriate handling of “ Kurtzals loop” (LoopK from now on) shorten significantly the solution when that loop exists. In fact, Easter Monster could be solved without level 4 after handling of LoopK.

The scale of difficulty measured in processing time is about: (provisional figures end of 2007)

3 seconds for coloin 02805
25 to 32 seconds for Easter Monster and # m_b_metcalf
50 seconds for DML155
120 seconds for golden nugget.

GOLDEN NUGGET

Golden Nugget is an extraordinary difficult puzzle. In that first shot, my raw print is about 1000K in size. I have seen some possibilites to improve the process, nevertheless, at least with the tools I use, it will remain a non human puzzle.

I wanted to give the full solution for several reasons:
. It's not fair to say that the puzzle can be solved without T&E not publishing the solution,
. The way the solver did it can give new ideas to others
. I had anyway to check the solution.

The weakness of the puzzle seems to be in colums 4,5, with a key role played by 1r7c4. This could be the clue for human cracking.

GOLDEN NUGGET START has been transferred on my new website at this point.

http://pagesperso-orange.fr/gpenet/UX/Sample7GN/GN_fichiers/V00.htm
Last edited by champagne on Tue May 13, 2008 2:31 am, edited 9 times in total.
champagne
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### coloin 02805

Code: Select all
`600000002090400050001000700050943000000105000000800040007000600030009080200000001 coloin 02805 `

a new version of this puzzle 2008 02 26 can be seen at that point

http://pagesperso-orange.fr/gpenet/UX/sample1/s1.htm

Part of my sample file It includes a detailed analysis of the SK loop,
Last edited by champagne on Mon Mar 24, 2008 2:39 am, edited 2 times in total.
champagne
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Code: Select all
`100000002090400050006000700050903000000070000000850040700000600030009080002000001  #  JPF 04/07/01 (Easter Monster) `

This post has been transferred on my website at that point
http://pagesperso-orange.fr/gpenet/UX/sample3EM/EM_fichiers/V0_01.htm
Last edited by champagne on Sun Apr 13, 2008 4:56 am, edited 9 times in total.
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Code: Select all
`100900000020050030004006000600000100030080020007000004000300700000020050080004009 dml `

This first shot on dml155 is now transferred on my website as well at this point where the version end of April will come soon.

http://pagesperso-orange.fr/gpenet/UX/Sample4dml/dml.htm

All versions end of November 2007 are now available on my site at that point

http://pagesperso-orange.fr/gpenet/UX/UX.htm
Last edited by champagne on Tue May 13, 2008 2:28 am, edited 8 times in total.
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Code: Select all
`#500000009020100070008000300040600000000050000000207010003000800060004020900000005 # m_b_metcalf `

This version has ben transferred here

http://pagesperso-orange.fr/gpenet/UX/Sample5metc/metc.htm

At the same point you will find the full solution end of April 2008.
Last edited by champagne on Tue May 13, 2008 2:34 am, edited 2 times in total.
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deleted
Last edited by champagne on Mon Mar 31, 2008 4:22 am, edited 9 times in total.
champagne
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Interesting work here.
i have to say that the puzzle you have used comes from a series I submitted to gsf [to exclude isomorphs] and it was one of many.
The ones which I documented had a suexrat9 of around 1100 here This puzzle did not quite make this list !.

As you can see they all come from the same group of "16-templates" that we used to make these puzzles, so perhaps many will have the loopK.

The thinking behind the sort of "rating " approach that you are doing is interesting, and will add fuel to the debate. In particular, the Easter Monster puzzle, as SK has shown succumbs to a manouvere.....does this therefore reduce its apparent difficulty ?

It is appropriate that analysis of the strong/weak inferences, red/green, and your tagging is integral to the rating of our apparently hardest puzzles.etc

I have just got dukuso to modify his suexrat9 program, in an effort to analyse puzzles furthur.

Suexrat9 analysed the average node count in say, 100 isomorphic variations of the same puzzle, the solver is DLX based and attempts to solve puzzles initially at a bivalue cell.

