Call for contribution

Advanced methods and approaches for solving Sudoku puzzles

Call for contribution

Postby champagne » Thu Sep 20, 2007 2:18 pm

Hello,

My thread on "full tagging" is sleeping. I am coming back asking for external contribution.
The reason why I came here from time to time is the search for additional tools.

One simple way is for sure to get non T&E solutions for puzzles I (my solver) do not crack.

Here is the bottom list of unsolved puzzles in GSF list. I partially posted it in Denis Berthier’s thread.

Nobody answered, but I don’t know if this means that there is no known solution without T&E, which would be surprising.

Can anybody help me, either confirming the fact that there is no positive answer or bringing me to the right place to see the solution.


Code: Select all
600000002090400050001000700050800000000942000000305040002000600030009080700000001,coloin-04-10_09716,106,1253,
600000002090040050001000700000895000030410080000300000007000600050080040200000001,jpf-04/07,0,_08737,110,1794,
600000002090400050001000700050308000000604000000095040002000600030009080700000001,coloin-04-10_08656,106,1489,
600000002090400050001000700050943000000800000000025040002000600030009080700000001,coloin-04-10_08499,107,1614,
600000002090400050001000700050100000000904000000853040002000600030009080700000001,coloin-04-10_07657,106,1230,
100000002030040050006000700000534000040810090000900000002000600080090030700000001,jpf-04/05,0,_07397,109,1657,
100000002030040050006000700000538000040960080000400000002000600090080030700000001,jpf-04/02,0,_07346,110,1711,
100000000006020700080005030300006800002070090040100000007030060000800500000009004,ravel-04/02,_07150,105,0790,
100000006020500040003000700040050000000810400000020080007000300050009020600000001,gsf-2007-05-_04519,104,1273,
003050000400009000080200000200004000090800000005060001000000217001000806000070503,rw-04-06,0,0_04220,106,0910,
100000002090400050006000700050903000000010009000800040700000600030009080002000001,gsf-2007-05-_03465,107,1059,
003050000400009000080200000200004000090800000005060001000000097001000806000070203,rw-04-06,0,0_03349,104,0900,
600000002090400050001000700050943000000105000000800040007000600030009080200000001,coloin-04-10_02805,098,1223,


Another way to crack these puzzles would be to combine forces. I understood than RONK have the possibility to start at any point of a puzzle in a specific solver.

I give hereafter the final status for puzzles my solver could crack partially.

The firs one is

Code: Select all
 jpf-04/07,0,_08737,110,1794,
clear 6r3c6
clear 6r9c6
clear 6r6c3
clear 6r6c9
==
clear 7r1c6
clear 2r3c6
clear 2r6c3
clear 7r6c9
clear 7r6c1
clear 2r6c7
clear 2r7c6
clear 7r9c6

ending here

6     478    3458  |1579  357  1389   |13489 139   2     
378   9      238   |1267  4    123678 |138   5     368   
3458  248    1     |2569  2356 389    |7     369   34689
--------------------------------------------------------
147   12467  246   |8     9    5      |1234  12367 3467 
579   3      2569  |4     1    267    |259   8     5679 
14589 124678 4589  |3     267  267    |1459  12679 459   
--------------------------------------------------------
13489 148    7     |1259  235  1349   |6     239   58   
139   5      369   |12679 8    123679 |239   4     379   
2     468    34689 |5679  3567 349    |58    379   1     


Next one is

Code: Select all
coloin-04-10_08656,106,1489,

clear 7r8c5
==
clear 2r3c5
===
clear 1r8c5
===
clear 7r5c9
===
clear 1r7c1
clear 1r5c1
===
clear 1r4c1
===
clear 2r8c5
===


6     478   34578 |15789 13578  137   |13489  139   2     
238   9     378   |4     123678 12367 |138    5     368   
23458 248   1     |2589  3568   236   |7      369   34689
---------------------------------------------------------
249   5     4679  |3     127    8     |129    12679 679   
2389  1278  3789  |6     127    4     |123589 12379 3589 
1238  12678 3678  |127   9      5     |1238   4     3678 
---------------------------------------------------------
4589  148   2     |1578  134578 137   |6      379   34579
145   3     456   |1257  456    9     |245    8     457   
7     468   45689 |258   234568 236   |23459  239   1     



And the last one I propose here

Code: Select all
jpf-04/05,0,_07397,109,1657,

clear 6r1c6
clear 6r9c6
clear 6r6c1
clear 6r6c9
===
clear 2r6c7
clear 7r6c9
clear 7r1c6
clear 2r3c6
clear 7r7c6
clear 2r9c6
clear 2r6c1
clear 7r6c3
===

1     579   45789 |367   5678 3589   |3489  468    2     
289   3     789   |1267  4    126789 |189   5      689   
24589 259   6     |123   258  13589  |7     148    3489 
--------------------------------------------------------
2689  12679 1789  |5     3    4      |128   12678  678   
2356  4     357   |8     1    267    |235   9      3567 
358   12567 1358  |9     267  267    |13458 124678 3458 
--------------------------------------------------------
3459  159   2     |1347  578  1358   |6     478    45789
456   8     145   |12467 9    12567  |245   3      457   
7     569   3459  |2346  2568 358    |24589 248    1     


Thanks for help.
champagne
2017 Supporter
 
Posts: 5675
Joined: 02 August 2007
Location: France Brittany

Postby champagne » Mon Oct 22, 2007 1:19 pm

Finally "Help yourself" seems to be the best way to go ahead.

I tried my last idea for the following step in my "full tagging" process. It works.

All theese puzzles but one (a remaining bug in my program) seem cracked by the new version of the solver.

I made a quick check, Eater Monster should be cracked as well, in a relatively easy way. Again, I feel that ranking proposed by gsf and jpf are not in line with "full tagging" capability to solve puzzles.

Having done the test in a quick and dirty mode, I have to stay cautious regarding the new capabilities, but for sure, full tagging have strong additional ones.

I have still to work on the process to find out to the "simplest" solution, which should be done within one or two weeks. Then, I'll post one or two detailed solutions.
champagne
2017 Supporter
 
Posts: 5675
Joined: 02 August 2007
Location: France Brittany

Postby champagne » Wed Oct 24, 2007 5:35 pm

Hello,

I have now enough results to be confident in the new version of "full taging".

I tested it on the top list of jpf and gsf. In both cases; puzzles are cracked.

I have not that much time in the near future, so I start a full explanation of how it solves EasterMonster.

I start with the first clearing of candidates and I'll add other clearing progressively.

PRINTING RULES:

The rules have been described in the thread "full tagging". I have only to define how I will work with the new stuff.

I'll do it using the puzzle at the start



Code: Select all
1      47d8  345f78 |3567y  3689e  5678   |34h89   36i9  2     
2o38   9     37a8   |4      12368  1267A8 |1g38    5     36I8   
2345F8 2P48  6      |1235   12389E 1258   |7       1G39  34H89 
---------------------------------------------------------------
2468   5     147x8  |9      124j6  3      |128     1267C 678   
234689 12468 13489  |126    7      124J6  |1235b89 12369 35B689
2369   1267D 1379   |8      5      126    |1239    4     367x9 
---------------------------------------------------------------
7      1N48  14589k |1235   12348  12458  |6       2l39  3459   
456v   3     1M45   |12567c 1246   9      |2L45    8     457C   
45689K 46w8  2      |3567   3468   4567y8 |3459    37c9  1     


I indicate "almost cell" using |*.
eg :
. r1c3 r3c1 is an "almost cell"
. 4(r1c3 r3c1)/2r3c1 |*r1c3r3c1
is the weak link 4/2 in that "almost cell".

Similarly, I indicate the new stuff ALS/"Almost cell" freedom 2 here after "AC2"(two digit TRUE and two digit FALSE) using ||*
eg : ||*(r1c2 r3c2).

We need as well a convention to identify a "couple tag".
eg : in ||*(r1c2 r3c2) the two valid digits can be 2 and 4.
. To avoid use of symbols, I'll write this {2;4||*r1c2r3c2)

A weak link using "couple tags" will be written
. (2;4)/(2;6)||*(r1c2 r3c2) inside ||*(r1c2 r3c2)
. 4(r1c3r3c1)/(2;4)||*r1c2r3c2 for a native weak link out of ||*r1c2r3c2
....
==================================
The first clearing move for Easter Monster uses two AC2 as Choices and two others as targets to prepare the final clearing:

Intermediate targets are:

||*r1c2r3c2 where we intend to cancel (4;8) => (2;7) in ||*r1c3r2c1r2c3r3c1 (complementary set)
nota: as in ||*r1c2r3c2 (2;7) is tagged (P;d) in ||*r1c3r2c1r2c3r3c1 (2;7) is tagged (p;D)

||*r2c1r2c3 where we intend to cancel {3;8} => (2;7) or (O;A) in ||*r1c2r1c3r3c1r3c2

AC2 used as choices are

||*r8c7r8c9 2r8c7-L 4(r8c7r8c9) 5(r8c7r8c9) 7r8c9-C
. "couple tags" (2;4) (2;5) (2;7) (4;5) (4;7) (5;7)

||*r7c8r9c8 2r7c8-l 3(r7c8r9c8) 7r9c8-c 9(r7c8r9c8)
. "couple tags" (2;3) (2;7) (2;9) (3;7) (3;9) (7;9)

==================================
XX= {(4;8)||*r1c2r3c2} ; {(2;7)||*r1c3r2c1r2c3r3c1} not valid => weak link p/D

one chain used several times

Code: Select all
#[]4(r7c3r9c1)/XX   []4(r7c3r9c1)/8(r7c3r9c1)|*r7c3r9c1_8(r7c2r9c2)/XX  ||*r1c2r3c2


