The Effortless Extremes thread

Everything about Sudoku that doesn't fit in one of the other sections

Postby ronk » Sun Jun 25, 2006 8:47 pm

Mike Barker wrote:26 TUVWXYZ-wing
2.....93...57..........3..41..2....5.4....61...7........3..426..68.2...........9.

I didn't find that TUVWXYZ-wing, but I presume there are [edit: 7] cells involved. There is a smaller (5-cell) step using the xz-rule ...
Code: Select all
 2    8    1    | 4    56   B56   | 9    3    7
 4    3    5    | 7    9     2    | 1    8    6
 6    7    9    | 18   18    3    | 5    2    4
----------------+-----------------+---------------
 1    9    6    | 2    4     8    | 3    7    5
 8    4    2    | 35   357   57   | 6    1    9
 3    5    7    | 169  16   B169  | 8    4    2
----------------+-----------------+---------------
 79   1    3    | 59  A57    4    | 2    6    8
 79   6    8    | 139  2    B179  | 4    5    13
 5    2    4    | 1368 1368 B16   | 7    9    13

 ALS sets A = {r7c5} = {57}, B = {r1689c6} = {15679}, x = 7, z = 5, r1c5<>5

... followed by singles.

Mike Barker wrote:23 WXYZ-wing
.2.13.9.795......4......1..18..7....3.....476...36.2......8..6.5...1.....4......3
.7......9....4.1.61.....28...36.......8423...5.6..8...3.....8...4..8.69....5....1

I must have a blind spot for those two WXYZ-wings. Would you please provide a hint for each?

TIA, Ron
Last edited by ronk on Sun Jun 25, 2006 7:01 pm, edited 1 time in total.
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Postby Mike Barker » Sun Jun 25, 2006 9:46 pm

I should have specified that these are generalized versions of mYZ-wings. I guess its up to RW whether he wants to include these or the more restrictive form. In the latter case examples are much harder to find. The TUVWXYZ-wing is also an ALS xz-rule:
Code: Select all
+-----------+------------------+-----------+
|   2  8  1 |     4    56   56 |  9  3   7 |
|   4  3  5 |     7     9    2 |  1  8   6 |
|   6  7  9 |    18    18    3 |  5  2   4 |
+-----------+------------------+-----------+
|   1  9  6 |     2     4    8 |  3  7   5 |
|   8  4  2 |   -35   357  *57 |  6  1   9 |
|   3  5  7 |   169    16  169 |  8  4   2 |
+-----------+------------------+-----------+
|  79  1  3 |   #59    57    4 |  2  6   8 |
|  79  6  8 |  #139     2 #179 |  4  5  13 |
|   5  2  4 | #1368 #1368  #16 |  7  9  13 |
+-----------+------------------+-----------+


The WXYZ-wings are:
Code: Select all
+----------------+---------------+-------------+
|    8   2     4 |    1  3     6 |    9  5   7 |
|    9   5     1 |    7  2     8 |    6  3   4 |
|   67  36    37 |    9  4     5 |    1  2   8 |
+----------------+---------------+-------------+
|    1   8     6 |   24  7    24 |    3  9   5 |
|    3   9     2 |    8  5     1 |    4  7   6 |
|    4   7     5 |    3  6     9 |    2  8   1 |
+----------------+---------------+-------------+
|   27   1   379 |  245  8  2347 |   57  6  29 |
|    5 #36 -3789 |  *26  1  *237 |   78  4  29 |
|  267   4    78 |  256  9   *27 |  578  1   3 |
+----------------+---------------+-------------+

+------------+-------------------+----------------+
|  6   7  24 |    8     13   #12 |   5    34    9 |
|  8  35  29 | -239      4    59 |   1     7    6 |
|  1  35  49 |  379  35679  5679 |   2     8   34 |
+------------+-------------------+----------------+
|  4  29   3 |    6    159   159 |   7    12    8 |
|  7   1   8 |    4      2     3 |   9     6    5 |
|  5  29   6 |  179    179     8 |  34  1234  234 |
+------------+-------------------+----------------+
|  3   6   1 | *279    *79 -2479 |   8     5  247 |
|  2   4   5 |  137      8   *17 |   6     9   37 |
|  9   8   7 |    5     36  -246 |  34   234    1 |
+------------+-------------------+----------------+
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Postby ronk » Mon Jun 26, 2006 2:21 am

Mike Barker wrote:The WXYZ-wings are ..............

After r8c3<>4 for the first, it takes another WXYZ-wing for r7c3<>9 to solve the puzzle. Does it count because the two WXYZ-wings are back-to-back?