I have got him to adapt the program to give the node count of the lowest 2%. This was in response to puzzles recently made which have a high suexrat9 value, but possibly arnt that hard. here The premise being that the low node count reflects ease of solving, which reflects "hardness". I dont know if this is a correct extrapolation.

Comparitve stats for the 5 puzzles.
Code: Select all
`puzzle            gsf -q1                                 SX9       SXT[2%]      coloin 02805      #  2805 FNP C22.m/M2.49.133             1005 ,     452 ,    3Easter Monster    # 99408 FNBP C21.m/M3.566.938           1864 ,     761 ,    25dml  11/155       # 95111 FNP C21.m/M2.15.3933            1339 ,     958 ,    50m_b_metcalf       # 69658 FNP C20.m/S2.a/M2.3.63423       1291 ,     790 ,    32Golden Nugget     # 95649 FNP C21.m/M2.1.164025           3617 ,    2100 ,    120`

dukuso's view was to develop a SAT solver, but I dont know of any ratings programs which use this....the output in terms of "time to solve" -[as opposed to back-track] by your method may be a step forward in this direction too.

AW and ravel had "black box" rating programs which we are awaiting their view on GN.

C
coloin

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Joined: 05 May 2005

Coloin wrote

The thinking behind the sort of "rating " approach that you are doing is interesting, and will add fuel to the debate.
In particular, the Easter Monster puzzle, as SK has shown succumbs to a manouvere.....does this therefore reduce its apparent difficulty ?

First of all, I do not intend here to introduce another rating procedure. The figures I gave relate to processing time under specific conditions.

I got for example about 17 seconds for Easter Monster running it at levels 1/3 when it was possible. Reversely, I got for the same puzzle more than 100 seconds forcing level 4 all along the processing.

I did not try to solve coloin 02805 below level 4 before the loopK had been established because I intended to clarify how level 4 was working.

I think optimized processing for that puzzle would be below 2 seconds(but this is in no way a target).

What is for sure is that all puzzles having the LoopK should be downgraded.

The loopk can be established thru several approachs, for example ALS net, SK approach, Virus pattern approach and, as I did in my first trial for Easter Monster, with full tagging level 4 without virus patterns.

I am convinced that establishing that the loopK has exclusive Ors is relatively easy whatever tool you are using (this is true for the three puzzle among the five having the LoopK).

Then crackng such puzzles is much easier.

Regarding DML 155 and Golden Nugget, although I have still to implement some functions in the programm to fulfill my specifications, I think the processing time will not change significantly.
To be honest, I know the solver cracked them, but for Golden Nugget, I did not yet investigated to understand how he did it.
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deleted
Last edited by champagne on Mon Mar 31, 2008 4:23 am, edited 2 times in total.
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deleted
Last edited by champagne on Fri Apr 04, 2008 2:03 am, edited 1 time in total.
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GOLDEN NUGGET summary

First shot for Golden nugget is now fully published.

It has been a long and tough job, and I have to apologize for possible mistakes I would have introduced in reshaping the solver proposal.

Going thru the print is somehow boring. I would make a quick summary for anybody willing to work on this puzzle.

Obviously, solving this puzzle requires AC2 analysis.

I prepared a list of used AC2 (some were not AC2 at the start point).
The first column is just a label to locate the first use of the AC2
The second column is the number of “couple tags” killed during the process
The third column is the number of main uses of that AC2
The fourth column is the number of secondary uses.

