Challenge: New set of 11 'Unsolvables'

Advanced methods and approaches for solving Sudoku puzzles

Challenge: New set of 11 'Unsolvables'

Postby AndrewStuart » Wed Sep 13, 2006 4:50 pm

A new set of eleven Michael Mepham 'unsolvable' sudokus has been released on
www.sudoku.org.uk/bifurcation.htm { broken link }.
The lessons have been learnt from the two previous batches which generated a good deal of elegant strategy work by many people. The new eleven is much more difficult than the previous 22.

They are roughly sorted by the number of candidates that current elegant techniques can eliminate, 'easiest' at the top. Number 33 will make grown men weep. I can see only 1 candidate to eliminate using multi-colouring.

Printable versions and a data file are available on the page.

For Glory and Fame to be heaped upon thee merely supply a solve route in this forum or the forum on sudoku.org.uk (Eureka section) and a credit will be added in your honour on that page.
AndrewStuart
 
Posts: 21
Joined: 28 December 2005

Postby Mike Barker » Wed Sep 13, 2006 8:17 pm

Here's a solution for #25. It uses two of the new techniques we've been developing over the last several weeks based in part on previous work including a Kraken Fish Exclusion (Almost Fish) and a Death Blossom (an Advanced Aligned Pair Exclusion - named from "The Last Starfighter" - I'm a Robert Preston fan). The solution also included BUG Repellent (an advanced BUG elimination). I haven't determined a minimal set of techniques yet, but the Death Blossom was the most advanced technique used. To shorten things I'm not showing singles in the summary.

[Edit] I'm reposting the solutions without use of uniqueness tests since there is apparently some disagreement over their acceptability.

My solver did not solve this puzzle without Death Blossom. The most recent changes to my solver have been addition of grouped nice loops where cells of the loop can overlap at the beginning and ending nodes. It may be that other cells can be shared between nodes and this will allow solution without Death Blossom. This is a currently ongoing area of investigation.

The names are something I made up for the new techniques since something thats capable of solving an unsolvable puzzle deserves a better name than "Adanced Pair Exclusion" or "Almost X-wing" or "Advanced BUG elimination". As always I will probably revert to the more benign names in the future, but couldn't resist the temptation. On the other hand, there's still "Overlapping Nice Loop" which needs a little more spice!

Removed
Last edited by Mike Barker on Tue Jun 05, 2007 9:49 am, edited 17 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:20 pm

[Edit: I'm reposting these computer generated solutions for the unsolvables because of several requests to repost them. They were removed in order to stimulate alternative, human generated solutions. I still hope others post alternative solutions, but for those looking for examples of grouped nice loops and multi-inference nice loops, they are here. Also per David's request I've summarized all of the techniques used in order of the number of occurances. I've also included more PMs and have updated the solutions and comments based on my latest solver]

#25 uses two of the new techniques we've been developing over the last several weeks based in part on previous work including a Kraken Fish Exclusion and a Death Blossom (an Advanced Aligned Pair Exclusion - named from "The Last Starfighter" - I'm a Robert Preston fan).

My solver did not solve this puzzle without Death Blossom (refered to as Kraken Blossom in my updated solver which allows for more link possibilities including strong links and grouped strong links as well as multiple links). The most recent changes to my solver have been addition of grouped nice loops where cells of the loop can overlap at the beginning and ending nodes. Updates to grouped nice loops did not eliminate the need for the Death Blossom. I haven't determined a minimal set of techniques yet, but the Death Blossom was the most advanced technique used. To shorten things I'm not showing singles in the summary.

Since the primary purpose of these solutions is to show application of various techniques I left in Uniqueness Tests (I personally think they are an excellent solving technique in their own right).

The names are something I made up for the new techniques since something thats capable of solving an unsolvable puzzle deserves a better name than "Adanced Pair Exclusion" or "Almost X-wing" or "Advanced BUG elimination". As always I will probably revert to the more benign names in the future, but couldn't resist the temptation. On the other hand, there's still "Overlapping Nice Loop" which needs a little more spice!
    1) Naked Single (42)
    2) Hidden Single (15)
    3) Locked Line/Box (5)
    4) Naked Pair (2)
    5) Nice Loops with 3 Strong Links/BV Cells (2)
    6) Locked Box/Box (1)
    7) Finned X-wing (1)
    8) 4-node XY-chain (1)
    9) UR+2K(X,D),UR+3K(X,D) (1)
    10) Advanced BUG-Lite with 3 lines (1)
    11) Advanced Colouring with 3 Links (1)
    12) Advanced Colouring with 6 Links (1)
    13) Grouped Nice Loops with 4 GSL/ALS (1)
    14) B=1 cell ALS-xy rule (1)
    15) 5-valued/1-link Kraken Blossom (1)
    16) Bivalued/1-link Kraken X-wing (1)
Code: Select all
Locked Column Line/Box: r46c3 => r123c3<>8
Naked Column Pair: r13c3 => r2c3<>39,r46c3<>3,r8c3<>9,r9c3<>39
Locked Column Line/Box: r13c2 => r5c2<>7
Locked Column Line/Box: r79c2 => r1235c2<>3
Locked Column Box/Box: r279c2|r29c3 => r46c3<>5
Naked Column Pair: r13c2 => r2c2<>8
3-element Nice Loop: r5c4=1=r6c4=6=r6c3-6-r5c2-1-r5c4 => r6c4=16
3-element Nice Loop: r6c5=8=r6c3=6=r5c2-6-r5c6~3~r6c5 => r6c5<>3
B=1 cell ALS xy-rule: r4c3569-3-r5c6-6-r6c14789 => r4c7<>2
UR+2KX (7,8): r13c28, r2c78 => r1c8<>8
Bivalued/1-element Kraken Row X-Wing (r37/c9, fins=r3c4|r7c27) (r3c4=4=r3c5-4-, r7c2-6-r8c3-4-, r7c7=4=r7c45-4-): r3c49|r7c279=6 => r8c5<>4
+-----------------+---------------------+--------------------+
|   4    78   39  |   368      1  3689  | 23679   2379    5  |
|   6    15   15  |     2    389     7  |    39    389    4  |
|   2    78   39  | 3468*b  3489b    5  |     1   3789   67* |
+-----------------+---------------------+--------------------+
| 357     4   18  |     9   2378   238  |   357      6  127  |
|  37    16    2  |  1367      5    36  |     8      4    9  |
| 357     9  168  |    16    278     4  |  2357  12357  127  |
+-----------------+---------------------+--------------------+
|   9  2356*   7  |   348d  2348d  238  | 2456*d   125  126* |
|   8    26   46c |     5  279-4     1  | 24679    279    3  |
|   1   235   45  |   347      6   239  | 24579   2579    8  |
+-----------------+---------------------+--------------------+
4-element Grouped Nice Loop: r2c7-3-ALS:r12389c8-5-r9c3-4-r8c3=4=r8c7~9~r2c7 => r8c7<>9
+-----------------+-------------------+---------------------+
|   4    78   39  |  368     1  3689  |  23679  2379*b   5  |
|   6    15   15  |    2   389     7  |     39*  389*b   4  |
|   2    78   39  | 3468  3489     5  |      1  3789*b  67  |
+-----------------+-------------------+---------------------+
| 357     4   18  |    9  2378   238  |    357      6  127  |
|  37    16    2  | 1367     5    36  |      8      4    9  |
| 357     9  168  |   16   278     4  |   2357  12357  127  |
+-----------------+-------------------+---------------------+
|   9  2356    7  |  348  2348   238  |   2456    125  126  |
|   8    26   46* |    5   279     1  | 2467-9*  279*b   3  |
|   1   235   45* |  347     6   239  |  24579  2579*b   8  |
+-----------------+-------------------+---------------------+
Row Finned X-Wing: r2c578|r8c58 => r13c8<>9
6-element Advanced Colouring: r2c8=8=r2c5-8-r6c5=8=r6c3=6=r5c2-6-r5c6=6=r1c6=9=r9c6-9-r8c5=9=r8c8~9~r2c8 => r2c8<>9
Locked Column Line/Box: r12c7 => r9c7<>9
Advanced 3-line BUG Lite (SL:r3c3=9=r3c5, ALS:r1c7-3-r2c8-3-r2c5): r1c37|r3c35|r2c57 => r1c7<>3
5-valued/1-element Kraken/Death Blossom (r8c5-2-r8c2-6-, r8c5-7-r46c5|r45c6-6-, r8c5-9-r4579c6-6-): r8c5=279 => r5c2<>6
+-----------------+-------------------+-------------------+
|   4    78   39  |  368     1  3689  | 2679    237    5  |
|   6    15   15  |    2   389     7  |   39     38    4  |
|   2    78   39  | 3468  3489     5  |    1    378   67  |
+-----------------+-------------------+-------------------+
| 357     4   18  |    9  2378c 238cd |  357      6  127  |
|  37   1-6    2  | 1367     5   36cd |    8      4    9  |
| 357     9  168  |   16   278c    4  | 2357  12357  127  |
+-----------------+-------------------+-------------------+
|   9  2356    7  |  348  2348   238d | 2456    125  126  |
|   8    26b  46  |    5   279*    1  | 2467    279    3  |
|   1   235   45  |  347     6   239d | 2457   2579    8  |
+-----------------+-------------------+-------------------+
Locked Column Line/Box: r46c7 => r2c7<>3
3-element Advanced Colouring: r1c8=2=r1c7-2-r6c7=2=r6c9=7=r3c9~7~r1c8 => r1c8<>7
4-node XY-chain (r1c8-3-r3c8-7-r3c9-6-r7c9-2-) => r89c8<>2
Last edited by Mike Barker on Sat Jan 26, 2008 12:51 pm, edited 8 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:24 pm