#[]{(2,4)||*r8c7r8c9}/XX
[]4(r7c3r9c1)/XX|#
[]4(r8c1r8c3)/4(r8c7r8c9)/{(2,4)||*r8c7r8c9}
[]4(r7c2r9c2)/XX ||*r1c2r3c2

#[]5(r8c1r8c3r8c7)/{(2,5)||*r8c7r8c9}
[]7r8c9-C/(2,5)||*r8c7r8c9
[]4r8c9/(2,5)||*r8c7r8c9}
[]5r8c9/5(r8c1r8c3r8c7)

#[]2r5c2/{(2,7)||*r8c7r8c9}
[]2r7c8-l/(2,7)||*r8c7r8c9}
[]2r4c8/7r4c8-C_c/(2,7)||*r8c7r8c9}
[]2r5c8/2r5c2

#[]2(r3c2r6c2)/XX
[]2(r4c1r5c1r6c1)-P/XX
[]2r6c2/7r6c2-D_d/XX
2r5c2

#[]m/{(4,5)||*r8c7r8c9}
1r8c3-M
[]4r8c3/(4,5)||*r8c7r8c9
[]5r8c3/(4,5)||*r8c7r8c9

#[]M/XX
[]1r7c2/1(r7c4r7c5r7c6)-M
[]4r7c2/XX
[]8r7c2/XX

#[]{(4,7)||*r8c7r8c9}/XX
[]4(r7c3r9c1)/XX|#
[]4(r8c1r8c3)/(4,7)||*r8c7r8c9}
[]4(r7c2r9c2)/XX ||*r1c2r3c2

#[]5(r5c7r9c7)/{(5,7)||*r8c7r8c9}
[]2r8c7-L/(5,7)||*r8c7r8c9}
[]4r8c7/(5,7)||*r8c7r8c9}
5r8c7

#[]XX thru||*r8c7r8c9 (2;4) (2;5) (2;7) (4;5) (4;7) (5;7)
[](2;4)/XX|#
[](2;5)/5(r8c1r8c3r8c7)|#_5(r8c4r8c9)/5(r8c1r8c3)_5(r7c3r9c1)/8(r7c3r9c1)|*r7c3r9c1 _8(r7c2r9c2)/XX
[](2;7)/2r5c2|#_2(r3c2r6c2)/XX|#
[](4;5)/m|#_M/XX|#
[](4;7)/XX|#
[](5;7)/5(r5c7r9c7)|#_5r8c7/5(r8c1r8c3)_5(r7c3r9c1)/8(r7c3r9c1)|*r7c3r9c1 _8(r7c2r9c2)/XX
==========================================
YY= {{3;8}||*r2c1r2c3} or {(2;7) (O;A)||*r1c2r1c3r3c1r3c2} not valid => weak link O/A
in a similar way

a chain reused
Code: Select all
#[]3(r1c7r3c9)/YY   []3(r1c7r3c9)/8(r1c7r3c9)|*r1c7r3c9 _8(r2c7r2c9)/YY


#[]g/||{(3;9)||*r7c8r9c8}
1r3c8-G
[]9r3c8/(3;9)||*r7c8r9c8
[]3r3c8/(3;9)||*r7c8r9c8

#[]G/YY
1r2c7-g
[]8r2c7/YY
[]3r2c7/YY

#[]2r2c5/{(2;7)||*r7c8r9c8}
[]2r8c7-L/(2;7)||*r7c8r9c8}
[]2r8c4/7r8c4-c_ C/(2;7)||*r7c8r9c8}
[]2r8c5/2r2c5

#[]2(r2c1r2c6)/YY
[]2r2c1-o/YY
[]2r2c6/7r2c6-A_a/YY
2r2c5

#[]YY/{(2;3)||*r7c8r9c8}
[]3(r1c7r3c9)/YY|#
[]3(r2c7r2c9)/YY
[]3(r1c8r3c8)/(2;3)||*r7c8r9c8

#[]9(r9c1r9c7)/{(2;9)||*r7c8r9c8}
[]7r9c8-c/(2;3)||*r7c8r9c8
[]3r9c8/(2;3)||*r7c8r9c8
9r9c8

#[]YY/{(3;7)||*r7c8r9c8}
[]3(r1c7r3c9)/YY|#
[]3(r2c7r2c9)/YY
[]3(r1c8r3c8)/(3;7)||*r7c8r9c8}

#[]9(r7c3r7c9)/{(7;9)||*r7c8r9c8}
[]2r7c8-l/(7;9)||*r7c8r9c8
[]3r7c8/(7;9)||*r7c8r9c8
9r7c8

#[]YY thru ||*r7c8r9c8 (2;3) (2;7) (2;9) (3;7) (3;9) (7;9)
[](2;3)/YY|#
[](2;7)/2r2c5|#_2(r2c1r2c6)/YY|#
[](2;9)/9(r9c1r9c7)|#_9r9c8/9(r1c8r3c8)_9(r1c7r3c9)/8(r1c7r3c9)|*r1c7r3c9 _8(r2c7r2c9)/YY
[](3;7)/YY|#
[](3;9)/g|#_G/YY|#
[](7;9)/9(r7c3r7c9)|#_9r7c8/... as above
======================
Having derived two weak links p/D and O/A, we have now a Nice loop

[]ad Dp Po OA []7r2c3-a/7r1c2-d_ /p_2(r4c1r5c1r6c1)-P/2r2c1-o_O/A

clearing thru
=7r2c3 =7r1c2
and =2(r4c1r5c1r6c1) =2r2c1
====> start edit one

I will not cover the remaining part of the "Kurzhals loop" cleaning for two reasons:

- I will likely introduce the "virus pattern" analysis and may be the "Kurzhals loop" identification, so the rest is obsolete,
- I have a small problem in backtracking of clearing due to incomplete handling of "couple tags" clearing and I need time to solve it.

I have no problem with the next steps, so I can comment the solver proposal

Here is the situation at the end of "Kurzhals loop" cleaning.


Code: Select all
1     47A8  345h8  |3567Ã 389f 5678  |34j89 36k9  2     
2g38  9     37a8   |4     126  1267A |1i38  5     36K8 
345H8 2G48  6      |1235  389F 1258  |7     1I39  34J89
-------------------------------------------------------
24b68 5     14B7Â8 |9     126  3     |128   1267D 678   
389   126   389    |126   7    4     |35c89 126   35C89
2369  1267a 1379   |8     5    126   |1239  4     367Â9
-------------------------------------------------------
7     1l48  4589n  |1235  34e8 1258  |6     2o39  3459 
456m  3     1L45   |1267d 126  9     |2O45  8     457D 
4589N 46M8  2      |3567  34E8 567Ã8 |3459  37d9  1 


This is the status after basic tagging. The "Kurzhals loop" is still there with a lot of new strong links.

In fact, "G" is "a"; "K" is "i"; "o" is "d"; "M" is "l" for the visible part of it.
Unless I missed something, Loop effect is of no use in the following sequence

We intend to show that 1r6c7 can be cleared.

Two chains re used later

#[]6r5c2/6r8c4 []6r5c2/6r9c2_6r8c1/6r8c4
#[]1r2c5/1r4c8 []1r2c5/1r2c7-i_1r3c8-I/1r4c8

And we start deriving weak links

#[]1r8c4/1r6c7 []1r5c4/1r8c4 []1r5c2/1r7c2_1r8c3/1r8c4
[]1r5c8/1r6c7
#[]1r8c4/1r2c5 []1r5c8/1r3c8_1r2c7/1r2c5 +..
#[]1r2c6/8r3c9 []7r1c2-==7r2c6-A/1r2c6 []4r1c2/4r1c7_4r3c9/8r3c9
[]8r1c2/8(r2c1r2c3)_8(r2c7r2c9)/8r3c9
#[]6r2c5/6r8c4 []6r5c8/6r1c8_6r2c9/6r2c5
[]6r5c4/6r8c4 []6r5c2/6r8c4|#
#[]Ù/1r4c8 []1r8c5/2r8c5-Ù []1r4c5/1r4c8 []1r2c5/1r4c8|#
#[]Ù/6r4c8 []6r8c5/2r8c5-Ù []6r4c5/6r4c8 []6r2c5/6r2c9_6r1c8/6r4c8
#[]2r2c5/2r8c4 []2r5c8/2r7c8_2r8c7/2r8c4-Ö []2r5c4/2r8c4-Ö []2r5c2/2r3c2_2r2c1/2r2c5
#[]2r5c8/6r8c4 []6r5c8/2r5c8 []6r5c4/6r8c4 []6r5c2/6r8c4|#
#[]1r2c5/1r4c3 []1r8c3/1r4c3 []1r8c5/1r2c5 []1r8c4/1r2c5|#
#[]d/Ù 7r4c8-D []1r4c8/Ù|# []2r4c8/2r7c8_2r8c7/2r8c5-Ù []6r4c8/Ù|#
#[]2r8c4-Ö/2r4c7 []2r8c5-Ù/2r8c4-Ö []2r4c5/2r4c7 []2r2c5/2r8c4-Ö|#
#[]2(r4c7r6c7)-D/2r2c5 2r8c7-d []2r8c5-Ù/2r2c5 []2r8c4-Ö/2r2c5|#
#[]2(r4c8r5c8)-d/6r8c4 2r7c8-D []2r5c8/6r8c4|# []2r4c8/7r4c8-D_7r8c4-d/6r8c4
#[]1r2c5/1r6c7 []1r4c5/1r2c5 []1r4c3/1r2c5|# []1r4c8/1r2c5|# []1r4c7/1r6c7
#[]d/2r4c7 []2r8c7/2r4c7 []2r8c5-Ù/d|# []2r8c4/7r8c4-d