Going thru the list it appears that:
- about 25 AC2 are necessary to start cracking the puzzle
- 16 of them are intensively used in clearing,
- Most of them are in the central vertical band, but those using cells r12c7,r4c12,r5679c3,r7c12 play key roles as well. This can be explained thru several factors:
1. 1r7c4 and 1r3c2 are key positions in the puzzle
2. in box 4, the bi values on 2 and 4 create additional links
3. in lines 4 and 7 connection with AC2 located in the central band is obvious
4. r7c7 is also a link between AC2 r12c7 and AC2 located in line 7

Code: Select all
`25678 14568  1K24567 |268      2467   4678b  |1I247  3       9     26789 4689   2467    |23a68À9â 23A467 1      |247    246c7   5     2679  1I469  3       |269      5      4679ä  |8      1Ê246C7 1247  ------------------------------------------------------------------2d35  34e5   8       |1j35     9      357w   |123457 1247    6     3569f 7      4E56    |13568b   1L36   2      |13459  1489    1348  1     3569F  2D56    |4        367Z   35678B |23579  2789    2378  ------------------------------------------------------------------367x  136    9       |12h36    8      34p6   |12347  5       12347 3578g 2      157y    |135S9ä   134Q   3459   |6      14789ã  13478 4     13568G 156     |7        12H36  35r69ã |1239å  1289    1238  `

2 1 7 0 |*r4c4r5c5
4 1 153 24 |*r7c12
7 1 213 28 |*r4c14
7 1 150 24 |*r4c12r6c3
7 1 443 57 |*r4c12
7 1 287 70 |*r56c3
10 3 71 6 |*r48c4
13 3 34 0 |*r4c6r6c5
16 1 141 20 |*r4c12r5c3
19 3 230 43 |*r4c46
21 1 185 29 |*r56c5
22 1 168 20 |*r12c7
30 2 139 18 |*r7c4r89c5
37 3 196 20 |*r89c3
44 1 44 2 |*r4c26
88 1 45 1 |*r59c3
89 2 163 13 |*r7c6r8c5
89 1 52 2 |*r7c26
104 3 181 22 |*r37c4
105 1 285 39 |*r7c46r9c5
118 0 222 29 |*r4c24
142 2 166 20 |*r17c4
143 2 86 14 |*r126c5
144 1 87 6 |*r69c3

145 0 40 3 |*r7c16
210 2 70 4 |*r2c37
226 1 46 2 |*r137c4
233 1 45 2 |*r13c4
233 0 46 2 |*r59c5
233 0 58 2 |*r58c5
262 3 134 17 |*r2c24
267 2 189 25 |*r2c12
268 2 99 13 |*r2c14
296 0 109 6 |*r3c14
297 2 64 4 |*r7c24
302 4 67 5 |*r3c146
327 1 53 4 |*r2c78
332 2 47 4 |*r24c4
352 2 67 6 |*r2c12r3c2
354 2 78 6 |*r2c38
359 2 61 6 |*r2c127
399 2 58 4 |*r12c4
409 1 52 7 |*r25c3
416 3 70 7 |*r12c5
422 1 60 7 |*r2c35
425 0 71 12 |*r157c4
434 0 81 13 |*r4c1r56c3
437 2 67 10 |*r45c4
439 0 82 14 |*r145c4
442 0 73 14 |*r78c4r9c5
446 1 65 13 |*r129c5
473 2 64 11 |*r7c2r9c3
483 2 56 11 |*r45c4r5c5

The second table is the list of used AC in the first part of the process

2 0 43 0 |*r5c1r6c2
2 0 46 0 |*r5c4r6c6
2 0 60 0 |*r8c1r9c2
2 0 20 10 |*r8c46r9c6
13 0 12 1 |*r4c1r6c3
44 0 87 1 |*r2c124
62 0 25 1 |*r7c4r9c5
124 0 28 3 |*r16c6
142 0 38 2 |*r23c8

Again, compared to the total number of ACs (about 200), a very small number has been used. If you analyze the print, they are mainly used to communicate thru AIChains between AC2s.

My feeling is that somebody having identified the property of useful stuff can crack such a puzzle without computer assistance. This will likely be the case in few months.

Regarding this first shot of the solver I would add some remarks:

This version of the solver has a poor handling of the vicinity pattern of AC2s. The tagging process is very strict and does not allow non symmetric weak links. Nevertheless, analyzing the vicinity pattern of AC2s, some very simple reflexive links can be found.

To-day, the computer founds them thru “nice loops” or long sequences. I cut in some of them but I did not look for alternative sequences. On top of it, handling of “Nice loops” with “couple tags” is very poor. I have to add a memory of these loops.