#26 uses 23 grouped nice loops where the start and end nodes overlap for seven of them. The overlap in the GNL apparently eliminated the need for a Kraken Blossom Exclusion. I have to believe that this could be solved in fewer steps even with nice loops limited to bivalues, bilocals, grouped strong links and ALS. My solver goes through an ordered list of techniques and then searches for eliminations based on the programmed search order. It starts again with naked singles whenever it finds an elimination, so it may not be finding the most effective eliminations. It does somewhat mimick a human solver by finding the shortest elimination first, however, as David has pointed out it does not necessarily restrict the size of ALS, so a human solver may find a longer chain which smaller ALS first.
    1) Naked Single (50)
    2) Grouped Nice Loops with 4 GSL/ALS (12)
    3) Grouped Nice Loops with 3 GSL/ALS (11)
    4) Locked Line/Box (8)
    5) Hidden Single (6)
    6) Naked Triple (3)
    7) Nice Loops with 4 Strong Links/BV Cells (3)
    8) Naked Pair (2)
    9) Finned X-wing (2)
    10) Nice Loops with 3 Strong Links/BV Cells (2)
    11) Locked Box/Box (1)
    12) Finned Swordfish (1)
    13) Empty Rectangle (1)
    14) XY-wing (1)
    15) 4-node XY-chain (1)
    16) Advanced Colouring with 4 Links (1)
    17) Advanced Colouring with 5 Links (1)
    18) Nice Loops with 5 Strong Links/BV Cells (1)
    19) Nice Loops with 6 Strong Links/BV Cells (1)
Code: Select all
Locked Column Line/Box: r12c1 => r579c1<>7
Locked Column Box/Box: r38c8|r389c9 => r46c8<>6,r5c9<>6
Empty Column Rectangle: r35c1|r5c9 => r3c9<>1
5-element Advanced Colouring: r8c6=1=r7c5-1-r7c7=1=r6c7-1-r6c2=1=r5c1=6=r5c6=5=r1c6~1~r8c6 => r1c6<>1
6-element Nice Loop: r1c6=5=r5c6=6=r5c1=1=r6c2-1-r6c7=1=r7c7-1-r7c5=1=r8c6-1-r2c6~8~r1c6 => r1c6<>8
3-element Grouped Nice Loop: r3c5=2=r2c4-2-ALS:r12467c8-4-r7c3=4=r3c3~4~r3c5 => r3c5<>4
+--------------------+--------------------+-------------------+
| 13478     2     6  | 3458    1348   45  |  9   137*b  1378  |
|  1378     9     5  |  238*      6   18  |  4  1237*b 12378  |
|  1348   138   348* |    9  1238-4*   7  |  5   1236   2368  |
+--------------------+--------------------+-------------------+
|     9  3678  2378  |    1    2478  468  | 36    37*b     5  |
|   136     4    37  |   57      79  569  |  2      8   1379  |
|     5  1678   278  |  278    2789    3  | 16   179*b     4  |
+--------------------+--------------------+-------------------+
|   348     5  3478* |    6  134789    2  | 13  1349*b   139  |
| 23468   368     9  |  348       5  148  |  7  12346   1236  |
|  2346   367     1  |  347    3479   49  |  8      5   2369  |
+--------------------+--------------------+-------------------+
Locked Row Line/Box: r1c456 => r1c1<>4
3-element Grouped Nice Loop: r2c6-1-r8c6=1=r7c5-1-ALS:r7c1789~8~ => r2c1<>8
+--------------------+--------------------+--------------------+
|  1378     2     6  | 3458    1348   45  |   9    137   1378  |
| 137-8     9     5  |  238       6   18* |   4   1237  12378  |
|  1348   138   348  |    9    1238    7  |   5   1236   2368  |
+--------------------+--------------------+--------------------+
|     9  3678  2378  |    1    2478  468  |  36     37      5  |
|   136     4    37  |   57      79  569  |   2      8   1379  |
|     5  1678   278  |  278    2789    3  |  16    179      4  |
+--------------------+--------------------+--------------------+
|  348*b    5  3478  |    6  134789*   2  | 13*b 1349*b  139*b |
| 23468   368     9  |  348       5  148* |   7  12346   1236  |
|  2346   367     1  |  347    3479   49  |   8      5   2369  |
+--------------------+--------------------+--------------------+
3-element Grouped Nice Loop: ALS:r4c278-8-ALS:r456c3-7-r7c3=7=r7c5~7~ => r4c5<>7
+---------------------+--------------------+-------------------+
|  1378     2      6  | 3458    1348   45  |  9    137   1378  |
|   137     9      5  |  238       6   18  |  4   1237  12378  |
|  1348   138    348  |    9    1238    7  |  5   1236   2368  |
+---------------------+--------------------+-------------------+
|     9  3678* 2378*b |    1   248-7  468  | 36*    37*     5  |
|   136     4    37*b |   57      79  569  |  2      8   1379  |
|     5  1678   278*b |  278    2789    3  | 16    179      4  |
+---------------------+--------------------+-------------------+
|   348     5   3478* |    6  134789*   2  | 13   1349    139  |
| 23468   368      9  |  348       5  148  |  7  12346   1236  |
|  2346   367      1  |  347    3479   49  |  8      5   2369  |
+---------------------+--------------------+-------------------+
Overlap 3-element Grouped Nice Loop: ALS:r159c6-6-r5c1=6=r89c1-6-ALS:r9c2456~4~ => r8c6<>4
+---------------------+---------------------+-------------------+
|   1378     2     6  | 3458    1348    45* |  9    137   1378  |
|    137     9     5  |  238       6    18  |  4   1237  12378  |
|   1348   138   348  |    9    1238     7  |  5   1236   2368  |
+---------------------+---------------------+-------------------+
|      9  3678  2378  |    1     248   468  | 36     37      5  |
|    136*    4    37  |   57      79   569* |  2      8   1379  |
|      5  1678   278  |  278    2789     3  | 16    179      4  |
+---------------------+---------------------+-------------------+
|    348     5  3478  |    6  134789     2  | 13   1349    139  |
| 23468*b  368     9  |  348       5  18-4  |  7  12346   1236  |
|  2346*b 367*c    1  | 347*c  3479*c  49*c |  8      5   2369  |
+---------------------+---------------------+-------------------+
Naked Column Pair: r28c6 => r4c6<>8
3-element Grouped Nice Loop: ALS:r9c2456-6-r89c1=6=r5c1-6-ALS:r5c456|r46c5|r6c4~4~ => r7c5<>4
+---------------------+----------------------+-------------------+
|   1378     2     6  | 3458     1348    45  |  9    137   1378  |
|    137     9     5  |  238        6    18  |  4   1237  12378  |
|   1348   138   348  |    9     1238     7  |  5   1236   2368  |
+---------------------+----------------------+-------------------+
|      9  3678  2378  |    1     248*c   46  | 36     37      5  |
|    136*    4    37  |  57*c     79*c 569*c |  2      8   1379  |
|      5  1678   278  | 278*c   2789*c    3  | 16    179      4  |
+---------------------+----------------------+-------------------+
|    348     5  3478  |    6  13789-4     2  | 13   1349    139  |
| 23468*b  368     9  |  348        5    18  |  7  12346   1236  |
|  2346*b  367*    1  |  347*    3479*   49* |  8      5   2369  |
+---------------------+----------------------+-------------------+
4-element Grouped Nice Loop: r7c7=1=r6c7=6=r6c2-6-ALS:r89c2|r7c13-4-r7c8=4=r8c8~1~r7c7 => r8c8<>1
+---------------------+-------------------+--------------------+
|  1378     2      6  | 3458   1348   45  |  9     137   1378  |
|   137     9      5  |  238      6   18  |  4    1237  12378  |
|  1348   138    348  |    9   1238    7  |  5    1236   2368  |
+---------------------+-------------------+--------------------+
|     9  3678   2378  |    1    248   46  | 36      37      5  |
|   136     4     37  |   57     79  569  |  2       8   1379  |
|     5  1678*   278  |  278   2789    3  | 16*    179      4  |
+---------------------+-------------------+--------------------+
|  348*b    5  3478*b |    6  13789    2  | 13*   1349*   139  |
| 23468  368*b     9  |  348      5   18  |  7  2346-1*  1236  |
|  2346  367*b     1  |  347   3479   49  |  8       5   2369  |
+---------------------+-------------------+--------------------+
Row Finned Swordfish: r2c1689|r5c19|r8c69 => r1c9<>1
4-element Grouped Nice Loop: r2c6=8=r8c6=1=r7c5-1-ALS:r7c1789-8-r1c1=8=r3c123~8~ => r3c5<>8
+--------------------+-------------------+--------------------+
|  1378*    2     6  | 3458   1348   45  |   9    137    378  |
|   137     9     5  |  238      6   18* |   4   1237  12378  |
| 1348*c 138*c 348*c |    9  123-8    7  |   5   1236   2368  |