#[]2r8c4-Ö/1r6c7[]2r8c7/2r8c4-Ö []2r6c7/1r6c7 []2r4c7/2r8c4-Ö|#
#[]þ/6r8c4 1r2c5 (þ is any counterpart of 1r2c5)
[]2r2c5/2(r4c7r6c7)-D|#_2(r4c8r5c8)-d/6r8c4|# []6r2c5/6r8c4|#
#[]6r8c4/1r6c7 []6r8c4/þ|#_1r2c5/1r6c7|#
#[]1r6c7/8r3c9 []1r2c7-i/1r6c7 []1r2c5/1r6c7|# []1r2c6/8r3c9|#
#[]1r6c7/2r4c7 []7r8c4-d/2r4c7|# []1r8c4/1r6c7|# []2r8c4-Ö/1r6c7|# []6r8c4/1r6c7|#
#[]D/1r6c7 7r8c4-d
[]1r8c4/1r6c7|# []2r8c4-Ö/1r6c7|# []6r8c4/1r6c7|#
#[]É/1r6c7 []1r4c7/1r6c7 []2r4c7/1r6c7|# []8r4c7/8(r1c7r2c7)-É
#[]1r6c7/6r4c9 []7r8c9-D/1r6c7|# []7r6c9-Â/1r6c7|*r5c7r5c9r6c7r6c9 []7r4c9/6r4c9
#[]K/1r6c7 []8(r1c7r2c7)-É/1r6c7|# []8r2c9/6r2c9-K []8r3c9/1r6c7|#
#[]k/1r6c7 6r2c9-K
[]6r6c9/1r6c7|*r5c7r5c9r6c7r6c9 []6r4c9/1r6c7|#
#[]1r6c7/1r6c7 []1r6c7/K|#_k/1r6c7|#

Nota: the sequence as such is valid. However, on can notice that the computer has tagged -Ö 2r8c4 and 2r5c2.
This is not used in the best way in the sequence.

The refreshed tagging situation

Code: Select all
1     47A8  345i8  |3567Å 389f 5678  |34j89 36k9  2     
2h38  9     37a8   |4     126  1267A |1g38  5     36K8 
345I8 2H48  6      |1235  389F 1258  |7     1G39  34J89
-------------------------------------------------------
24b68 5     14B7Ä8 |9     126  3     |1G28  1267D 678   
389   126   389    |126   7    4     |35c89 1Q26  35C89
2369  1267a 1379   |8     5    1P26  |239   4     367Ä9
-------------------------------------------------------
7     1l48  4589n  |1235  34e8 1258  |6     2o39  3459 
456m  3     1L45   |1267d 126  9     |2O45  8     457D 
4589N 46M8  2      |3567  34E8 567Å8 |3459  37d9  1     


and showing 1r2c6 is not valid

#[]L/1r2c6 1r7c2-l []1r5c2/1(r6c2r6c3)_1r6c6/1r2c6 []1r6c2/7r6c2_7r2c6/1r2c6
#[]2r5c8/1r8c4 []1r5c8/2r5c8 []1r5c4/1r8c4 []1r5c2/1r7c2_1r8c3/1r8c4
#[]2r5c8/6r8c4 []6r5c8/2r5c8 []6r5c4/6r8c4 []6r5c2/6r9c2_6r8c1/6r8c4
#[]1r8c5/6r4c8 []6r8c5/1r8c5 []6r4c5/6r4c8 []6r2c5/6r2c9_6r1c8/6r4c8
#[]1r5c2/2r2c5 []1r8c5/1r8c3_1r7c2/1r5c2 []1r4c5/1r6c6_1(r6c2r6c3)/1r5c2 []1r2c5/2r2c5
#[]D/2r5c8 7r8c4-d []1r8c4/2r5c8|# []2r8c4/2r8c7_2r5c8/2r7c8-D []6r8c4/2r5c8|#
#[]l/6r4c8 1r8c3-L []1r8c5/6r4c8|# []1r8c4/7r8c4_7r4c8/6r4c8
#[]6r5c8/2r2c5 []1r5c2/2r2c5|# []2r5c2/2r3c2_2r2c1/2r2c5 []6r5c2/6r5c8
#[]2r5c8/1r2c6 []7r4c8-D/2r5c8|# []1r4c8/1r4c7_1r2c7/1r2c6
[]2r4c8/2r5c8 []6r4c8/l|#_L/1r2c6|#
#[]6r5c8/1r2c6 []1r2c5/1r2c6 []2r2c5/6r5c8|# []6r2c5/6r2c9_6r1c8/6r5c8
#1r2c6 []1r5c8/1r4c7-G_1r2c7-g/1r2c6 []2r5c8/1r2c6|# []6r5c8/1r2c6|#

and the refresed situation

Code: Select all
1     47B8  345i8  |3567Å 389g 5678  |34j89 36k9  2     
2h38  9     37b8   |4     1a26 267B  |1A38  5     36K8 
345I8 2H48  6      |1235  389G 1258  |7     1a39  34J89
-------------------------------------------------------
24c68 5     14C7Ä8 |9     126  3     |1a28  1267E 678   
389   126   389    |126   7    4     |35d89 1Q26  35D89
2369  1267b 1379   |8     5    1P26  |239   4     367Ä9
-------------------------------------------------------
7     1l48  4589n  |1235  34f8 1258  |6     2o39  3459 
456m  3     1L45   |1267e 126  9     |2O45  8     457E 
4589N 46M8  2      |3567  34F8 567Å8 |3459  37e9  1


Proving 4r3c1 and 4r7c2 are not valid is interessing.
It is the last very difficult clearing, still far from the end.

The first step is to show they have the same tag.
We will show that 4r3c1 forces 4r7c2 and 4r7c2 forces r3c1, which is enough to have the same tag for both.

Common chains

#[]4r7c9/4r3c1 []4r3c1/4(r1c2r3c2)_4(r7c2r9c2)/4(r8c1r8c3)_4(r8c7r8c9)/4r7c9
#[]2r4c8/2r8c5 []2r8c5/2r8c7_2r7c8/2r4c8

1) 4r3c1 forces 4r7c2
#[]E/4r3c1 []4r3c9-J/4r3c1 []4r8c9/7r8c9-E []4r7c9/4r3c1|#
#[]2r8c5/1r4c8 []1r2c5==1r4c7-a/1r4c8 []1r8c5/2r8c5 []1r4c5/1r4c8
#[]2r8c5/6r4c8 []6r8c5/2r8c5 []6r4c5/6r4c8 []6r2c5/6r2c9_6r1c8/6r4c8
#[]1r8c5/4r3c1 []1r8c3/1r8c5 []5r8c3/5r1c3_5r3c1/4r3c1 []4r8c3/4r4c3-4r4c1/4r3c1
#[]2r8c5/4r3c1 []7r4c8-E/4r3c1|# []1r4c8/2r8c5|# []2r4c8/2r8c5|# []6r4c8/2r8c5|#
#[]4r9c2/4r3c1 []1r8c5/4r3c1|# []2r8c5/4r3c1|# []6r8c5/6r8c1_6r9c2/4r9c2
and Final 4r7c2 []4(r1c2r3c2)/4r3c1 []4r9c2/4r3c1|#

2) 4r7c2 forces 4r3c1


#[]4r8c1/4r1c3 []4r8c1/4r4c1_4r4c3/4r1c3
#[]5r8c1/4r1c3 []5r8c1/5r3c1_5r1c3/4r1c3
#[]6r8c4/4r1c3 []6r8c1/6r8c4 []5r8c1/4r1c3|# []4r8c1/4r1c3|#
#[]6r8c4/4r3c1 []4r3c9/4r3c1 []4r8c9/6r8c4|*r8c4r8c9 []4r7c9/4r3c1|#
#[]6r8c4/4r7c2 []4(r1c2r3c2)/4r7c2 []4r3c1/6r8c4|# []4r1c3/6r8c4|#
2r8c5 forces 'E'
#[]e/2r8c5 7r4c8-E []1r4c8/2r8c5|# []2r4c8/2r8c5|# []6r4c8/2r8c5|#
#[]6r8c5/4r1c3 []6r8c1/6r8c5 []5r8c1/4r1c3|# []4r8c1/4r1c3|#
#[]2r8c5/4r7c2 []7r8c4-e/2r8c5|# []1r8c4/1r8c3_1r7c2/4r7c2 []2r8c4/2r8c5 []6r8c4/4r7c2|#
#[]4r7c2/4r1c3 []1r8c5/1r8c3_1r7c2/4r7c2 []2r8c5/4r7c2|# []6r8c5/4r1c3|#
and final 4r3c1 []4(r1c2r3c2)/4r7c2 []4r1c3/4r7c2|#

We can now justify the clearing with 4r7c2 == 4r3c1 (same tag here XX)
We will re use from previous step
#[]e/2r8c5 2r8c5 forces 'E'
#[]E/XX
#[]6r8c4/XX
#[]2r8c5/XX
#[]2r8c5/1r4c8
#[]2r8c5/2r4c8
#[]2r8c5/6r4c8

And the sequence startng with chains

#[]1r4c5/1r5c2 []1r5c2/1(r6c2r6c3)_1r6c6/1r4c5
#[]1r8c5/1r5c2 []1r5c2/1r7c2_1r8c3/1r8c5
#[]1r8c5/XX []1r8c5/1r8c3_1r7c2/4r7c2-XX
#[]5r1c4/XX []5r1c4/5r1c3_5r3c1/4r3c1-XX
#[]5r8c1/4r1c3 []5r8c1/5r3c1_5r1c3/4r1c3
#[]4r8c1/4r1c3 []4r8c1/4r4c1_4r4c3/4r1c3
#[]2r2c5/2r5c2 []2r5c2/2r3c2_2r2c1/2r2c5
#[]6r8c5/6r5c2 []6r5c2/6r9c2_6r8c1/6r8c5
#[]6r2c5/6r4c8 []6r2c5/6r2c9_6r1c8/6r4c8
#[]4r7c9/XX []4r3c1-XXX/4(r1c2r3c2)_4(r7c2r9c2)/4(r8c1r8c3)_4(r8c7r8c9)/4r7c9
#[]6r6c1/6r1c4 []6r6c6/6r6c1 []6r2c6/6r1c4 []6r9c6/6r9c2_6r8c1/6r6c1 []6r1c6/6r1c4