One additional remark relates to T-chains. T-chains (extended form) are fully integrated in the tagging process. Any T-chain has an equivalent tagging form. Nevertheless, T-chains are compact compared to the tagging equivalent form. This can be a way to shorten the print.. The solver will not do it for several reasons.

Again the main figures for that puzzle

Code: Select all
`Time to check validity 190 millisecondsProcessing time 115 secondsSize of the raw print 850K`

A second shot will come if improvements in preparation bring enough changes. I am not waiting for changes in the clearing sequence, but more for lighter validation sequences.
champagne
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Tarek 191 of the hardest puzzles list p48 is an interesting case. I think at least the start is something human players can do.

Various rating are shown below:

#tarek-191##95765#1254#692 47 3s7 7s265

The three last figures are
- counting time in milliseconds,
- processing time at level 3
- processing time forcing level 4.

As usually, when a puzzle can be cracked at level 3, the processing time is shorter than at level 4.
However, for that puzzle having the SK loop, the start at level 4 has some specificity.

8.....4...2..1..6...3.....9....65....7.9........1.4.2.4.......3.1...6.7...9...8..

I quickly pass the step of the SK loop.

Code: Select all
`8      569B  1g567   |2356d7  23579Ä  2379    |4      13i5   12h57  579b   2     4a57    |34A578  1       3789B   |3I57   6      578j   1G567  4A56  3       |2456D78 24U578  278     |12H57  158J   9      -------------------------------------------------------------------1239   34a89 1248    |2O37k8  6       5       |1379   13489f 1478   12356  7     124S568 |9       2Ì3í8   2É3Ê8Ë  |1356   13458  14568  3569   35689 568     |1       3Ç7K8È  4       |35679Ã 2      5678   -------------------------------------------------------------------4      568â  2567l8  |2578    25789   1e2789Ä |1256m9 159F   3      23q5   1     258á    |23458   234589c 6       |259C   7      24T5   23567L 3r56  9       |23457   23457   1E237   |8      14V5   12456M `

SK loop
plus
Jelly (XW4) digit 5 columns 1379 rows 2568

Code: Select all
`8     569B  1f67    |2356d7  23579Ê 2379    |4      13h5  12g7  579b  2     4a57    |34A8    1      389B    |3H57   6     578i  1F67  4A56  3       |2456D78 24W578 278     |12G7   158I  9     ---------------------------------------------------------------1239  34a89 1248    |2S37j8  6      5       |1379   3489C 1478  12356 7     124V568 |9       238    238     |1356   348   14568 3569  389   568     |1       37J8   4       |35679É 2     5678  ---------------------------------------------------------------4     568m  267l    |2578    25789  1e2789Ê |126o   159c  3     23k5  1     258M    |348     3489c  6       |259C   7     24n5  267L  3K56  9       |23457   23457  1E237   |8      14N5  126O  `

At that point, we have

Code: Select all
`(4&9)r2c13 == (5&6)r13c2 == (3&8)r79c2 == (2&5)r8c13.....(5&7)r2c79 loop  and (5&7)r2c13 == (3&8)r2c79......==(4&9)r13c2 loop`

and up to now, I have always seen the solver proving immediately that both lines are not valid.
Here, although it is still true that both are not valid, only the second one is detected as not valid because it implies 4r8c4 and 4r2c4.

Before looking at the next clearings, two remarks:

The '5' in the SK loop are now forming a closed chain of strong links
5r2c13 = 5r2c79 = ..... 5r8c13 = 5r79c2 = 5r13c2 loop

You have another layer (Q,q for the solver) in the same loop
7r2c13.q = 7r2c79.Q = 1r13c8.q = 1r79c8.Q = 2r8c79.q = 2r8c13.Q = 6r79c2.q = 6r13c2.Q loop
(we have other links as 7r13c2 = r1c3r3c1 in that layer)

We will show #6r7c3 and #6r9c1, we then can expand the two loops in the following way.
#6r7c3r9c1.Q all 'q' are valid 6r79c2 is valid.
As (5&6)r79c2 is not valid, 5r79c2 is not valid .....