+--------------------+-------------------+--------------------+
|     9  3678  2378  |    1    248   46  |  36     37      5  |
|   136     4    37  |   57     79  569  |   2      8   1379  |
|     5  1678   278  |  278   2789    3  |  16    179      4  |
+--------------------+-------------------+--------------------+
|  348*b    5  3478  |    6  13789*   2  | 13*b 1349*b  139*b |
| 23468   368     9  |  348      5   18* |   7   2346   1236  |
|  2346   367     1  |  347   3479   49  |   8      5   2369  |
+--------------------+-------------------+--------------------+
4-element Grouped Nice Loop: r9c6-4-ALS:r4c2678-8-ALS:r456c3-7-r7c3=7=r7c5~9~r9c6 => r7c5<>9
+----------------------+--------------------+-------------------+
|  1378      2      6  | 3458    1348   45  |   9   137    378  |
|   137      9      5  |  238       6   18  |   4  1237  12378  |
|  1348    138    348  |    9     123    7  |   5  1236   2368  |
+----------------------+--------------------+-------------------+
|     9  3678*b 2378*c |    1     248  46*b | 36*b  37*b     5  |
|   136      4    37*c |   57      79  569  |   2     8   1379  |
|     5   1678   278*c |  278    2789    3  |  16   179      4  |
+----------------------+--------------------+-------------------+
|   348      5   3478* |    6  1378-9*   2  |  13  1349    139  |
| 23468    368      9  |  348       5   18  |   7  2346   1236  |
|  2346    367      1  |  347    3479   49* |   8     5   2369  |
+----------------------+--------------------+-------------------+
Locked Row Line/Box: r9c56 => r9c9<>9
Overlap 4-element Grouped Nice Loop: ALS:r4c78-6-r6c7=6=r6c2-6-ALS:r89c2|r7c13-4-ALS:r1467c8~7~ => r2c8<>7
+---------------------+------------------+-------------------+
|  1378     2      6  | 3458  1348   45  |  9   137*c   378  |
|   137     9      5  |  238     6   18  |  4  123-7  12378  |
|  1348   138    348  |    9   123    7  |  5   1236   2368  |
+---------------------+------------------+-------------------+
|     9  3678   2378  |    1   248   46  | 36*   37*c     5  |
|   136     4     37  |   57    79  569  |  2      8   1379  |
|     5  1678*   278  |  278  2789    3  | 16*  179*c     4  |
+---------------------+------------------+-------------------+
|  348*b    5  3478*b |    6  1378    2  | 13  1349*c   139  |
| 23468  368*b     9  |  348     5   18  |  7   2346   1236  |
|  2346  367*b     1  |  347  3479   49  |  8      5    236  |
+---------------------+------------------+-------------------+
Overlap 4-element Grouped Nice Loop: ALS:r47c7-6-r6c7=6=r6c2-6-ALS:r89c2|r7c13-4-ALS:r7c789~1~ => r7c5<>1,r8c9<>1
+---------------------+-------------------+--------------------+
|  1378     2      6  | 3458   1348   45  |   9    137    378  |
|   137     9      5  |  238      6   18  |   4    123  12378  |
|  1348   138    348  |    9    123    7  |   5   1236   2368  |
+---------------------+-------------------+--------------------+
|     9  3678   2378  |    1    248   46  |  36*    37      5  |
|   136     4     37  |   57     79  569  |   2      8   1379  |
|     5  1678*   278  |  278   2789    3  |  16*   179      4  |
+---------------------+-------------------+--------------------+
|  348*b    5  3478*b |    6  378-1    2  | 13*c 1349*c  139*c |
| 23468  368*b     9  |  348      5   18  |   7   2346  236-1  |
|  2346  367*b     1  |  347   3479   49  |   8      5    236  |
+---------------------+-------------------+--------------------+
3-element Grouped Nice Loop: r2c4-2-ALS:r2c89|r1c8-7-ALS:r1389c9~3~ => r2c9<>3
+--------------------+-----------------+-------------------+
|  1378     2     6  | 345   134   45  |  9  137*b   378*c |
|   137     9     5  |  23*    6    8  |  4  123*b 127-3*b |
|  1348   138   348  |   9   123    7  |  5  1236   2368*c |
+--------------------+-----------------+-------------------+
|     9  3678  2378  |   1   248   46  | 36    37       5  |
|   136     4    37  |  57    79  569  |  2     8    1379  |
|     5  1678   278  | 278  2789    3  | 16   179       4  |
+--------------------+-----------------+-------------------+
|   348     5  3478  |   6   378    2  | 13  1349     139  |
| 23468   368     9  | 348     5    1  |  7  2346    236*c |
|  2346   367     1  | 347  3479   49  |  8     5    236*c |
+--------------------+-----------------+-------------------+
3-element Grouped Nice Loop: ALS:r14c8-1-r1c5=1=r3c5-1-ALS:r3c123~3~ => r3c8<>3
+--------------------+-----------------+------------------+
|  1378     2     6  | 345   134*  45  |  9    137*  378  |
|   137     9     5  |  23     6    8  |  4    123   127  |
| 1348*b 138*b 348*b |   9   123*   7  |  5  126-3  2368  |
+--------------------+-----------------+------------------+
|     9  3678  2378  |   1   248   46  | 36     37*    5  |
|   136     4    37  |  57    79  569  |  2      8  1379  |
|     5  1678   278  | 278  2789    3  | 16    179     4  |
+--------------------+-----------------+------------------+
|   348     5  3478  |   6   378    2  | 13   1349   139  |
| 23468   368     9  | 348     5    1  |  7   2346   236  |
|  2346   367     1  | 347  3479   49  |  8      5   236  |
+--------------------+-----------------+------------------+
Overlap 3-element Grouped Nice Loop: ALS:r14c8-1-ALS:r1c456|r2c4-2-ALS:r124c8~3~ => r78c8<>3,r6c8<>7
+--------------------+------------------+------------------+
|  1378     2     6  | 345*b 134*b 45*b |  9   137*c  378  |
|   137     9     5  |  23*b    6    8  |  4   123*c  127  |
|  1348   138   348  |    9   123    7  |  5    126  2368  |
+--------------------+------------------+------------------+
|     9  3678  2378  |    1   248   46  | 36    37*c    5  |
|   136     4    37  |   57    79  569  |  2      8  1379  |
|     5  1678   278  |  278  2789    3  | 16   19-7     4  |
+--------------------+------------------+------------------+
|   348     5  3478  |    6   378    2  | 13  149-3   139  |
| 23468   368     9  |  348     5    1  |  7  246-3   236  |
|  2346   367     1  |  347  3479   49  |  8      5   236  |
+--------------------+------------------+------------------+
3-element Nice Loop: r7c7=1=r6c7-1-r6c8-9-r7c8=9=r7c9~1~r7c7 => r7c9<>1
3-element Grouped Nice Loop: ALS:r1c4568-7-r4c8=7=r5c9-7-ALS:r5c13456~1~ => r1c1<>1
+--------------------+------------------+----------------+
| 378-1     2     6  | 345*  134*   45* |  9  137*  378  |
|   137     9     5  |  23     6     8  |  4  123   127  |
|  1348   138   348  |   9   123     7  |  5  126  2368  |
+--------------------+------------------+----------------+
|     9  3678  2378  |   1   248    46  | 36   37*    5  |
|  136*b    4   37*b | 57*b  79*b 569*b |  2    8  1379* |
|     5  1678   278  | 278  2789     3  | 16   19     4  |
+--------------------+------------------+----------------+
|   348     5  3478  |   6   378     2  | 13  149    39  |
| 23468   368     9  | 348     5     1  |  7  246   236  |
|  2346   367     1  | 347  3479    49  |  8    5   236  |
+--------------------+------------------+----------------+
3-element Grouped Nice Loop: ALS:r7c13|r89c2-4-ALS:r12467c8-2-ALS:r12589c4~8~ => r8c1<>8
+---------------------+------------------+-----------------+
|    378     2     6  | 345*c  134   45  |  9  137*b  378  |
|    137     9     5  |  23*c    6    8  |  4  123*b  127  |
|   1348   138   348  |    9   123    7  |  5   126  2368  |
+---------------------+------------------+-----------------+
|      9  3678  2378  |    1   248   46  | 36   37*b    5  |
|    136     4    37  |  57*c   79  569  |  2     8  1379  |
|      5  1678   278  |  278  2789    3  | 16   19*b    4  |
+---------------------+------------------+-----------------+
|    348*    5  3478* |    6   378    2  | 13  149*b   39  |
| 2346-8   368*    9  | 348*c    5    1  |  7   246   236  |
|   2346   367*    1  | 347*c 3479   49  |  8     5   236  |
+---------------------+------------------+-----------------+
4-element Grouped Nice Loop: r4c3=2=r4c5-2-ALS:r3c1235-8-ALS:r389c9-3-r5c9=3=r5c13~3~r4c3 => r4c3<>3