#[]A/1r5c2 1r2c5-a []1r8c5/1r5c2|# []1r4c5/1r5c2|#
#[]7r1c4/XX []4r3c9/4r3c1-XX []4r8c9/7r8c9_7r8c4/7r1c4 []4r7c9/XX|#
== []5r8c1/4r1c3|# []4r8c1/4r1c3|#
#[]6r8c5/4r1c3 []6r8c1/6r8c5
#[]6r8c4/4r1c3 []6r8c1/6r8c4

#[]1r5c2/2r2c5 []1r2c5/2r2c5 []1r8c5/1r5c2|# []1r4c5/1r5c2|#
#[]6r5c2/6r4c8 []6r8c5/6r5c2|# []6r4c5/6r4c8 []6r2c5/6r4c8|#


#[]6r8c4/XX []4(r1c2r3c2)/4r7c2-XX []4r3c1-XX/6r8c4|# []4r1c3/6r8c4|#
#[]6r8c5/2r2c5 []1r5c2/2r2c5|# []2r5c2/2r2c5|# []6r5c2/6r8c5|#
#[]6r8c5/3r3c8 []1r2c5==1r3c8-a/3r3c8 []2r2c5/6r8c5|# []6r2c5/6r8c5

#[]6r2c5/6r4c8 []6r2c5/6r2c9_6r1c8/6r4c8
#[]m/6r4c8 []6r8c5/6r8c1-m []6r4c5/6r4c8 []6r2c5/6r4c8|#
#[]2r5c2/2r4c8 []2r8c5/2r4c8|# []2r4c5/2r4c8 []2r2c5/2r5c2|#
#[]a/2r4c8 []2r8c5/2r4c8|# []2r4c5/2r4c8 []2r2c5/1r2c5-a
#[]6r5c2/6r1c4 []6r1c8/6r1c4 []6r5c8/6r5c2 []6r4c8/6r5c2|#
#[]6r4c8/6r1c4 []6r8c1/6r4c8|# []6r4c1/6r4c8 []6r6c1/6r1c4|#
#[]ø/2r4c8 6r5c2 []1r5c2/A|#_a/2r4c8|# []2r5c2/2r4c8|# (ø complementary to 6r5c2)
#[]l/XX 1r8c3-L []5r8c3/5r1c3_5r3c1/4r3c1-XX []4r8c3/4r4c3_4r4c1/4r3c1-XX
#[]L/1r4c8 []1r2c5==1r4c7-a/1r4c8 []1r8c5/1r8c3-L []1r4c5/1r4c8
#[]6r1c4/XX []7r4c8-E/4r3c1-XX|# []1r4c8/L|#_l/4r3c1-XX|# []2r4c8/ø|#_6r5c2/6r1c4|# []6r4c8/6r1c4|#
#[]3r1c8/XX []7r1c4/4r3c1-XX|# []3r1c4/3r1c8 []5r1c4/4r3c1-XX|# []6r1c4/4r3c1-XX|#

#[]8r7c5/XX []7r1c4/XX|# []3r1c4/3(r7c4r9c4)_8(r1c5r3c5)/8r7c5 []5r1c4/4r3c1-XX|# []6r1c4/4r3c1-XX|#
#[]XX/4r1c3-§Q []1r8c5/XX|# []2r8c5/XX|# []6r8c5/4r1c3|#
#[]T/XX []4r7c5/4r7c2-XX []3r7c5/3(r7c8r7c9)-T []8r7c5/XX|#
#[]XX/3r3c8 []1r8c5/XX|# []2r8c5/XX|# []6r8c5/3r3c8|#
#[]3r9c8/XX []4r3c9/4r3c1-XX []4r8c9/3r9c8|*r8c9r9c8 []4r7c9/XX|#
#[]t/XX []3r9c8/XX|# []3r7c8/3(r7c4r7c5)-t []3r3c8/XX|# []3r1c8/XX|#
T/XX t/XX XX is dead clear 4r3c1 4r7c2


For the following steps, as the program will likely change the sequence taking benefit of the virus pattern structures, I'll give the clearing sequence.
If anybody wants more details, i'll give them.
Next steps (short sequences unless specified

- clear ch=2r2c5
- clear ch=6r2c6
- clear ch=6r6c9
- clear ch=2r6c6
- clear ch=8r7c3
- clear ch=8r1c2
- .clear ch=7r1c6
.clear ch=2r7c4
two medium size sequences
- clear ch=6r4c5 clear ch=6r8c4 medium size sequence
-. clear ch=8r1c7 clear ch=8r2c1
. clear ch=4r9c7
-.clear ch=3r6c3
.clear ch=3r2c7
- clear ch=3r3c1
-.clear ch=2r4c1
.clear ch=8r5c9 clear ch=7r4c9
.clear ch=8r3c6s
-.clear ch=8r9c5
.clear ch=1r5c2 clear ch=6r1c6 clear ch=6r4c8 clear ch=6r6c1
.clear ch=8r4c3
.clear ch=3r9c4
-.clear ch=9r6c3
.clear ch=5r8c1

we are there
Code: Select all
1       4B7b    3S4Z5K8Ã |356a7B 389o  5p8P    |34c9   36A9   2     
2b3B    9       37B8Ä    |4      1a6A  2B7b    |1A8a   5      3S6a8 
5k8K    2B4c8Æ  6        |12j35  38Ã9O 125     |7      1a39   34C8Ä9
--------------------------------------------------------------------
4e6a8Å  5       1i4E7f   |9      1D2d  3       |1a2D8  1f7F   6A8a   
389     2q6Q    3B8ç9m   |1g2D6i 7     4       |35h8Å9 1G2j6a 35H9   
2B3U9è  1l26i7B 1r7R     |8      5     1i6I    |2q39   4      37f9   
--------------------------------------------------------------------
7       1L8l    459M     |13V5   34n8P 12j58   |6      2J39   34y59 
4a6A    3       1l45À    |127f   12D6a 9       |2j4C5  8      457F   
45K8Æ9m 4Z6a8   2        |567    3n4N  56i7B8l |359    37f9   1     


Three steps are missing, in the next n, the tagging sequence clears 5r9c4 (saturation)
In the next one, similarly 5r3c6 and 1r7c4 are cleared
in addition, 3r7c8is cleared thru a chain

The last step is here

Code: Select all
1       4B7b    3U4à5D8Ã |356a7B 389o  5p8P     |34c9   36A9   2     
2b3B    9       37B8Ä    |4      1a6A  2B7b     |1A8a   5      3U6a8 
5d8D    2B4c8Æ  6        |12l35D 38Ã9O 1q2Q     |7      1a39   34C8Ä9
---------------------------------------------------------------------
4f6a8Å  5       1j4F7g   |9      1E2e  3        |1a2E8  1g7G   6A8a   
389     2r6R    3B8ç9m   |1h2E6j 7     4        |35i8Å9 1H2l6a 35I9   
2B3W9è  1K26j7B 1s7S     |8      5     1j6J     |2r39   4      37g9   
---------------------------------------------------------------------
7       1k8K    459M     |3P5p   34n8P 1K2l58   |6      2L9l   3n4z59
4a6A    3       1K45Á    |127g   12E6a 9        |2l4C5  8      457G   
45D8Æ9m 4à6a8   2        |6t7T   3n4N  5â6j7B8K |359    3X7g9  1



several possibilities,

'B' 'g' 'D' 'a' are cleared, the puzzle is cracked

Edit one 2007 10 31 clearing 1r6c7 1r2c6
Edit 2 2007 11 01 clearing 4r3c1 4r7c2 and after
Last edited by champagne on Thu Nov 01, 2007 1:01 pm, edited 5 times in total.
champagne
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Posts: 5675
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Location: France Brittany

Postby champagne » Sat Oct 27, 2007 2:58 pm

I mark a pause in the printing of my solution to Easter Monster to make a comparison with another solution.

Thanks to him Glyn brought me on that post from Ronk at the start of Easter Monster.

Code: Select all
  1      A478     34578   | 3567    3689    5678    | 3489   I369    2
 L238     9      L378     | 4      K12368  K12678   |J138     5      J368
 23458  A248     6       | 1235    12389   1258    | 7      I139     3489
--------------------------+-------------------------+----------------------- 
 2468    5       1478    | 9       1246    3       | 128    H1267    678 
 234689 B12468   13489   | 126     7       1246    | 123589 H12369   35689 
 2369   B1267    1379    | 8       5       126     | 1239    4       3679
--------------------------+-------------------------+----------------------- 
 7      C148     14589   | 1235    12348   12458   | 6      G239     3459
 D456    3      D145     |E12567  E1246    9       |F245     8      F457 
 45689  C468    2        | 3567    3468    45678   | 3459   G379     1
(27)r13c2=(27-16)r56c2=(16)r79c2-(16)r8c13=(16-27)r8c45=(27)r8c79-(27)r79c8
 =(27- 16)r45c8=(16)r13c8-(16)r2c79=(16-27)r2c56=(27)r2c13 - loop

Note that nodes marked A, C, D, F, G, I, J and L are all AALSs..


I don’t know if Ronk has a short explanation to tell why that loop is operative, but for sure if you start with the assumption that one of 2r3c2_7r1c2 is valid, we have that kind of loop


The first step in my solution was precisely to show that 2r3c2_7r1c2 is a strong link.