To show #6r7c3 and #6r9c1,we need an intermediate step.

We show first that in four pairs of AC2 having nearly the same pattern, (1&6) and (2&7) are not valid.

Pairs are r1c39 and r3c17 ; r7c37 and r9c19 ; r39c1 and r17c3 ; r37c7 and r19c9
I show why for the first pair r1c39 and r3c17.

Both AC2 have free digits 1267
First, we can see that 2r1c39 = 2r3c17 (trivial) 7r1c39 = 7r3c17 (thru box 2, trivial as well)
so (2&7)r1c39<=>(1&6)r3c17 and (1&6)r1c39<=>(2&7)r3c17
In both cases, we are in conflict for '1' in box 3.

Having similarly established (1&6);(2&7) not valid in r1c39 r3c17 r7c37 r9c19 r39c1 r17c3 r37c7 r19c9
we have possibility to have several clearing sequence again very similar.
Here after the sequences for #6r7c3 and #6r9c1

#6r7c3
[]1r3c1 - 6r39c1 = 6r56c3 - 6r7c3
[]1r1c8 - 1r79c8.Q = 6r79c2.q - 6r7c3
[]1r1c9 - 1r45c9 = 1r37c7 - 6r7c7 = 6r7c7 - 6r7c3

#6r9c1
[]1r3c1.F - 6r39c1 = 6r56c1 - 6r9c1
[]1r3c8 - 1r79c8.Q = 6r79c2.q - 6r9c1
[]1r3c7 - 1r45c7.r = 1r37c7 - 6r7c7 = 6r9c9 - 6r9c1

and the final situation after that step

Code: Select all
`8     5B9b    1a6A     |2356a7  23579o  2379    |4      1A3a  2d7D  7b9B  2       4b7B     |3â4B8ã  1       3à8á9b  |3A5a   6     5A8a  1A6a  4B5b    3        |2456A78 24I578  278r    |2D7d   1a8A  9     -------------------------------------------------------------------1239  3ë4b8ì9 1248     |2G37e8  6       5       |1379   3489D 1478  12356 7       124H5U68 |9       238     238     |1356   34Æ8  14568 3569  389Í    56v8     |1       37E8    4       |35679n 2     5678  -------------------------------------------------------------------4     6C8c    2B7b     |2578    25789   1c2789o |1C6c   5D9d  3     3c5C  1       5c8C     |34É8    3è48ê9d 6       |2d9D   7     2D4d  2b7B  3C6c    9        |23457   23457   1C237   |8      4D5d  1c6C  `

This is the most interesting part of that puzzle in the solution.

I will give in an update the equivalent steps in level 3, and later on, after having checked that "vicinity analysis" does not lead to shorter paths, the rest of the solution.
champagne
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I think it is interesting to compare how the solver behave for tarek 191 at level 3.
The first part of the solution ends at the same point.
The start in level 3 uses mostly ACs r1c3r3c1; r1c9r3c7; r7c3r9c1 and r7c7r9c9.
I will uses derived weak links directly. (eg: 7r1c9r3c7 - 1r1c9r3c7)

The first step is done of long AIC's chains. In full tagging, there is nearly no difference between a short and a long AIC.
In hand procesing it's more complex but here, one could have been willing to work on symetries.

At the end of the first sub lot, I indicate an obvious Nicre loop posibility to simplify the AICs.
The solver did not ue it.