+---------------------+-----------------+-----------------+
|   378     2      6  | 345   134   45  |  9  137    378  |
|   137     9      5  |  23     6    8  |  4  123    127  |
| 1348*b 138*b  348*b |   9  123*b   7  |  5  126  2368*c |
+---------------------+-----------------+-----------------+
|     9  3678  278-3* |   1   248*  46  | 36   37      5  |
|  136*d    4    37*d |  57    79  569  |  2    8   1379* |
|     5  1678    278  | 278  2789    3  | 16   19      4  |
+---------------------+-----------------+-----------------+
|   348     5   3478  |   6   378    2  | 13  149     39  |
|  2346   368      9  | 348     5    1  |  7  246   236*c |
|  2346   367      1  | 347  3479   49  |  8    5   236*c |
+---------------------+-----------------+-----------------+
4-element Grouped Nice Loop: r4c8-3-ALS:r12c8|r2c9-2-r2c4=2=r6c4-2-r6c3=2=r4c3~7~r4c8 => r4c3<>7
+-------------------+-----------------+-----------------+
|  378     2     6  | 345   134   45  |  9  137*b  378  |
|  137     9     5  |  23*    6    8  |  4  123*b 127*b |
| 1348   138   348  |   9   123    7  |  5   126  2368  |
+-------------------+-----------------+-----------------+
|    9  3678  28-7* |   1   248   46  | 36    37*    5  |
|  136     4    37  |  57    79  569  |  2     8  1379  |
|    5  1678   278* | 278* 2789    3  | 16    19     4  |
+-------------------+-----------------+-----------------+
|  348     5  3478  |   6   378    2  | 13   149    39  |
| 2346   368     9  | 348     5    1  |  7   246   236  |
| 2346   367     1  | 347  3479   49  |  8     5   236  |
+-------------------+-----------------+-----------------+
Overlap 4-element Grouped Nice Loop: ALS:r6c345-9-r5c5-7-r7c5=7=r7c3-7-ALS:r456c3~8~ => r6c2<>8
+--------------------+-----------------+----------------+
|  378      2     6  | 345   134   45  |  9  137   378  |
|  137      9     5  |  23     6    8  |  4  123   127  |
| 1348    138   348  |   9   123    7  |  5  126  2368  |
+--------------------+-----------------+----------------+
|    9   3678   28*b |   1   248   46  | 36   37     5  |
|  136      4   37*b |  57    79* 569  |  2    8  1379  |
|    5  167-8  278*b | 278* 2789*   3  | 16   19     4  |
+--------------------+-----------------+----------------+
|  348      5  3478* |   6   378*   2  | 13  149    39  |
| 2346    368     9  | 348     5    1  |  7  246   236  |
| 2346    367     1  | 347  3479   49  |  8    5   236  |
+--------------------+-----------------+----------------+
4-element Grouped Nice Loop: ALS:r7c789-4-ALS:r7c13|r89c2-6-r89c1=6=r5c1-6-ALS:r5c3456~3~ => r7c3<>3
+----------------------+------------------+----------------+
|   378     2       6  | 345   134    45  |  9  137   378  |
|   137     9       5  |  23     6     8  |  4  123   127  |
|  1348   138     348  |   9   123     7  |  5  126  2368  |
+----------------------+------------------+----------------+
|     9  3678      28  |   1   248    46  | 36   37     5  |
|   136*    4     37*d | 57*d  79*d 569*d |  2    8  1379  |
|     5   167     278  | 278  2789     3  | 16   19     4  |
+----------------------+------------------+----------------+
|  348*b    5  478-3*b |   6   378     2  | 13* 149*   39* |
| 2346*c 368*b      9  | 348     5     1  |  7  246   236  |
| 2346*c 367*b      1  | 347  3479    49  |  8    5   236  |
+----------------------+------------------+----------------+
Overlap 4-element Grouped Nice Loop: ALS:r5c359-1-r2c9=1=r123c8-1-ALS:r67c8-4-ALS:r4567c3~3~ => r5c1<>3
+-------------------+-----------------+-----------------+
|  378     2     6  | 345   134   45  |  9  137*b  378  |
|  137     9     5  |  23     6    8  |  4  123*b  127* |
| 1348   138   348  |   9   123    7  |  5  126*b 2368  |
+-------------------+-----------------+-----------------+
|    9  3678   28*d |   1   248   46  | 36    37     5  |
| 16-3     4   37*d |  57    79* 569  |  2     8  1379* |
|    5   167  278*d | 278  2789    3  | 16   19*c    4  |
+-------------------+-----------------+-----------------+
|  348     5  478*d |   6   378    2  | 13  149*c   39  |
| 2346   368     9  | 348     5    1  |  7   246   236  |
| 2346   367     1  | 347  3479   49  |  8     5   236  |
+-------------------+-----------------+-----------------+
5-element Nice Loop: r1c5=1=r1c8-1-r2c9=1=r5c9-1-r5c1-6-r5c6=6=r4c6=4=r4c5~4~r1c5 => r1c5<>4
Naked Block Triple: r2c4|r13c5 => r1c4<>3
3-element Grouped Nice Loop: r1c4=4=r1c6-4-ALS:r4c2678-8-r8c2=8=r8c4~4~r1c4 => r8c4<>4
+-------------------+------------------+-----------------+
|  378      2    6  |   45*   13   45* |   9  137   378  |
|  137      9    5  |   23     6    8  |   4  123   127  |
| 1348    138  348  |    9   123    7  |   5  126  2368  |
+-------------------+------------------+-----------------+
|    9  3678*b  28  |    1   248  46*b | 36*b 37*b    5  |
|   16      4   37  |   57    79  569  |   2    8  1379  |
|    5    167  278  |  278  2789    3  |  16   19     4  |
+-------------------+------------------+-----------------+
|  348      5  478  |    6   378    2  |  13  149    39  |
| 2346    368*   9  | 38-4*    5    1  |   7  246   236  |
| 2346    367    1  |  347  3479   49  |   8    5   236  |
+-------------------+------------------+-----------------+
Locked Row Line/Box: r9c456 => r9c1<>4
4-element Grouped Nice Loop: r9c5=4=r4c5-4-ALS:r4c2678-8-ALS:r46c3-7-r7c3=7=r9c2~7~r9c5 => r9c5<>7
+--------------------+------------------+-----------------+
|  378      2     6  |  45     13   45  |   9  137   378  |
|  137      9     5  |  23      6    8  |   4  123   127  |
| 1348    138   348  |   9    123    7  |   5  126  2368  |
+--------------------+------------------+-----------------+
|    9  3678*b  28*c |   1    248* 46*b | 36*b 37*b    5  |
|   16      4    37  |  57     79  569  |   2    8  1379  |
|    5    167  278*c | 278   2789    3  |  16   19     4  |
+--------------------+------------------+-----------------+
|  348      5   478* |   6    378    2  |  13  149    39  |
| 2346    368     9  |  38      5    1  |   7  246   236  |
|  236    367*    1  | 347  349-7*  49  |   8    5   236  |
+--------------------+------------------+-----------------+
Overlap 4-element Grouped Nice Loop: ALS:r4c278-6-r4c6=6=r5c6-6-r5c1-1-ALS:r4689c2~8~ => r3c2<>8
+-------------------+-----------------+----------------+
|  378      2    6  |  45    13   45  |  9  137   378  |
|  137      9    5  |  23     6    8  |  4  123   127  |
| 1348   13-8  348  |   9   123    7  |  5  126  2368  |
+-------------------+-----------------+----------------+
|    9  3678*b  28  |   1   248   46* | 36*  37*    5  |
|   16*     4   37  |  57    79  569* |  2    8  1379  |
|    5   167*b 278  | 278  2789    3  | 16   19     4  |
+-------------------+-----------------+----------------+
|  348      5  478  |   6   378    2  | 13  149    39  |
| 2346   368*b   9  |  38     5    1  |  7  246   236  |
|  236   367*b   1  | 347   349   49  |  8    5   236  |
+-------------------+-----------------+----------------+
Column Finned X-Wing: r48c2|r68c4 => r4c5<>8
Locked Row Line/Box: r6c45 => r6c3<>8
3-element Nice Loop: r6c5=8=r7c5=7=r7c3-7-r6c3~2~r6c5 => r6c5<>2
4-element Advanced Colouring: r5c3=3=r4c2=8=r8c2-8-r8c4=8=r7c5=7=r7c3~7~r5c3 => r5c3<>7
Column Finned X-Wing: r67c3|r567c5 => r6c4<>7
Naked Column Triple: r268c4 => r9c4<>3
4-element Nice Loop: r8c4=3=r2c4=2=r6c4-2-r6c3-7-r7c3=7=r7c5~3~r8c4 => r7c5<>3
Naked Column Triple: r567c5 => r9c5<>9
4-element Nice Loop: r2c1=7=r2c9=1=r5c9-1-r5c1=1=r6c2-1-r3c2~3~r2c1 => r2c1<>3
4-element Nice Loop: r2c8=3=r2c4=2=r6c4-2-r6c3-7-r4c2=7=r4c8~3~r2c8 => r4c8<>3
Locked Row Line/Box: r6c23 => r6c5<>7
Locked Column Line/Box: r789c9 => r13c9<>3
Naked Row Pair: r1c58 => r1c1<>3
Locked Row Line/Box: r3c12 => r3c5<>3
4-node XY-chain (r3c2-1-r3c5-2-r4c5-4-r9c5-3-) => r9c2<>3
XY-wing => r9c1<>6,r4c2<>6,r8c1<>6
Last edited by Mike Barker on Sat Jan 26, 2008 12:54 pm, edited 6 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:25 pm