The solver does not recognize the loop as such. In place, it clears individually

8r2c6 3r2c5 8r2c5 3r5c8 9r5c8 1r7c3 6r9c1
4r8c5 5r8c4 4r5c2 8r5c2

Just following what I have already shown. (will be the first edit of the post)

Ronk made a fantastic job discovering that loop.

Clearly, it’s following another logic that what I made in step four.

The stuff is more or less the same, Ronk is working on couples in OR condition (may be exclusive OR) while I am working on couples in And condition.

There is likely some room for improvement using Ronk way in addition of what I made.

This meet another topic I wanted to raise after having published the first step of the solution.

In AC2 (here ||*r1c2r3c2 ), if you have identified a strong link 2r3c2_7r1c2, then the rest is also a strong link (4(r1c2r3c2)_8(r1c2r3c2).

This has also to be included in the processing. We see that here it’s part of the powerful analysis made by Ronk.
champagne
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Location: France Brittany

Postby ronk » Sat Oct 27, 2007 4:23 pm

champagne wrote:... it’s part of the powerful analysis made by Ronk.

The credit for that deduction goes to Stephen Kurzhals. See his hidden pair loop topic on the Eureka! forum. [20120331 edit: repaired link]

a long ago champagne wrote:I understood than RONK have the possibility to start at any point of a puzzle in a specific solver.

Sorry, I'm sure some posters here have solvers with that capability, but I'm not one of them. Been wishing though.:)
Last edited by ronk on Sat Oct 27, 2007 2:03 pm, edited 1 time in total.
ronk
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Posts: 4764
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Location: Southeastern USA

Postby champagne » Sat Oct 27, 2007 4:57 pm

Ronk wrote
champagne wrote:
... it’s part of the powerful analysis made by Ronk.

The credit for that deduction goes to Stephen Kurzhals. See his hidden pair loop topic on the Eureka! forum.


Glyn pushed me on the right place. Your post in that thread was much closer to my presentation and in a quick reading I neglected the rest of the thread.

EDIT one
Just a remark regarding "Kurzhals loop".

You can find it at the start of these three puzzles at the top list of jpf.

11.4 # 500000009020100070008000300040600000000050000000207010003000800060004020900000005 # m_b_metcalf
11.4 # 500000009020100070008000300040002000000050000000706010003000800060004020900000005 # StrmCkr
11.4 # 100000002090400050006000700050903000000070000000850040700000600030009080002000001 # JPF 04/07/01 (Easter Monster)


You have it as well in the three puzzles shown at the top of this thread.

It is not in dml55 I used to introduce step four, but it's not so far.

Code: Select all
1     56u7   3B568 |9       34A7   2f3O78 |24568  4e678 25678
789   2      6S89  |14a78   5      178    |4A689â 3     1L67 
3b578 579â   4     |12F78   13B7   6      |2589   1m79å 12578
-------------------------------------------------------------
6     4D59   2h8H  |2457    4a79   23c579 |1      7Z89  3C578
4d59  3      1g59  |14D56t7 8      1579   |569    2     567w 
2H8h  1G59   7     |1256    13O6V9 12359  |3c5689 689   4     
-------------------------------------------------------------
259   14e569 12569 |3       169ä   15i8À9 |7      14E68 12j68
34D79 1467y9 1369  |1678á   2      1789à |34e68  5     13c68
2357X 8      12356 |15I67   167    4      |2J3n6  1k6K  9 



No surprise, some of these extreme puzzle have a common basis.
champagne
2017 Supporter
 
Posts: 5675
Joined: 02 August 2007
Location: France Brittany

Postby champagne » Tue Nov 06, 2007 7:19 pm

Example of a level 2 puzzle.

Easter Monster is not the best way to show full tagging capabilities.
I have choosen a puzzle not exceeding level 2 as first example.
A second will follow requesting a short step in level3
This puzzle has been published on Gould forum in 2005.


Code: Select all
600040003010000070005000800000502000300090002000103000008000900070000050200030004


Code: Select all
6     289   279   |2789  4     15a789 |125   129    3     
489   1     2349  |23689 2568  689    |246   7      569   
479   2349  5     |23679 1267  1679   |8     12469  169   
-----------------------------------------------------------
14789 4689  14679 |5     678   2      |13467 134689 16789 
3     568   167   |4678  9     4678   |1567  168    2     
45789 24689 24679 |1     678   3      |467   4689   56789
----------------------------------------------------------
145   346   8     |2467  12567 1467   |9     23     167   
149   7     13469 |24689 1268  14689  |23    5      168   
2     569   169   |6789  3     156789 |167   168    4   


Here basic taging doesn't help. The only "group tag" used is the Empty Rectangle pattern in box 9 6(r9c78)/6(r78c9)

As shown in another thread, the solver starts with that Nice Loop

Code: Select all
[]6(r9c78)/6(r9c23)_6(r7c2r8c3)/4(r7c2r8c3)|*r7c2r8c3_4(r78c1)/4(r23c1)_4(r2c3r3c2)/2(r2c3r3c2)|*r2c3r3c2
 _2(r1c23)/2(r1c78)_2(r2c7r3c8)/6(r2c7r3c8)|*r2c7r3c8_6(r23c9)/6(r78c9)


As you can see, weak links requesting level 2 are generated in AHS |*r7c2r8c3 |*r2c3r3c2 and |*r2c7r3c8.
Strong links ALS_AHS are also generated in level 2.

Code: Select all
6     28f9   27e9   |789    4      1j5a789 |125A   129Æ    3     
48F9  1      23b4   |23B689 25A68  689     |24g6   7       5a69
47E9  23B4   5      |23b679 1m267  1679    |8      24G6    1j69
----------------------------------------------------------------
1l789 4689   14679  |5      678    2       |13B467 13b4689 1789 
3     5A68   1K67   |4c678  9      4C678   |15a67  168     2     
5a789 2d4689 2D4679 |1      678    3       |467    4689    5A789
----------------------------------------------------------------
145A  3b46   8      |2467   125a67 1467    |9      2b3B    167h 
149Ä  7      3B46   |24689  1268   14689   |2B3b   5       168i 
2     5a69   1l69   |789    3      15A789  |167H   168I    4


Four similar ternary chains (symetry).

Code: Select all
#2r3c8
 []3r2c3==2r7c8-b/2r3c8
 []4r2c3/4r2c7-g_4r3c8-G/2r3c8
 []2r2c3/2(r1c23)-o_2(r1c78)-O/2r3c8


Code: Select all
#4r2c3
 []4r2c7-g/4r2c3
 []2r2c7/2r8c7-B_3r2c3-b/4r2c3
 []6r2c7/6(r23c9)-o_4(r23c1)-O/4r2c3


Code: Select all
#2r2c7
 []3r3c2==2r8c7-B/2r2c7
 []4r3c2/4r3c8-G_4r2c7-g/2r2c7
 []2r3c2/2(r1c23)-o_2(r1c78)-O/2r2c7


Code: Select all
#4r3c2
 []4r3c8-G/4r3c2
 []2r3c8/2r7c8-b_3r3c2-B/4r3c2
 []6r3c8/6(r23c9)-o_4(r23c1)-O/4r3c2


Now in level 1

Code: Select all
6     89    79    |789   4      1B5b   |125B  12     3   
489   1     23    |23689 25B68  689    |46    7      5b9B
479   23    5     |23679 1267   1679   |8     46     1B9b
---------------------------------------------------------
1n789 4689  14679 |5     678    2      |13467 134689 178 
3     5B68  167   |4678  9      4678   |15b67 168    2   
5b789 24689 24679 |1     678    3      |467   4689   5B78
---------------------------------------------------------
1b5B  34    8     |2467  125b67 1467   |9     23     167 
19    7     34    |24689 1268   14689  |23    5      168 
2     5b69  1n69  |789   3      15B789 |17    18     4 


[]np PB bn []1r9c3-n/1(r9c7r9c8)_1(r7c9r8c9)/1r3c9-B_1r7c1-b/1r9c3-n

nota []np PB bn
is our prefered way to show that clearing of 1r9c3 1r4c1
P,p layer is not visible and needs additionnal comment in preferred mode

Code: Select all
6    89     79     |789    4     15    |12a5   1a2A     3   
489  1      2A3a   |23A689 2568  689   |46     7        59 
479  2a3A   5      |23a679 1267  1679  |8      46       19 
-----------------------------------------------------------
789  4689   14679  |5      678   2     |13A467 13a4689i 178
3    568    167    |4678   9     4678  |1567   168      2   
5789 2A4689 2a4679 |1      678   3     |467    4689I    578
-----------------------------------------------------------
15   3a4A   8      |2467   12567 1467  |9      2a3A     167
19   7      3A4a   |24689  1268  14689 |2A3a   5        168
2    569    69     |789    3     15789 |17     18       4   


Here we have (level 1)

Clearing inside the Bb layer thru
=1r7c1 =1r1c6
=1r7c1 =1r3c9
=9r8c1 =9r2c9

Clearing out of the weak link []ai => OR {AI}
=2r6c2 =9r6c8

locked set 15 r7c15

Refreshing tagging leads to 2r7c4-A
2r3c4 is cleared

And we restart a level 2


Code: Select all
6      8d9D  7c9C   |7C8D9S  4       1B5b    |12a5B  1a2A     3     
4d8D   1     2A3a   |2m3A689 25B68   689     |4D6d   7        5b9B   
4D7C9S 2a3A  5      |3a679   1l2A67p 1679    |8      4d6D     1B9b   
--------------------------------------------------------------------
789    4689  1g4679 |5       678     2       |13A467 13a4689h 178   
3      5B68  1G67   |4e678   9       4E678   |15b67  168      2     
5b789  2A468 2a4679 |1       678     3       |467    4689H    5B78   
--------------------------------------------------------------------
1b5B   3a4A  8      |2A467   1B5b    467     |9      2a3A     6i7I   
1B9b   7     3A4a   |24689   12m68   14689   |2A3a   5        1k6I8j
2      5b6f9 6F9f   |789     3       1k5B789 |1I7i   1j8J     4   


