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.
Challenge: New set of 11 'Unsolvables'
Challenge: New set of 11 'Unsolvables'
by AndrewStuart » Wed Sep 13, 2006 4:50 pm
- AndrewStuart
- Posts: 21
- Joined: Wed Dec 28, 2005 5:00 pm
by 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
[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: Sun Jan 22, 2006 5:00 pm
by 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!
#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: Sun Jan 22, 2006 5:00 pm
by 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: Sun Jan 22, 2006 5:00 pm
by 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: Sun Jan 22, 2006 5:00 pm
by 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: Sun Jan 22, 2006 5:00 pm
by 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: Sun Jan 22, 2006 5:00 pm
by 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.
- Mike Barker
- Posts: 458
- Joined: Sun Jan 22, 2006 5:00 pm
by 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.
- Mike Barker
- Posts: 458
- Joined: Sun Jan 22, 2006 5:00 pm
by 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...
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.
- udosuk
- Posts: 2698
- Joined: Sun Jul 17, 2005 4:00 pm
by 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.
- Mike Barker
- Posts: 458
- Joined: Sun Jan 22, 2006 5:00 pm
by 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?
- udosuk
- Posts: 2698
- Joined: Sun Jul 17, 2005 4:00 pm
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