Code: Select all
`8      569B  1g567   |2356d7  23579Ä  2379    |4      13i5   12h57  579b   2     4a57    |34A578  1       3789B   |3I57   6      578j   1G567  4A56  3       |2456D78 24U578  278     |12H57  158J   9      -------------------------------------------------------------------1239   34a89 1248    |2O37k8  6       5       |1379   13489f 1478   12356  7     124S568 |9       2Ì3í8   2É3Ê8Ë  |1356   13458  14568  3569   35689 568     |1       3Ç7K8È  4       |35679Ã 2      5678   -------------------------------------------------------------------4      568â  2567l8  |2578    25789   1e2789Ä |1256m9 159F   3      23q5   1     258á    |23458   234589c 6       |259C   7      24T5   23567L 3r56  9       |23457   23457   1E237   |8      14V5   12456M `

two sub chains to start

Code: Select all
`#[]7r2c13 - 2r8c13   []7r2c13 - 7r2c79 = 7r1c9r3c7 - 1r1c9r3c7 = 1r13c8 - 1r79c8 = 1r7c7r9c9 - 2r7c7r9c9 = 2r8c79 - 2r8c13 #[]6r79c2 - 2r8c13    []6r79c2 - 6r13c2 = 6r1c3r3c1 - 7r1c3r3c1 = 7r2c13 - 2r8c13 `

three clearing AIC's using subchains

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`[]    3r9c1 - 6r7c3r9c1 = 6r79c2 - 2r8c13 = 2r7c3r9c1 - 3r9c1[]    8r7c3 - 6r7c3r9c1 = 6r79c2 - 2r8c13 = 2r7c3r9c1 - 8r7c3[]5r7c3r9c1 - 6r7c3r9c1 = 6r79c2 - 2r8c13 = 2r7c3r9c1 - 5r7c3r9c1`

and two working in the same are

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`[]5r1c3r3c1 - 7r1c3r3c1 = 7r2c13 - 2r8c13 = 2r7c3r9c1 - 6r7c3r9c1 = 6r79c2 - 6r13c2 = 6r1c3r3c1 - 5r1c3r3c1[]5r1c9r3c7 - 7r1c9r3c7 = 7r2c79 - 7r2c13 = 7r1c3r3c1 - 6r1c3r3c1 = 6r13c2 - 6r79c2 = 6r7c3r9c1 - 2r7c3r9c1 = 2r8c13 - 2r8c79  = 2r7c7r9c9 - 1r7c7r9c9 = 1r79c8 - 1r13c8 = 1r1c9r3c7 - 5r1c9r3c7`

Two obvious loops out of these chains

#[]6r79c2 - 2r8c13 and 2r8c13 = 2r7c3r9c1 - 6r7c3r9c1 = 6r79c2 => 2r8c13==6r7c3r9c1
#[]7r2c13 - 2r8c13 and 7r2c13 = 7r1c3r3c1 - 6r1c3r3c1 = 6r13c2 - 6r79c2 = 6r7c3r9c1 - 2r7c3r9c1 = 2r8c13 =>
========
a second lot without clear sub chain

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`[]7r2c46 - 7r2c79 = 7r1c9r3c7 - 1r1c9r3c7 = 1r13c8 - 1r79c8 = 1r7c7r9c9 - 2r7c7r9c9 = 2r8c79 - 2r8c13 = 2r7c3r9c1 - 6r7c3r9c1 = 6r79c2 - 6r13c2 = 6r1c3r3c1 - 7r1c3r3c1 = 7r2c13 - 7r2c46[]2r8c45 - 2r8c79 = 2r7c7r9c9 - 1r7c7r9c9 = 1r79c8 - 1r13c8 = 1r1c9r3c7 - 7r1c9r3c7 = 7r2c79 - 7r2c13 = 7r1c3r3c1 - 6r1c3r3c1 = 6r13c2 - 6r79c2 = 6r7c3r9c1 - 2r7c3r9c1 = 2r8c13 - 2r8c45`

=====
and a third lot with a sub chain
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`#[]2r8c79 - 1r1c9r3c7   []2r8c79 - 2r8c13 = 2r7c3r9c1 - 6r7c3r9c1 = 6r79c2 - 6r13c2 = 6r1c3r3c1 - 7r1c3r3c1 = 7r2c13 - 7r2c79 = 7r1c9r3c7 - 1r1c9r3c7 `