From now on we have to take care of additionnal tagging

-1r7c5-B 1r9c6-k 1(r8c56)
-1r1c6-B 1r9c6-k 1(r38c6)
-1r3c9-B 1r8c9-k 1r4c9 1r4c9==1(r38c6)==1(r8c56) (same tag)


-1r7c5-B 1r3c5-l 1r8c5
-1r1c6-B 1r3c5-l 1r3c6 1r3c6==1r8c5

and six candidates are cleared

Code: Select all
#6r3c5
 []5r5c2-5r1c7-B/2r1c7-a_2r3c5-A/6r3c5
 []8r5c2/8r1c2-d_6r3c8-D/6r3c5
 []6r5c2/6(r5c46)-o_6(r46c5)-O/6r3c5

#8r6c2
 []6r5c8/6r3c8-D_8r1c2-d/8r6c2
 []1r5c8/1r1c8-a_2r6c2-A/8r6c2
 []8r5c8/8r9c8-J_1r9c8-j/1r1c8-a_2r6c2-A/8r6c2

#6r4c7
 []6r5c8/6r4c7
 []1r5c8/1r1c8-a_3r4c7-A/6r4c7
 []8r5c8/8r9c8-J_1r9c8-j/1r1c8-a_3r4c7-A/6r4c7

#6r2c4
 []6r5c8/6r3c8-D_6r2c7-d/6r2c4
 []1r5c8/1r1c8-a_3r2c4-A/6r2c4
 []8r5c8/8r9c8-J_1r9c8-j/1r1c8-a_3r2c4-A/6r2c4

#6r5c7   
 []7(r5c46)==7r3c5-p/2r3c5-A_2r1c7-a/5r1c7-B_5r5c7-b/6r5c7
 []7r5c7/6r5c7
 []7r5c3/7r1c3-c_7r1c4-C/8r1c4-D_6r2c7-d/6r5c7

#1r8c6   
 []7(r5c46)==7r3c5-p/1r3c5-l_1(r78c5)-L/1r8c6
 []7r5c7/5r5c7-b_1r7c5-B/1r8c6
 []7r5c3/1r5c3-G_1r4c3-g/1r4c9==1(r38c6)_1(r19c6)/1r8c6



Code: Select all
6      8d9D  7c9C   |7C8D9R 4      1B5b    |12a5B 1a2A     3     
4d8D   1     2A3a   |2l3A89 25B68  689     |4D6d  7        5b9B   
4D7C9R 2a3A  5      |3a679  1k2A7o 1679    |8     4d6D     1B9b   
-----------------------------------------------------------------
789    4689  1g4679 |5      678    2       |13A47 13a4689h 178   
3      5B68  1G67   |4e678  9      4E678   |15b7  168      2     
5b789  2A46  2a4679 |1      678    3       |46D7  4689H    5B78   
-----------------------------------------------------------------
1b5B   3a4A  8      |2A467  1B5b   467     |9     2a3A     6i7I   
1B9b   7     3A4a   |24689  12l68  4689    |2A3a  5        1k6I8j
2      5b6f9 6F9f   |789    3      1k5B789 |1I7i  1j8J     4 


still
1r4c9==1(r3c6)==1(r8c5)
and now
-2r3c5-A 2r2c4-l 2r2c5
-2r7c4-A 2r2c4-l 2r8c4 2r8c4==2r2c5

from AHS/ALS r367c2 we have 4r4c2==6r6c2
both are cleared thru
Code: Select all
 []5r5c2==5r1c7-B/2r1c7-a_2r6c2-A/6r6c2
 []6r5c2/6r6c2
 []8r5c2/8r1c2-d_6r6c7-D/6r6c2



Code: Select all
6      8d9D  7c9C    |7C8D9R 4      1B5b    |12a5B 1a2A     3     
4d8D   1     2A3a    |2l3A89 25B68  689     |4D6d  7        5b9B   
4D7C9R 2a3A  5       |3a679  1k2A7o 1679    |8     4d6D     1B9b   
------------------------------------------------------------------
789    689   1g4m679 |5      678    2       |13A47 13a4689h 178   
3      5B68  1G67    |4e678  9      4E678   |15b7  168      2     
5b789  2A4a  2a4679  |1      678    3       |46D7  4689H    5B78   
------------------------------------------------------------------
1b5B   3a4A  8       |2A467  1B5b   467     |9     2a3A     6i7I   
1B9b   7     3A4a    |24689  12l68  4689    |2A3a  5        1k6I8j
2      5b6f9 6F9f    |789    3      1k5B789 |1I7i  1j8J     4   

still
1r4c9==1(r3c6)==1(r8c5)
2r8c4==2r2c5

Code: Select all
#k
 []4r4c3/4r6c2-a_2r3c5-A/1r3c5-k
 []4r4c7==7r6c7-ä/7r9c7-i_6r8c9-I/1r8c9-k
 []4r4c8/3r4c8-a_2r3c5-A/1r3c5-k


#7r7c4
 []4r4c3/4r6c2-a_2r7c4-A/7r7c4
 []4r4c7==7r6c7-ä/7r9c7-i_7r7c9-I/7r7c4
 []4r4c8/3r4c8-a_2r7c4-A/7r7c4


#1r4c7
 []4r4c3/4r6c2-a_3r4c7-A/1r4c7
 []4r4c7-ä/1r4c7
 []4r4c8/3r4c8-a_3r4c7-A/1r4c7


#7r4c7
 []4r4c3/4r6c2-a_3r4c7-A/7r4c7
 []4r4c7-ä/7r4c7
 []4r4c8/3r4c8-a_3r4c7-A/7r4c7



Code: Select all
6     89   79     |789    4      1B5b  |12a5B 1a2A    3   
48    1    2A3a   |2j3A89 25B68  689   |46    7       5b9B
479   2a3A 5      |3a679  2A7a   1b679 |8     46      1B9b
----------------------------------------------------------
789   689  14679  |5      678    2     |3A4a  13a4689 1b78
3     5B68 167    |4678   9      4678  |15b7  168     2   
5b789 2A4a 2a4679 |1      678    3     |467   4689    5B78
----------------------------------------------------------
1b5B  3a4A 8      |2A46   1B5b   467   |9     2a3A    67   
1B9b  7    3A4a   |24689  1b2j68 4689  |2A3a  5       68   
2     5b69 69     |789    3      5B789 |17    18      4



[]jb Ba Aj []2r8c5-j/1r8c5-b_5r1c7-B/2r1c7-a_3r2c4-A/2r2c4-j

Code: Select all
6      8d9D  7c9C    |7C8D9N 4      1B5b  |12a5B 1a2A     3   
4d8D   1     2A3a    |3A89   2a5B68 689   |4D6d  7        5b9B
4D7C9N 2a3A  5       |3a679  2A7a   1b679 |8     4d6D     1B9b
--------------------------------------------------------------
789    689   1h4j679 |5      678    2     |3A4a  13a4689i 1b78
3      5B68  1H67    |4e678  9      4E678 |15b7  168      2   
5b789  2A4a  2a4679  |1      678    3     |46D7  4689I    5B78
--------------------------------------------------------------
1b5B   3a4A  8       |2A46   1B5b   467f  |9     2a3A     6f7F
1B9b   7     3A4a    |2a4689 1b68   4689  |2A3a  5        6F8f
2      5b6g9 6G9g    |7l89   3      5B789 |1F7f  1f8F     4   

still
1r4c9==1(r3c6)==1(r8c5)
2r8c4==2r2c5

and now
-5r5c7-b 1r5c7 7r5c7
-1r4c9-b 1r5c7 1(r45c8) 7r5c7==1(r45c8)
followed by
-1r1c8-a 1(r45c8) 1r9c8-f
-7(r5c46)-a 7r5c7 7r5c3 7r5c3 is 'f'

-4r6c2-a 4r4c3-j 4r6c3
-4r4c7-a 4r4c3-j 4r4c8 4r4c8==4r6c3

a sub chain common to the three chains

[]fH hb []7r5c3-f/1r5c3-H_1r4c3-h/1r4c9-b


Code: Select all
[]1r1c7/1r9c7-F_fb_5r1c7-B/1r1c7
[]8r9c6/8r9c8-F_fb_5r9c6-B/8r9c6
[]7r6c9/7r7c9-F_fb_5r6c9-B/7r6c9



Code: Select all
6      8c9C  7b9B    |7B8C9M 4      1a5A  |2A5a  1A2a     3     
4c8C   1     2a3A    |3a89   2A5a68 689   |4C6c  7        5A9a 
4C7B9M 2A3a  5       |3A679  2a7A   1A679 |8     4c6C     1a9A 
---------------------------------------------------------------
789    689   1g4i679 |5      678    2     |3a4A  13A4689h 1A7e8
3      5a68  1G67    |4d678  9      4D678 |1e5A7 168      2     
5A789  2a4A  2A4679  |1      678    3     |46C7  4689H    5a8A 
---------------------------------------------------------------
1A5a   3A4a  8       |2a46   1a5A   467e  |9     2A3a     6e7E 
1a9A   7     3a4A    |2A4689 1A68   4689  |2a3A  5        6E8e 
2      5A6f9 6F9f    |7k8e9  3      5a79  |1E7e  1e8E     4



5r2c5-a 2r2c5-A clearing 68(r2c5)

[]AC 4r4c7-A/4r2c7-C =5r5c2 =8r1c2 clearing 8r5c2

ending with two Nice loops

Code: Select all
6     89   79     |789    4     1a5A  |2A5a  1A2a    3     
48    1    2a3A   |3a89   2A5a  689   |46    7       5A9a 
479   2A3a 5      |3A679  2a7A  1A679 |8     46      1a9A 
----------------------------------------------------------
789   689  14679  |5      678   2     |3a4A  13A4689 1A7e8
3     5a6A 167    |4678   9     4678  |1e5A7 168e    2     
5A789 2a4A 2A4679 |1      678   3     |467   4689    5a8A 
----------------------------------------------------------
1A5a  3A4a 8      |2a46   1a5A  467e  |9     2A3a    6e7E 
1a9A  7    3a4A   |2A4689 1A68E 4689  |2a3A  5       6E8e 
2     5A69 69     |78e9   3     5a79  |1E7e  1e8E    4   




[]em ME []8r9c4-e/8r8c5-m_8r5c8-M/8r9c8-E

[]AE eA []1r8c5-A/8r8c5-E_1r9c8-e/1r1c8-A



1 r1c6=1 B
Nothing special to the end
champagne
2017 Supporter
 
Posts: 5675
Joined: 02 August 2007
Location: France Brittany

Postby champagne » Tue Nov 06, 2007 10:00 pm

example of level 3 puzzle in full tagging method


This puzzle N°52 in the top 1465 list is a good example for level 3
One advantage to choose a top1465 puzzle is that they are well known by most SUDOKU players, giving a better chance to compare with other methods.