#27 is more of the the same. Again the Kraken Blossom seems to be playing a roll. The original solution used a Kraken X-wing since Death Blossom didn't find eliminations where Kraken Blossom does. The original Kraken X-wing was:
Code: Select all
1-element Kraken Row X-Wing (r37/c8, fins=r3c12|r7c24) (r7c2|r3c2|r3c1-1-r2c2-6-, r7c4-1-r89c5-6-): r3c128|r7c248=1 => r2c5<>6
+------------------+-------------------+--------------------+
|   58  569  3578  | 3567  2467     1  |  2379  2349   239  |
|    4   16b  137  |    9  27-6     8  |  1237   123     5  |
|  157* 159*    2  |  357    47   347  |     6  1349*    8  |
+------------------+-------------------+--------------------+
|   29    3    46  |    8     5    46  |    29     7     1  |
| 1259    8   145  |  137   147  2347  |   359     6  2349  |
|  125    7  1456  |  136     9   236  |   235     8   234  |
+------------------+-------------------+--------------------+
|    3  125*    9  |  167*    8    67  |     4   125*   26  |
|    6   12    18  |    4    13c    5  | 12389  1239     7  |
| 1578    4  1578  |    2   136c    9  |   138   135    36  |
+------------------+-------------------+--------------------+

    1) Naked Single (45)
    2) Locked Line/Box (11)
    3) Hidden Single (11)
    4) UR+2(X,D,B)/1SL (Type 4,...) (2)
    5) Advanced Colouring with 3 Links (2)
    6) Naked Pair (1)
    7) Finned X-wing (1)
    8) 4-node XY-chain (1)
    9) 5-node XY-chain (1)
    10) UR+3(X,C,N,U,E)/2SL (1)
    11) UR+4(X,C)/3SL (1)
    12) Grouped Advanced Colouring with 3 Links (1)
    13) Grouped Advanced Colouring with 4 Links (1)
    14) Strong Nice Loops with 3 GSL/BV Cells (1)
    15) Grouped Nice Loops with 3 GSL/ALS (1)
    16) Grouped Nice Loops with 4 GSL/ALS (1)
    17) Bivalued/2-link Kraken Blossom (1)
    18) 3-valued/2-link Kraken Blossom (1)
Code: Select all
Locked Column Line/Box: r45c1 => r13c1<>9
Locked Row Line/Box: r9c13 => r9c5<>7
Locked Column Line/Box: r46c3 => r12c3<>6
Locked Column Line/Box: r12c5 => r5c5<>2
Locked Column Line/Box: r89c5 => r1235c5<>3
Locked Column Line/Box: r56c7 => r9c7<>5
Locked Column Line/Box: r56c9 => r1c9<>4
Naked Row Pair: r4c17 => r4c6<>2
UR+2B/1SL (2,9): r45c17 => r5c7<>2
UR+2B/1SL (4,6): r46c36 => r6c6<>4
UR+4C/3SL (8,7): r19c13 => r1c1<>7
Bivalued/2-element Kraken Blossom (r5c5-1-r56c4=1=r7c4=7=r7c6-7-, r5c5-4-r4c6-6-r7c6-7-): r5c5=147 => r5c6<>7
+------------------+--------------------+--------------------+
|   58  569  3578  | 3567  2467      1  |  2379  2349   239  |
|    4   16   137  |    9   267      8  |  1237   123     5  |
|  157  159     2  |  357    47    347  |     6  1349     8  |
+------------------+--------------------+--------------------+
|   29    3    46  |    8     5     46c |    29     7     1  |
| 1259    8   145  |  137b  147* 234-7  |   359     6  2349  |
|  125    7  1456  |  136b    9    236  |   235     8   234  |
+------------------+--------------------+--------------------+
|    3  125     9  |  167b    8    67bc |     4   125    26  |
|    6   12    18  |    4    13      5  | 12389  1239     7  |
| 1578    4  1578  |    2   136      9  |   138   135    36  |
+------------------+--------------------+--------------------+
3-valued/2-element Kraken Blossom (r7c8-1-r3c8=1=r3c12-1-r2c2-6-, r7c8-2-r7c9-6-r9c9=6=r9c5-6-, r7c8-5-r78c2-1-r2c2-6-): r7c8=125 => r2c5<>6
+------------------+------------------+--------------------+
|   58  569  3578  | 3567  2467    1  |  2379  2349   239  |
|    4  16bd  137  |    9  27-6    8  |  1237   123     5  |
|  157b 159b    2  |  357    47  347  |     6  1349b    8  |
+------------------+------------------+--------------------+
|   29    3    46  |    8     5   46  |    29     7     1  |
| 1259    8   145  |  137   147  234  |   359     6  2349  |
|  125    7  1456  |  136     9  236  |   235     8   234  |
+------------------+------------------+--------------------+
|    3  125d    9  |  167     8   67  |     4   125*   26c |
|    6   12d   18  |    4    13    5  | 12389  1239     7  |
| 1578    4  1578  |    2   136c   9  |   138   135    36c |
+------------------+------------------+--------------------+
4-element Grouped Advanced Colouring: r8c3=8=r8c7=9=r8c8-9-r3c8=9=r3c2=1=r78c2~1~r8c3 => r8c3<>1
UR+3U/2SL (2,7): r12c57 => r2c7<>2
3-element Grouped Nice Loop: r7c9-2-r78c8=2=r12c8-2-ALS:r1c23479~6~ => r7c4<>6
+------------------+-------------------+---------------------+
|    8  59*d 357*d | 3567*d 2467    1  | 2379*d 2349*c 239*d |
|    4    6   137  |     9    27    8  |   137   123*c    5  |
|  157  159     2  |   357    47  347  |     6   1349     8  |
+------------------+-------------------+---------------------+
|   29    3    46  |     8     5   46  |    29      7     1  |
| 1259    8   145  |   137   147  234  |   359      6  2349  |
|  125    7  1456  |   136     9  236  |   235      8   234  |
+------------------+-------------------+---------------------+
|    3  125     9  |  17-6     8   67  |     4   125*b   26* |
|    6   12     8  |     4    13    5  |  1239  1239*b    7  |
|  157    4   157  |     2   136    9  |     8    135    36  |
+------------------+-------------------+---------------------+
3-element Advanced Colouring: r1c4=6=r1c5-6-r9c5=6=r7c6=7=r3c6~7~r1c4 => r1c4<>7
3-element Strong Nice Loop: r5c4=7=r5c5=1=r89c5-1-r7c4-7-r5c4 => r5c5=17,r3c4<>7
Locked Column Line/Box: r45c6 => r3c6<>4
3-element Grouped Advanced Colouring: r5c4=7=r7c4-7-r7c6=7=r3c6=3=r13c4~3~r5c4 => r5c4<>3
Locked Row Line/Box Pair: r5c45 => r5c13<>1
Locked Row Line/Box: r6c13 => r6c4<>1
4-element Grouped Nice Loop: r7c9=6=r7c6-6-r9c5=6=r1c5-6-ALS:r1c23479-2-r12c8=2=r78c8~2~r7c9 => r7c9<>2
+-----------------+------------------+---------------------+
|   8  59*b 357*b | 356*b 2467*   1  | 2379*b 2349*c 239*b |
|   4    6   137  |    9    27    8  |   137   123*c    5  |
| 157  159     2  |   35    47   37  |     6   1349     8  |
+-----------------+------------------+---------------------+
|  29    3    46  |    8     5   46  |    29      7     1  |
| 259    8    45  |   17    17  234  |   359      6  2349  |
| 125    7  1456  |   36     9  236  |   235      8   234  |
+-----------------+------------------+---------------------+
|   3  125     9  |   17     8   67* |     4   125*d  6-2* |
|   6   12     8  |    4    13    5  |  1239  1239*d    7  |
| 157    4   157  |    2   136*   9  |     8    135    36  |
+-----------------+------------------+---------------------+
Column Finned X-Wing: r38c2|r28c7 => r3c8<>1
Locked Row Line/Box: r2c78 => r2c3<>1
4-node XY-chain (r2c5-7-r3c5-4-r3c8-9-r1c9-2-) => r1c5<>2,r2c8<>2
5-node XY-chain (r6c1-1-r3c1-7-r3c5-4-r3c8-9-r1c9-2-) => r6c9<>2
3-element Advanced Colouring: r8c2=1=r3c2=9=r3c8-9-r8c8=9=r8c7~1~r8c2 => r8c7<>1
Last edited by Mike Barker on Sat Jan 26, 2008 12:55 pm, edited 4 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:29 pm