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`[]            4r9c9 - 2r7c7r9c9  = 2r8c79 - 1r1c9r3c7 = 1r13c8 - 1r79c8 = 1r7c7r9c9 - 4r9c9[]         5r7c7r9c9 - 2r7c7r9c9 = 2r8c79 - 1r1c9r3c7 = 1r13c8 - 1r79c8 = 1r7c7r9c9 - 5r7c7r9c9[]              9r7c7 - 2r7c7r9c9 = 2r8c79 - 1r1c9r3c7 = 1r13c8 - 1r79c8 = 1r7c7r9c9 - 9r7c7[]1r5c8 - 1r79c8 = 1r7c7r9c9 - 2r7c7r9c9 = 2r8c79 - 1r1c9r3c7 = 1r13c8 - 1r5c8[]1r4c8 - 1r79c8 = 1r7c7r9c9 - 2r7c7r9c9 = 2r8c79 - 1r1c9r3c7 = 1r13c8 - 1r4c8`

and a clearing AIC in the same area

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`[]6r6c2 - 6r79c2 = 6r7c3r9c1 - 2r7c3r9c1 = 2r8c13 - 2r8c79 = 2r7c7r9c9 - 1r7c7r9c9 = 1r79c8 - 1r13c8   = 1r1c9r3c7 -  6r1c3r3c1 (see above) = 6r13c2 - 6r6c2`

ending by

Jelly (XW4) digit 5 columns 2458 rows 1379

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`8     569B  1f67    |2356d7  23579Ê 2379    |4      13h5  12g7  579b  2     4a57    |34A8    1      389B    |3H57   6     578i  1F67  4A56  3       |2456D78 24W578 278     |12G7   158I  9     ---------------------------------------------------------------1239  34a89 1248    |2S37j8  6      5       |1379   3489C 1478  12356 7     124V568 |9       238    238     |1356   348   14568 3569  389   568     |1       37J8   4       |35679É 2     5678  ---------------------------------------------------------------4     568m  267l    |2578    25789  1e2789Ê |126o   159c  3     23k5  1     258M    |348     3489c  6       |259C   7     24n5  267L  3K56  9       |23457   23457  1E237   |8      14N5  126O `

The second step is a kraken blossom

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`#[]f - 6r7c3   1r3c1.F []6r3c1 - 6r13c2 = 6r79c2 - 6r7c3 []7r3c1 - 7r9c1 = 7r7c3 - 6r7c3#[]§V - 2r7c7   6r7c3.§v []6r7c7 - 2r7c7 []6r7c2 - 6r13c2 = 2r8c79 - 2r7c7#[]F - 2r7c7   []2r3c7.G - 2r7c7 []1r3c7 - 1r3c1.F []7r3c7 - 7r2c79 = 2r8c79 - 2r7c7#[]7r1c3 - 2r7c7   []2r3c7.G - 2r7c7 []1r3c7 - 1r3c1 = 1r1c3 - 7r1c3 []7r3c7 - 7r2c79 = 7r2c13 - 7r1c3#2r7c7   []1r1c3.f - 6r7c3|# = §V - 2r7c7|# []6r1c3 - 1r1c3.f = F - 2r7c7|# []7r1c3 - 2r7c7|#`

then easily

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`[]1r3c7 - 1r13c8 = 2r8c13 - 2r8c7 = 2r3c7 - 1r3c7[]6r7c3 - 6r79c2 = 2r9c9 - 6r9c9 = 6r7c7 - 6r7c3`

then
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`[]7r3c1 - 7r2c13 = 1r79c8 - 1r3c8 = 1r3c1 - 7r3c1[]7r1c3 - 7r2c13 = 6r9c1 - 7r9c1 = 7r7c3 - 7r1c3`

some basic clearing and we finish here, not far from where we stopped before.