It has been solved in 5.3 seconds by my PC.
NOTA: Again, time is given more to show than this excludes any recursive search of chains.


....3..715..4.2............2..6..4...38.7..............7..8..1.6..5..2..........._52

Start with level 2

Code: Select all
489     2a4689  2A469   |8l9L    3      5b689   |5B689  7       1     
5       1c68Å9  7       |4       1C69   2       |3689   3689    3689   
1C3e89  689     3E69    |7       5z69   1c568é9 |5b689  2d4D    2D4d   
----------------------------------------------------------------------
2       159     1k59    |6       1O5W9ë 3f8F    |4      3F8f    7     
1O4g9   3       8       |12r9    7      14G5x9  |1n69   2569    2569   
7       456h9   456H9   |123t8L9 2m4v59 134589  |1N38è9 23589   23589 
----------------------------------------------------------------------
349     7       2i345j9 |2I39    8      346Á9   |369    1       345J69
6       148Æ9   1K3s49  |5       1P49   7       |2      3489    3489   
1P348ç9 2A45Y89 23459   |1Q239   2M46â9 13469   |7      345à689 345689



Code: Select all
#4r9c6
 []4r7c3/2r7c3-i_2r7c4-I/2r9c5-M_2r6c5-m/4r6c5-v_4(r89c5)-V/4r9c6
 []4r7c1/4r5c1-g_4r5c6-G/4r9c6
 []4r7c9/5r7c9-J_5r7c3
-j/2r7c3-i... as above
[]4r7c6/4r9c6

then we are forced to level 3 Here with only one loop, which means that all clearings done here are indirects.

We start with the clearing of 'O' =1r4c5 =1r5c1
£w is the tag for 3r2c7, £W is the tag for complementary sets 3(r2c89); 3(r79c7)
This is the logic applied by the solver

Code: Select all
#[]O/£W     derived weak link
 3r2c7
 []3r6c7/1r6c7-N_1r5c7-n/1r5c1-O
 []3r7c7/3(r8c89)-S_3r8c3/1r8c3-K_1r4c3-k/1r4c5-O


Code: Select all
#[]O/3r2c7 derived weak link
 []8r2c2/1r2c2-c_1r2c5-C/1r4c5-O
 []8r6c7/1r6c7-N_1r5c7-n/1r5c1-O
 []8r2c7/3r2c7


#[]O/O []O/£W|#_3r2c7/O|# Nice loop applied to derived weak links.

We could say as well : 'O'
- forces 3r2C7
- 'O' and 3r2c7 can not be both in the solution
- so 'O' is out.

We have here the two tools for level 3 (in fact it is nearly the same) :

In a very similar way, are cleared at the same moment

Code: Select all
clear 3r8c3
#[]P/3r8c3
 []8(r1c12)/8(r1c46)-É_8r3c6/1r3c6-c_1r2c5-C/1r8c5-P
 []8(r2c2r3c1)/3r3c1-e|*r2c2r3c1_3r3c3-E/3r8c3
 []8r3c2/8(r13c1)-Ç_8r9c1-ç/1r9c1-P
#[]p/3r8c3   
 1r8c5-P
 []1r2c5==1r3c1-C/3r3c1-e_3r3c3-E/3r8c3
 []1r4c5-O/1r4c3-k_1r8c3-K/3r8c3


here 8(r2c2r3c1)/3r3c1-e|*r2c2r3c1 is a weak link directly generated by the "Almost cell" r2c2r3c1


Code: Select all
clear 'v' =4r7c6  =4r6c5
#[]v/6(r2c89)
 []6(r1c23)/4(r1c23)|*r1c23 _4r1c1/4r5c1-g_4r5c6-G/4r7c6-v
 []6r1c6/6(r23c5)-Â_6r9c5-â/2r9c5-M_2r6c5-m/4r6c5-v
 []6r1c7/6(r2c89)
#[]v/6(r123c7)
 []6r7c6-Á/4r7c6-v
 []6r7c9/2r7c3-i|*r7c39_2r7c4-I/2r9c5-M_2r6c5-m/4r6c5-v
 []6r7c7/6(r123c7)


small difference here, 'v' is in weak link with candidates strongly linked.
two weak links out of "almost cells"

Code: Select all
clear ch=8r1c7
#[]I/8r1c7
 []5r4c5==5(r6c23)-W/4(r6c23)-G|*r6c23_4r5c1-g/4r1c1_4(r1c23)-ï/8(r1c267)|*r1c2367_8(r1c14)/8r1c7
 []5r3c5-z/5r1c6-b_5r1c7-B/8r1c7
 []5r6c5/2r6c5-m_2r9c5-M/2r7c4-I
#[]i/8r1c7
 []4r7c6-v/4r5c6-G_... as above
 []4(r7c3r7c9)/2r7c3-i|*r7c3r7c9
 []4r7c1/4r1c1_... as above


Code: Select all
clear ch=9r1c7
#[]I/9r1c7   
 []5r4c5==5(r6c23)-W/4(r6c23)-G|*r6c3_4r5c1-g/4r1c1_4(r1c23)-ï/9(r1c2367)|*r1c2367_9(r1c14)/9r1c7
 []5r3c5/5r1c6-b_5r1c7-B/9r1c7
 []5r6c5/2r6c5-m_2r9c5-M/2r7c4-I
#[]i/9r1c7
 []4r7c6-v/4r5c6-G_4r5c1-g/4r1c1_.. asz above
 []4(r7c39)/2r7c3-i|*r7c3r7c9
 []4r7c1/4r1c1_.. as above


In that example, all cases have generated weak links ending (in the process) with a two terms chain..
What is typical to level 3 is generation of weak links.
The end can be a longer chain, but as well a choice in weak link with the target.[/color]

Following steps are mostly in level 2.

Code: Select all
489     2a4689  2A469   |8m9M    3       5b689   |5B6b    7      1     
5       1c68Æ9  7       |4       1C69    2       |3q689   3689   3689   
1C3e89  689     3E69    |7       5z69    1c568Å9 |5b68Æ9ì 2d4D   2D4d   
-----------------------------------------------------------------------
2       1f59    1F59    |6       5W9w    3g8G    |4       3G8g   7     
4h9H    3       8       |12s9    7       14H5x9  |1p69    2569   2569   
7       456i9   456I9   |123u8M9 2n59    134h589 |1P3Q8é9 23589  23589 
-----------------------------------------------------------------------
349     7       2j345k9 |2J39    8       36Á9    |6Î9     1      4V5K69
6       148Ç9   1f49    |5       1c4o9   7       |2       3l489  3L489 
1c348è9 2A45Y89 23459   |1R239   2N4O6â9 1369    |7       45à689 45689



Code: Select all
[]3r3c1-e/3r7c1_3(r39c1)-ÿ/8(r39c1)-ý|*r39c1_8r1c1/8(r1c46)-å_8r3c6-Å/1r3c6-c_1r3c1-C/3r3c1-e

[]3r7c6/3r7c1_3(r39c1)-ÿ/8(r39c1)-ý|*r39c1_8r1c1/8r1c4-m_8r6c4-M/8r4c6-G_3r4c6-g/3r7c6

[]9(r379c1)/8(r39c1)-ý|*r379c1_8r1c1/8r2c2-Æ_8(r26c7)-æ/1r6c7-P|*r26c7_1(r6c46)-p/4r6c6-h|*r4c646_9r5c1-H/9(r379c1)

[]2r6c4/8r6c4-M_8r1c4-m/8r1c1_8(r39c1)-ý/3(r39c1)-ÿ|*r39c1 _3r7c1/3(r7c46)-T_3(r7c13)-t/2r7c3-j|*r7c139_2r7c4-J/2r6c4

[]9r2c5/9r4c5-w_9(r4c23)-W/9r5c1-H_4r6c6-h/1(r6c46)-p|*r4c6r6c46_1r6c7-P/8(r26c7)-æ|*r26c7_8r2c2-Æ/1r2c2-c_1r2c5-C/9r2c5

[]9(r6c46)/9r4c5-w_9(r4c23)-W/9r5c1-H_4r6c6-h/9(r6c46)|*r4c6r6c46

[]9r6c5/9r4c5-w_9(r4c23)-W/9r5c1-H_4r5c1-h/4r7c1_4(r7c39)-£O/2r7c3-j|*r7c39 _2r7c4-J/2r9c5-N_2r6c5-n/9r6c5