#28 is actually pretty straight forward with the most advanced technique being an ALS xy-rule (ALS chain).
    1) Naked Single (42)
    2) Hidden Single (14)
    3) Nice Loops with 4 Strong Links/BV Cells (4)
    4) Locked Line/Box (3)
    5) Nice Loops with 3 Strong Links/BV Cells (3)
    6) X-wing (2)
    7) Advanced Colouring with 4 Links (2)
    8) Strong Nice Loops with 4 GSL/BV Cells (2)
    9) Naked Pair (1)
    10) Empty Rectangle (1)
    11) Generalized WXYZ-wing (1)
    12) 6-node XY-chain (1)
    13) UR+2(X,D,B)/1SL (Type 4,...) (1)
    14) UR+4(X,C)/3SL (1)
    15) Advanced Colouring with 3 Links (1)
    16) Strong Nice Loops with 3 GSL/BV Cells (1)
    17) Strong Nice Loops with 6 GSL/BV Cells (1)
    18) Grouped Nice Loops with 2 GSL/ALS (1)
    19) B=2 cell ALS-xy rule (1)
Code: Select all
Locked Row Line/Box: r2c13 => r2c5<>9
Locked Row Line/Box: r5c78 => r5c5<>9
WXYZ-wing: r2c9|r13c8, r5c9 => r5c8<>3,r1c9<>3,r6c8<>3
4-element Strong Nice Loop: r9c2=4=r9c1=9=r9c8-9-r5c8-5-r5c1=5=r45c2~5~r9c2 => r9c2<>5
UR+4C/3SL (3,6): r13c28 => r1c8<>6
B=2 cell ALS xy-rule: r8c1347-2-r2c13-4-r2c79|r1c89|r3c8 => r8c9<>7
Empty Row Rectangle: r1c59|r9c9 => r9c5<>7
2-element Grouped Nice Loop: ALS:r8c1479-8-ALS:r9c4569~2~ => r9c8<>2
+-------------------+---------------------+--------------------+
|    1  2346     5  | 4679  24679     27  |    8     23   267  |
|   49     7   249  |    3   2468     28  |  456      1   256  |
|    8  2346   234  |    1   2467      5  |  467    236     9  |
+-------------------+---------------------+--------------------+
|    6   358   138  |  589   1589    138  |    2      7     4  |
|  457   458  1478  |    2  14578      6  |  159     59     3  |
|    2     9  1347  |  457   1457    137  |  156     56     8  |
+-------------------+---------------------+--------------------+
|    3   258  2789  | 5678  25678      4  | 5679  25689     1  |
|   57*    1   278  | 5678*     3      9  |  567*     4   256* |
| 4579   248     6  | 578*b 1258*b 1278*b |    3  589-2  257*b |
+-------------------+---------------------+--------------------+
6-element Strong Nice Loop: r1c9=7=r3c7=4=r2c7-4-r2c1-9-r9c1=9=r9c8=8=r7c8=2=r13c8~2~r1c9 => r1c9<>2
3-element Nice Loop: r3c2=6=r1c2-6-r1c9-7-r3c7=7=r3c5~6~r3c2 => r3c5<>6
3-element Strong Nice Loop: r1c6-7-r1c9-6-r2c79=6=r2c5~2~r1c6 => r2c5<>2
4-element Strong Nice Loop: r1c6-7-r1c9-6-r2c79=6=r2c5=8=r2c6~2~r1c6 => r2c6<>2
Row X-Wing: r28c39 => r37c3<>2,r9c9<>2
3-element Advanced Colouring: r7c8=2=r8c9-2-r2c9=2=r2c3=9=r7c3~9~r7c8 => r7c8<>9
3-element Nice Loop: r2c7=5=r2c9-5-r9c9-7-r1c9~6~r2c7 => r2c7<>6
4-element Advanced Colouring: r2c7=5=r2c9=2=r2c3=9=r7c3-9-r7c7=9=r5c7~5~r2c7 => r5c7<>5
4-element Nice Loop: r3c7=4=r2c7=5=r2c9-5-r9c9-7-r1c9~6~r3c7 => r3c7<>6
3-element Nice Loop: r3c2=6=r1c2-6-r1c9-7-r3c7~4~r3c2 => r3c2<>4
4-element Nice Loop: r2c9=5=r2c7=4=r3c7=7=r1c9-7-r9c9-5-r2c9 => r8c9<>5
4-element Advanced Colouring: r9c9=5=r2c9=2=r2c3=9=r2c1-9-r9c1=9=r9c8~5~r9c9 => r9c8<>5
4-element Nice Loop: r3c2=6=r1c2-6-r1c9-7-r3c7-4-r3c3~3~r3c2 => r3c2<>3
4-element Nice Loop: r9c6=2=r1c6-2-r1c8-3-r1c2=3=r4c2-3-r4c6~1~r9c6 => r9c6<>1
Naked Column Pair: r19c6 => r6c6<>7
Column X-Wing: r19c69 => r1c45<>7,r9c14<>7
UR+2B/1SL (1,3): r46c36 => r6c3<>3,r4c3<>1
6-node XY-chain (r6c8-5-r5c8-9-r9c8-8-r9c4-5-r9c9-7-r1c9-6-) => r3c8<>6
Locked Column Line/Box Pair: r13c8 => r7c8<>2
Last edited by Mike Barker on Sat Jan 26, 2008 12:56 pm, edited 4 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:33 pm