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`8     5d9D  1a6A    |2356a7  23579Á 2379    |4      1A3h5 2f7F  57c9d 2     4b57C   |34B8    1      3í89D   |3H5h   6     5I8i  1A6a  4B5b  3       |2456A78 24Q578 278Ä    |2F7f   1a58I 9     ---------------------------------------------------------------1239  34b89 1248    |2O37j8  6      5       |1379   3489G 1478  12356 7     124P568 |9       238    238     |1356   348   14568 3569  389   56È8    |1       37J8   4       |35679À 2     5678  ---------------------------------------------------------------4     56E8l 2C7c    |2578    25789  1e2789Á |1E6e   5G9g  3     3k5K  1     5l8L    |348     3489g  6       |2f59G  7     2F4m5 2c7C  3K56e 9       |23457   23457  1E237   |8      4M5m  1e6E  `

[]AC:r8c579(5r8c79.r - 4r8c59) = 4r8c4 - 4r2c4.B = 5r3c2.b - 5r2c13.r

Now we are exactly at the same point.

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`8     5B9b    1a6A     |2356a7  23579o  2379    |4      1A3a  2d7D  7b9B  2       4b7B     |3â4B8ã  1       3à8á9b  |3A5a   6     5A8a  1A6a  4B5b    3        |2456A78 24I578  278r    |2D7d   1a8A  9     -------------------------------------------------------------------1239  3ë4b8ì9 1248     |2G37e8  6       5       |1379   3489D 1478  12356 7       124H5U68 |9       238     238     |1356   34Æ8  14568 3569  389Í    56v8     |1       37E8    4       |35679n 2     5678  -------------------------------------------------------------------4     6C8c    2B7b     |2578    25789   1c2789o |1C6c   5D9d  3     3c5C  1       5c8C     |34É8    3è48ê9d 6       |2d9D   7     2D4d  2b7B  3C6c    9        |23457   23457   1C237   |8      4D5d  1c6C `

Later on, both way follow different paths. This will come with next posts

I have a peronnal feeling that the start is easier at level 4, mainly due to SK loop effect, but one could disagree.
champagne
2017 Supporter

Posts: 6350
Joined: 02 August 2007
Location: France Brittany

A lot has been done since this thread was open.

To get more flexibility, I created my own site

http://pagesperso-orange.fr/gpenet/

In that site, I created a specific entry for examples

http://pagesperso-orange.fr/gpenet/UX/UX.htm

And I started transferring some of the puzzles initially shown here.

Coloin puzzle directly in a new form

Easter Monster and Golden Nugget, as they were shown here,

I worked mainly on Golden Nugget, so a new version of Golden Nugget is also available here
http://pagesperso-orange.fr/gpenet/UX/Sample7GN/GN.htm

Next versions of the sample file will come as soon as I’ll have finished the new set of improvements which is on the way.
Corresponding sets of that thread will then be transferred of deleted.
champagne
2017 Supporter

Posts: 6350
Joined: 02 August 2007
Location: France Brittany

I start the solutions for the set of puzzles described in my last post

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`012000000030000400500167000080004007000050000100200060000623005009000020000000140_278H012000304400010000000004002004000560000070000083000200800700000000040009906000480_277H012000030040250060700000400300800000500070008000009006009000004060091050050000790_276H001000000234500000006370000005000006800090007100000200000083100000002458000000600_275H000120003000000400005006000000070021081040560250080000000800300006000000400037000_274H000102300400000005060070000600005002070040010300800004000080020800000009005609000_273H100020030040005001000000500000600070801000209030009000005000000300800010090040006_272H100000230000301000040500600070000084000090000830000010007004060000102000016000003_271H010234050000000000005000600000600027800010003470009000006000200000000000090583010_270H`

Edit one:

Here three puzzles. The URL goes to the file corresponding to the text.

The first puzzle has nothing special, the second one is a one shot already discussed.

I added number 270, a "single shot" for the solver but more difficult.
Another interesting point in that path is the use of two scenarios to clear one tag.

http://pagesperso-orange.fr/gpenet/UX/UX_fichiers/278_277_H.htm

Last edited by champagne on Fri Aug 29, 2008 7:07 am, edited 1 time in total.
champagne
2017 Supporter

Posts: 6350
Joined: 02 August 2007
Location: France Brittany

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