7 r3c3=3 B

Code: Select all
489g    2a4689  2A46h9 |8m9M  3       5b689   |5B6b    7      1     
5       1c68Â9È 7      |4     1C6c    2       |3q689   3689   3689 
1C8c    689     3      |7     5w69    1c568Á9 |5b68Â9È 2d4D   2D4d 
-------------------------------------------------------------------
2       1e59    1E59   |6     5T9t    3f8F    |4       3F8f   7     
4g9G    3       8      |12N9  7       14G5u9  |1p69    2569   2569 
7       456h9   456H9  |13s8M 2n5N    134g58  |1P3Q8å9 23589  23589
-------------------------------------------------------------------
3I4i    7       2i45j  |2I3i  8       6k9K    |6K9k    1      4j5J 
6       148Ã9   1e49   |5     1c4o9   7       |2       3l489  3L489
1c3i48ä 2A45V89 2459   |1R239 2N4O6Y9 13s69   |7       45X689 45689


Code: Select all
[]5r6c3/5(r4c23)-t_9(r4c23)-T/9r5c1-G_9r1c1-g/9(r1c46)-ç_9(r1c123)-Ç/6(r1c23)|*r1c123_6(r23c2)-£C/6r6c2-h_6r6c3-H/5r6c3

[]9r6c3/6r6c3-H_6r6c2-h/6(r23c2)-£C_6(r1c23)/9(r1c123)-Ç|*r1c123_9(r1c46)-ç/9r1c1-g_9r5c1-G/9r6c3


Code: Select all
489g    2a4689  2A46h9 |8m9M  3       5b689   |5B6b    7      1     
5       1c68Â9È 7      |4     1C6c    2       |3q689   3689   3689 
1C8c    689     3      |7     5w69    1c568Á9 |5b68Â9È 2d4D   2D4d 
-------------------------------------------------------------------
2       1e59    1E5V9  |6     5T9t    3f8F    |4       3F8f   7     
4g9G    3       8      |12N9  7       14G5u9  |1p69    2569   2569 
7       45T6h9É 4h6H   |13s8M 2n5N    134g58  |1P3Q8å9 23589  23589
-------------------------------------------------------------------
3I4i    7       2i45j  |2I3i  8       6k9K    |6K9k    1      4j5J 
6       148Ã9   1e49   |5     1c4o9   7       |2       3l489  3L489
1c3i48ä 2A45V89 2459   |1R239 2N4O6Y9 13s69   |7       45X689 45689


17 sequences with small variations (each one is supposed to be done independantly)

Code: Select all
#9(r89c5)
 []5r1c6==5r3c7-b/1r6c7-P|*r236c7_1(r6c46)-p/4r6c6-g|*r4c6r6c46_9r5c1-G/9(r4c23)-T_9r4c5-t/9(r89c5)
 []8r1c6/8r1c4-m_9r1c4-M/9r1c1-g_..as above
 []9r1c6/9r1c1-g_.. as above
 []6r1c6/6r7c6-k_9r7c6-K/9(r89c5)

#9r5c6
 []5r1c6==5r3c7-b/1r6c7-P|*r236c7_1(r6c46)-p/4r6c6-g|*r4c6r6c46_4r5c6-G/9r5c6
 []8r1c6/8r1c4-m_9r1c4-M/9r1c1-g_4r5c6-G/9r5c6
 []9r1c6/9r5c6
 []6r1c6/6r7c6-k_9r7c6-K/9r5c6

#c
 []5r3c5==5(r5c6r6c6)-w/1(r5c6r6c46)-£O|*r45c6r6c46_1r5c4/1r5c7-p_1r6c7-P/6(r123c7)|*r1236c7_6(r2c89)-Z/6r2c5-c
 []6r3c5/6r2c5-c
 []9r3c5/9r4c5-t_9(r4c23)-T/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_.. as above

#6r3c7
 []5r3c5==5(r56c6)-w/1(r5c6r6c46)-£O|*r456c6r6c4 _1r5c4/1r5c7-p_1r6c7-P/6(r123c7)|*r1236c7_6(r2c89)-Z/6r3c7
 []6r3c5/6r3c7
 []9r3c5/9r4c5-t_9(r4c2r4c3)-T/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_.. as above


#8r6c7
 []2r5c4==2r9c5-N/2r7c4-I_4r7c1-i/4(r15c1)_8r1c1/8r1c4-m_8r6c4-M/8r6c7
 []1r5c4/1r5c7-p_1r6c7-P/8r6c7
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_1r6c7-P/8r6c7


#1r6c4
 []2r5c4==2r9c5-N/2r7c4-I_4r7c1-i/4(r1c1r5c1)_8r1c1/8r1c4-m_8r6c4-M/1r6c4
 []1r5c4/1r6c4
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_1r6c7-P/1r6c4


#4(r8c89)
 []2r5c4==2r9c5-N/4r9c5-O_4r8c5-o/4(r8c89)
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8r8c2-Ã_8(r8c89)-ã/4(r8c89)|*r8c89
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_.. as above


#4r9c1
 []2r5c4==2r9c5-N/2r7c4-I_3r9c1-i/4r9c1
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8(r13c1)-Ä_8r9c1-ä/4r9c1
 []9r5c4/9r5c1-G_4r5c1-g/4r9c1

#8r1c2
 []2r5c4==2r9c5-N/2r9c2-A_2r1c2-a/8r1c2
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8r1c2
 []9r5c4/9r1c4-M_8r1c4-m/8r1c2

#6r2c7
 []2r5c4==2r9c5-N/2r7c4-I_3r9c1-i/8r9c1-ä_8(r13c1)-Ä/8r2c2-Â_8(r26c7)-â/6r2c7|*r26c7
 []1r5c4/1r5c7-p_1r6c7-P/6r2c7|*r26c7
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_.. as above

#8r3c2
 []2r5c4==2r9c5-N/2r7c4-I_3r9c1-i/8r9c1-ä_8(r13c1)-Ä/8r3c2
 []1r5c4/1r5c7-p_1r6c7-P/8(r2c7r6c7)-â|*r26c7_8r2c2-Â/8r3c2
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_..as above

#2r9c4
 []2r5c4==2r9c5-N/2r9c4
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8(r13c1)-Ä_8r9c1-ä/2r9c4|*r9c146
 []9r5c4/9r5c1-G_4r5c1-g/4r7c1-i_2r7c4-I/2r9c4

#9r9c4
 []2r5c4==2r9c5-N/2r7c4-I_4r7c1-i/4(r15c1)_8r1c1/8r1c4-m_9r1c4-M/9r9c4
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8(r13c1)-Ä_8r9c1-ä/9(r9c46)|*r9c146 _9(r9c23589)/9r9c4
 []9r5c4/9r9c4

#9(r26c7)
 []2r5c4==2r9c5-N/2r7c4-I_3r9c1-i/8r9c1-ä_8(r13c1)-Ä/8r2c2-Â_8(r26c7)-â/9(r26c7)|*r26c7
 []1r5c4/1r5c7-p_1r6c7-P/9(r26c7)|*r26c7
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_.. as above

#8r9c8
 []2r5c4==2r9c5-N/2r7c4-I_4r7c1-i/4(r15c1)_8r1c1/8r1c4-m_8r6c4-M/8r4c6-F_8r4c8-f/8r9c8
 []1r5c4/1r5c7-p_1r6c7-P/8(r26c7)-â|*r26c7_8r2c2-Â/8r8c2-Ã_8(r8c89)-ã/8r9c8
 []9r5c4/9r5c1-G_4r6c6-g/1(r6c46)-p|*r4c6r6c46_..as above

#u
 []9r1c4-M/9r1c1-g_4r5c6-G/5r5c6-u
 []9r9c4/9(r9c23589)_9(r9c46)/8r9c1-ä|*r9c146_8(r13c1)-Ä/8r2c2-Â_8(r26c7)-â/1r6c7-P|*r26c7_1(r6c46)-p/4r6c6-g|*r4c6r6c46_4r5c6-G/5r5c6-u
 []9r5c4/9r4c5-t_5r4c5-T/5r5c6-u


 []9r1c4-M/9r1c1-g_9r5c1-G/9(r5c789)-É
 []9r9c4/9(r9c23589)_9(r9c46)/8r9c1-ä|*r9c146 _8(r13c1)-Ä/8r2c2-Â_8(r26c7)-â/1r6c7-P|*r26c7 _1(r6c46)-p/4r6c6-g|*r4c6r6c46_9r5c1-G/9(r5c789)-É
 []9r5c4/9(r5c789)-É


8 r2c5=1 B
9 r3c1=1 B
10 r8c5=4

ending in level 2 with two Nice loops

Code: Select all
48D9c 2a46    2A46h  |8c9C   3      5b6p8   |5B6b   7      1     
5     6b8d9K  7      |4      1      2       |3d8D   369    369   
1     6p9P    3      |7      5o6D9c 568D    |5b8d9K 2e4E   2E4e   
-----------------------------------------------------------------
2     1f5F    1F5N9c |6      5c9C   3C8c    |4      3c8C   7     
4c9C  3       8      |1M2D9c 7      1c4C    |1D6d   25g6   25G6   
7     45c6h   4h6H   |3c8C   2d5D   1D4c5o  |1d3D   2389i  238R9I
-----------------------------------------------------------------
3d4D  7       2D45j  |2d3D   8      6k9K    |6K9k   1      4j5J   
6     1F8q9   1f9F   |5      4      7       |2      3l8R9  3L89   
3D8d  2A45N89 2459   |1m3M   2D6d   1M3c69k |7      4e5G69 4568q9


in |* r56c6 we can see that 'o' is 'M'. We have consequently the two Nice loops

[]Km MD dk []9r3c7-K/5(r3c67)-m|*r3c6789_1r9c6-M/1r6c6-D_6r9c5-d/6r7c6-k

[]pk Km MD dk KP []6r1c6-p/6r7c6-k_Km MD dk_9r3c7-K/9r3c2-P


a lot of clearings, the puzzle is finished
champagne
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