#29 is longer, but no real surprises. It does have one really nice continuous grouped nice loop.
    1) Naked Single (49)
    2) Locked Line/Box (10)
    3) Hidden Single (8)
    4) Nice Loops with 3 Strong Links/BV Cells (3)
    5) 4-node XY-chain (2)
    6) Grouped Advanced Colouring with 3 Links (2)
    7) Strong Nice Loops with 4 GSL/BV Cells (2)
    8) Grouped Nice Loops with 3 GSL/ALS (2)
    9) Naked Pair (1)
    10) Locked Box/Box (1)
    11) Finned X-wing (1)
    12) Generalized XYZ-wing (1)
    13) Generalized WXYZ-wing (1)
    14) 5-node XY-chain (1)
    15) Advanced Colouring with 3 Links (1)
    16) Grouped Advanced Colouring with 4 Links (1)
    17) Nice Loops with 4 Strong Links/BV Cells (1)
    18) Strong Nice Loops with 6 GSL/BV Cells (1)
    19) Grouped Nice Loops with 4 GSL/ALS (1)
    20) B=2 cell ALS-xy rule (1)
Code: Select all
Locked Row Line/Box: r4c45 => r4c3<>8
Locked Row Line/Box: r6c456 => r6c13<>4
Locked Row Line/Box: r9c79 => r9c13<>7
Locked Row Line/Box: r7c89 => r7c46<>1
Locked Column Box/Box: r68c1|r468c3 => r13c1<>7,r1c3<>7
3-element Nice Loop: r9c6=2=r7c6-2-r7c2-4-r7c9=4=r9c9~4~r9c6 => r9c6<>4
3-element Grouped Advanced Colouring: r5c8=3=r3c8=9=r1c7=1=r46c7~1~r5c8 => r5c8<>1
4-element Grouped Advanced Colouring: r1c1=3=r3c1=6=r2c3=8=r2c9=3=r2c56~3~ => r1c5<>3
6-element Strong Nice Loop: r5c2-8-r3c2-7-r1c2=7=r1c4=9=r1c7=1=r46c7-1-r5c9=1=r5c3~4~r5c2 => r5c3<>4
4-element Strong Nice Loop: r7c2-4-r5c2=4=r5c1=5=r6c1=2=r46c3~2~ => r9c3<>2
4-element Strong Nice Loop: r1c3-2-r46c3=2=r6c1=5=r5c1=4=r5c2~4~ => r1c2<>4
B=2 cell ALS xy-rule: r12357c9-4-r7c12-6-r1c123|r3c12 => r1c7<>2
3-element Grouped Nice Loop: ALS:r5c89-5-r5c1=5=r6c1-5-ALS:r6c456~1~ => r6c7<>1
+-----------------+----------------------+-------------------+
|  234  27    24  | 14579    145      8  |   159    6  1235  |
|    1   9  2468  |   456   3456   3456  |    25    7  2358  |
|  368  78     5  |  1679      2   1369  |     4  139   138  |
+-----------------+----------------------+-------------------+
|    9   3   127  |  1568   1568    156  |  1257    4  1257  |
|  458* 48    18  |     2      9      7  |     6   35*  135* |
|  257*  6   127  |  145*b 1345*b 1345*b | 257-1    8     9  |
+-----------------+----------------------+-------------------+
|  246  24     3  |  4569      7  24569  |     8  159   145  |
|  478   5  4789  |  1489    148    149  |     3    2     6  |
| 2468   1  4689  |     3   4568   2569  |   579   59   457  |
+-----------------+----------------------+-------------------+
3-element Grouped Nice Loop: ALS:r8c456-9-r8c3=9=r9c3-9-ALS:r9c789~4~ => r9c5<>4
+-----------------+----------------------+------------------+
|  234  27    24  | 14579    145      8  |  159    6  1235  |
|    1   9  2468  |   456   3456   3456  |   25    7  2358  |
|  368  78     5  |  1679      2   1369  |    4  139   138  |
+-----------------+----------------------+------------------+
|    9   3   127  |  1568   1568    156  | 1257    4  1257  |
|  458  48    18  |     2      9      7  |    6   35   135  |
|  257   6   127  |   145   1345   1345  |  257    8     9  |
+-----------------+----------------------+------------------+
|  246  24     3  |  4569      7  24569  |    8  159   145  |
|  478   5  4789* |  1489*   148*   149* |    3    2     6  |
| 2468   1  4689* |     3  568-4   2569  | 579*b 59*b 457*b |
+-----------------+----------------------+------------------+
4-element Grouped Nice Loop: r3c1=6=r2c3-6-ALS:r2c4567-2-ALS:r12357c9-4-ALS:r7c12-6-r3c1 (MER) => r2c3<>4,r1c45<>4,r2c9<>5,r2c9<>3,r3c6<>3,r4c9<>1,r49c9<>5,r7c46<>4,r7c6<>2,r9c1<>2,r9c1<>6
+--------------------+------------------------+--------------------+
|   234   27     24  | 1579-4   15-4       8  |  159    6   1235*c |
|     1    9  268-4* |   456*b 3456*b  3456*b |  25*b   7  28-53*c |
|   368*  78      5  |   1679      2   169-3  |    4  139    138*c |
+--------------------+------------------------+--------------------+
|     9    3    127  |   1568   1568     156  | 1257    4   27-15  |
|   458   48     18  |      2      9       7  |    6   35    135*c |
|   257    6    127  |    145   1345    1345  |  257    8       9  |
+--------------------+------------------------+--------------------+
|  246*d 24*d     3  |  569-4      7  569-42  |    8  159    145*c |
|   478    5   4789  |   1489    148     149  |    3    2       6  |
| 48-26    1   4689  |      3    568    2569  |  579   59    47-5  |
+--------------------+------------------------+--------------------+
Locked Row Line/Box: r8c456 => r8c13<>4
XYZ-wing: r6c7|r4c9, r2c7 => r4c7<>2
Row Finned X-Wing: r1c1239|r4c39 => r2c3<>2
Locked Row Line/Box: r1c123 => r1c9<>2
4-node XY-chain (r3c2-7-r1c2-2-r7c2-4-r9c1-8-) => r3c1<>8
3-element Advanced Colouring: r3c1=6=r2c3=8=r3c2=7=r3c4~6~r3c1 => r3c4<>6
3-element Nice Loop: r3c9=8=r3c2-8-r2c3-6-r3c1~3~r3c9 => r3c9<>3
3-element Nice Loop: r5c3=1=r5c9-1-r3c9-8-r3c2=8=r2c3~8~r5c3 => r5c3<>8
Locked Row Line/Box Pair: r5c89 => r5c1<>5
Locked Column Line/Box Pair: r46c3 => r1c3<>2
Naked Column Pair: r59c1 => r7c1<>4
3-element Grouped Advanced Colouring: r9c5=6=r9c3=9=r8c3=8=r8c45~8~r9c5 => r9c5<>8
Locked Row Line/Box: r8c45 => r8c3<>8
Locked Row Line/Box: r7c46 => r7c8<>9
4-element Nice Loop: r3c8=3=r3c1=6=r2c3=8=r3c2-8-r3c9~1~r3c8 => r3c8<>1
WXYZ-wing: r1c79|r3c8, r1c5 => r1c4<>5,r1c4<>1
5-node XY-chain (r7c9-4-r7c2-2-r1c2-7-r1c4-9-r1c7-5-) => r1c9<>5,r9c7<>5
4-node XY-chain (r9c8-9-r3c8-3-r1c9-1-r1c5-5-) => r9c5<>5
Last edited by Mike Barker on Sat Jan 26, 2008 12:57 pm, edited 4 times in total.
Mike Barker
 
Posts: 458
Joined: 22 January 2006

Postby Mike Barker » Wed Sep 13, 2006 8:56 pm

#30 is fairly simple with some big ALSs and a mutant Jellyfish (not necessary). The fact that the ALS are so big means that alternative solutions should be considered.
    1) Naked Single (52)
    2) Locked Line/Box (4)
    3) Hidden Single (4)
    4) Finned X-wing (3)
    5) Advanced Colouring with 3 Links (2)
    6) Grouped Nice Loops with 3 GSL/ALS (2)
    7) Hidden Pair (1)
    8) Finned Swordfish (1)
    9) Mutant Jellyfish (1)
    10) X-cycle with 3 Grouped Strong Links (1)
    11) 4-node XY-chain (1)
    12) Grouped Nice Loops with 2 GSL/ALS (1)
Code: Select all
Locked Row Line/Box: r4c46 => r4c1<>1
Locked Row Line/Box: r4c456 => r4c1<>3
Locked Row Line/Box: r6c46 => r6c9<>6
Locked Row Line/Box: r6c456 => r6c9<>9
Hidden Row Pair: r8c46 => r8c4=37,r8c6=37
Column Finned X-Wing: r19c5|r139c7 => r1c9<>8
Column Finned Swordfish: r1379c3|r19c5|r139c7 => r9c1<>8
3-element Advanced Colouring: r9c9=1=r7c8=5=r8c8-5-r8c1=5=r9c1~1~r9c9 => r9c1<>1
Mutant Jellyfish (r8c357/r13b79, fins=r9c5): r8c1289|r1379c3|r19c5|r139c7 => r9c9<>8
+--------------------+----------------------+-------------------+
| 1238      5  1378* |  13789  3789*  1379  | 478*    6  12479  |
|  168   1678     4  | 156789     2  15679  |   3   189   1789  |
|    9  12678  1378* |  13678     4   1367  |  78*  128      5  |
+--------------------+----------------------+-------------------+
|  248      9     6  |   1237    37   1237  |   5   248   2478  |
|  123    127   137  |      4     5      8  |  67    29   2679  |
|  248   2478     5  |   2679    79   2679  |   1     3   2478  |
+--------------------+----------------------+-------------------+
|    7    148   189* |    589     6    459  |   2  1458      3  |
| 4568*   468*    2  |     37     1     37  |   9   458*   468* |
|  456      3   189* |   2589    89#  2459  | 468*    7  146-8  |
+--------------------+----------------------+-------------------+
Common Overlap 2-element Grouped Nice Loop: ALS:r2c12|r13c3-3-ALS:r124689c1~1~ => r3c2<>1
+----------------------+----------------------+-------------------+
| 1238*b      5  1378* |  13789  3789   1379  | 478     6  12479  |
|  168*b   1678*    4  | 156789     2  15679  |   3   189   1789  |
|     9  2678-1  1378* |  13678     4   1367  |  78   128      5  |
+----------------------+----------------------+-------------------+
|  248*b      9     6  |   1237    37   1237  |   5   248   2478  |
|   123     127   137  |      4     5      8  |  67    29   2679  |
|  248*b   2478     5  |   2679    79   2679  |   1     3   2478  |
+----------------------+----------------------+-------------------+
|     7     148   189  |    589     6    459  |   2  1458      3  |
| 4568*b    468     2  |     37     1     37  |   9   458    468  |
|  456*b      3   189  |   2589    89   2459  | 468     7    146  |
+----------------------+----------------------+-------------------+
3-element Grouped Nice Loop: ALS:r5c789-7-r5c23=7=r6c2-7-ALS:r6c456~2~ => r6c9<>2
+-------------------+----------------------+-------------------+
| 1238     5  1378  |  13789  3789   1379  | 478     6  12479  |
|  168  1678     4  | 156789     2  15679  |   3   189   1789  |
|    9  2678  1378  |  13678     4   1367  |  78   128      5  |
+-------------------+----------------------+-------------------+
|  248     9     6  |   1237    37   1237  |   5   248   2478  |
|  123  127*b 137*b |      4     5      8  |  67*   29*  2679* |
|  248  2478*    5  |  2679*c  79*c 2679*c |   1     3  478-2  |
+-------------------+----------------------+-------------------+
|    7   148   189  |    589     6    459  |   2  1458      3  |
| 4568   468     2  |     37     1     37  |   9   458    468  |
|  456     3   189  |   2589    89   2459  | 468     7    146  |
+-------------------+----------------------+-------------------+
3-element Grouped Nice Loop: ALS:r3c7|r2c89-1-ALS:r24689c1-2-ALS:r1c13456~7~ => r1c79<>7,r1c7<>8,r2c46<>9,r1c9<>9
+---------------------+-------------------------+---------------------+
| 1238*c    5  1378*c |  13789*c 3789*c  1379*c | 4-78     6  124-79  |
|  168*b 1678      4  | 15678-9      2  1567-9  |    3   189*   1789* |
|     9  2678   1378  |   13678      4    1367  |   78*  128       5  |
+---------------------+-------------------------+---------------------+
|  248*b    9      6  |    1237     37    1237  |    5   248    2478  |
|   123   127    137  |       4      5       8  |   67    29    2679  |
|  248*b 2478      5  |    2679     79    2679  |    1     3     478  |
+---------------------+-------------------------+---------------------+
|     7   148    189  |     589      6     459  |    2  1458       3  |
| 4568*b  468      2  |      37      1      37  |    9   458     468  |
|  456*b    3    189  |    2589     89    2459  |  468     7     146  |
+---------------------+-------------------------+---------------------+
Column Finned X-Wing: r135c3|r35c7 => r3c2<>7
Column Finned X-Wing: r19c5|r39c7 => r3c4<>8
4-node XY-chain (r6c5-9-r9c5-8-r9c7-6-r5c7-7-) => r6c9<>7
Three Grouped Strong Links: r3c7=8=r9c7-8-r8c89=8=r8c12-8-r79c3=8=r13c3~8~ => r3c2<>8
3-element Advanced Colouring: r5c7=6=r5c9=9=r2c9=7=r3c7~7~r5c7 => r5c7<>7
Last edited by Mike Barker on Sat Jan 26, 2008 12:58 pm, edited 7 times in total.
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Postby Mike Barker » Wed Sep 13, 2006 9:00 pm

#31 gets solved with a couple of nice loops, the most complicated ones including grouped strong links.
    1) Naked Single (52)
    2) Locked Line/Box (5)
    3) Hidden Single (4)
    4) Nice Loops with 4 Strong Links/BV Cells (3)
    5) Finned X-wing (2)
    6) Naked Triple (1)
    7) Locked Box/Box (1)
    8) Mutant Swordfish (1)
    9) Advanced Colouring with 3 Links (1)
    10) Grouped Advanced Colouring with 4 Links (1)
    11) Strong Nice Loops with 3 GSL/BV Cells (1)
Code: Select all
Locked Row Line/Box: r4c13 => r4c456<>4
Locked Column Line/Box: r13c6 => r456c6<>9
Naked Row Triple: r3c246 => r3c1<>19,r3c8<>13
Endofin Mutant Swordfish (r28c8/c1b39): r2c179|r8c1789|r179c8 => r9c7<>6,r79c9<>6
+-----------------------+--------------------+------------------------+
|  12689  12369   1239  |  1347     5  3479  |   3678   1368*  13678  |
|    156*     4    135  |     2    17     8  |   3567*     9    1367* |
|     58    139      7  |    13     6    39  |      4     58       2  |
+-----------------------+--------------------+------------------------+
|   1249      8  12349  |  1356    19  2356  |    369      7    1369  |
|      7    139      6  |  1348  1489    34  |      2    138       5  |
|    129      5   1239  | 13678  1789  2367  |   3689      4   13689  |
+-----------------------+--------------------+------------------------+
|      3     69      8  |  4567     2  4567  |      1     56*  479-6  |
|   2456*     7    245  |     9    48     1  |   3568* 23568#   3468* |
| 124569   1269  12459  | 45678     3  4567  | 5789-6   2568* 4789-6  |
+-----------------------+--------------------+------------------------+
3-element Strong Nice Loop: r3c1=5=r3c8-5-r7c8-6-r8c789=6=r8c1~5~r3c1 => r8c1<>5
4-element Grouped Advanced Colouring: r8c5=4=r5c5=9=r5c2-9-r7c2=9=r7c9=4=r7c46-4-r8c5 => r5c5=49,r139c2<>9,r7c9=49,r9c46<>4
Locked Row Line/Box: r9c79 => r9c46<>7
Row Finned X-Wing: r5c48|r9c4789 => r8c8<>8
4-element Nice Loop: r5c8=8=r5c4-8-r6c5=8=r8c5=4=r5c5-4-r5c6~3~r5c8 => r5c8<>3
Row Finned X-Wing: r3c24|r5c246 => r46c4<>3
3-element Advanced Colouring: r1c2=2=r9c2-2-r9c8=2=r8c8=3=r1c8~3~r1c2 => r1c2<>3
4-element Nice Loop: r3c4=1=r3c2=3=r5c2-3-r5c6-4-r1c6=4=r1c4~1~r3c4 => r1c4<>1
4-element Nice Loop: r3c4=1=r2c5-1-r4c5-9-r5c5=9=r5c2=3=r3c2~3~r3c4 => r3c4<>3,r3c2<>1
Locked Row Line/Box Pair: r1c46 => r1c789<>3
Locked Column Line/Box: r12c1 => r89c1<>6
Locked Row Box/Box: r79c246 => r7c8<>6
Last edited by Mike Barker on Sat Jan 26, 2008 1:00 pm, edited 3 times in total.
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Postby StrmCkr » Wed Sep 13, 2006 9:08 pm

a quick question..

if they supposed to have single solutions? then y did a solution counter just tell me puzzel 33 hasl 47 solutions?

or is that part of the challenge? of unsolveable puzzles to find 1 of the unique 47 solutions.
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Postby udosuk » Wed Sep 13, 2006 9:21 pm

Most likely your solver is flawed, or you've made a typo mistake when inputting the puzzle to your solver...

A remote chance is that Michael Mepham has made a typo mistake himself when publishing these puzzles... But I don't really think so...:!:
Last edited by udosuk on Wed Sep 13, 2006 5:29 pm, edited 2 times in total.
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Postby Mike Barker » Wed Sep 13, 2006 9:26 pm

Try reentering it (did you mistakendly include the "33." at the start of the puzzle?). It only has one solution.
Code: Select all
 . 1 . | . . . | . 5 .
 7 . 8 | . . . | . . .
 . . 2 | 6 . 8 | 3 . .
 ------+-------+------
 9 . . | 3 . 5 | . . 7
 . . . | . . . | . . .
 8 . . | 4 . 2 | . . 6
 ------+-------+------
 . . 9 | 7 . 1 | 2 . .
 . . 3 | . . . | 4 . .
 . 8 . | . . . | . 9 .
Last edited by Mike Barker on Wed Sep 13, 2006 5:27 pm, edited 1 time in total.
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Postby StrmCkr » Wed Sep 13, 2006 9:26 pm

ive checked 3 times one a typing error on my part ive copied it out right...
so maybee he has a typo...

im checking it on this solver

http://www.scanraid.com/sudoku.htm

n e suggestions.?
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Postby udosuk » Wed Sep 13, 2006 9:29 pm

Code: Select all
316|249|758
748|153|962
592|678|314
---+---+---
921|365|847
634|817|529
875|492|136
---+---+---
469|731|285
253|986|471
187|524|693

This is the unique solution. Could you run that program to find at least 1 other solution?:?:
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Postby StrmCkr » Wed Sep 13, 2006 9:35 pm

werid... now its saying 1 solution...

hum that makes no sence... must have had a type o some where.
thanks!
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