For the second, didn't it already take another WXYZ-wing for the exclusion r2c6<>2 in order to get to your grid. As for the first, does it count because the two WXYZ-wings are back-to-back?

Would they count if some other technique (even singles) could be applied between the two wings?
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Postby Mike Barker » Mon Jun 26, 2006 4:42 am

I didn't catch the double WXYZ-wings. The same problem existed for the VWXYZ-wings. Here are some corrections and some other replacements which require simpler techniques (ie singles instead of pairs) or more variety

Code: Select all
9 Finned X-wing
.6.7..8.......3..2..2.8..9..1....4.....3...6764.1............5.82..76.......29..4 Column

10 Finned Swordfish
......6....569..7..2....5..3.9.....4....2.1.....4.7.....391..5..4..7...2..1..3.4. Column
8..5..9.7..1...8..2.........6.......4..6.1...7.3.9..2...697.....7.....8.9...826.. Column

10 Franken Swordfish
......6....569..7..2....5..3.9.....4....2.1.....4.7.....391..5..4..7...2..1..3.4. (delete - is only finned)

11 Franken Jellyfish (2 per puzzle)
..1...9......2...54.81.9.7..1..63..8..7.......3..1....2..7..15....6..82.3........ (delete - uses an XY-wing)

22 XYZ-wing
2.9...7...8..49..............41...9..639..4..5.82......3281..........6.5...43...1

23 WXYZ-wing
..3..1..7.9.56.3....6.......82.5........4.9...4.6.8......89...2..5....7982...76..
6.2....3..8.....7....72.6.9....19.....54....7.24..8........7.6.....9.3.8.1..3..2.
3..96..8.........21....5.3....3.......1....9..4721.........8..7..81..5....9..61..

24 VWXYZ-wing
.78...2....4.9..3..6.4..9..3....6.158...1....61...5...4.............28.9.......27
.763.........9...2....84.....3...16........4.2......8.1......2.6.9.75.....24.9..5

27 4-node XY-ring
...9.....35..2.6....7..4....267..5..5.9...3.....1.......8.....9....67.1.1....9.56

28 5-node XY-chain
..8.1...73...724........98......5..4.4..3.5....9...13.2.........5.9.4..8.1.2.....

32 7-node XY-chain
...9..7.5.7.....1..3.4........6....8.6.27.9.4...5.4.7.9.13...6.7....24..4.....5..

39 UR+1 (Type 1)
8.2..3.........7..6.1....8....78..2.75..9134..9..5........3.5..4....9...1..8..6..
....6.71...38...45.5...2..3.1...3....8...7.6.3.7....5...6.2..91.........4.1.98...

56 Nice Loop: r1c1=1=r1c4-1-r3c4=1=r3c9=5=r3c3~5~r1c1 => r1c1<>5
.43...7......6....68..79...........8..1.8.3.....5..1.4.....1.6..5...2..39.7...8..
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Postby Mike Barker » Tue Jun 27, 2006 3:35 am

Here's a grouped Turbot Fish and another TUVXYZ-wing along with some others which can replace previous puzzles which required pairs or triples.

Code: Select all
9 X-wing
.8..7..9.......81.7.6..4...5.....9...3.92....1..8....64....5..1....1..8....6..4.. ~row
.85...9.......9....6.5..1....3....48..1..4.2..5..3.......62...39.......5...7.1... ~column
.....7.8.8.4.6.3......1.....9..36...7....4.5.54....69.........8...7..9...7.45..1. ~column

18 Two grouped strong links (Grouped Turbot Fish)
.4.7..62.1...4...3....1..8....1...9.9.5.....8..84...........7.2...3...4..2..5..19 >

28 5-node XY-chain
......56.9.....2...8..2....2.9..4..53....9..71....2.36...46....4......1....5.1..3
1.9......6..58.......72..4....37...2......4.7..31...9.8.24...............5...29.1

25 UVWYXZ-wing
.72.........52.....8.43.9.6........32..68.4.7..5........63...9.....58....3..1..8. ~

26 TUVWXYZ-wing
....4..6...53.9....97............4.991.2.....58..17....7.6......2...37..8.......2 >

37 ALS xz-rule
...13.94..8..2...7..5...8.6.........4.8..7......5....83....1....91...4..7...4..6.
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Postby ronk » Tue Jun 27, 2006 11:57 am

Mike, except for a couple BUG+2 puzzles, the following all look like BUG+1 to me.

Mike Barker wrote:#23,#24 6-node XY-chain
.1.2...4..9.....3.5..4................75..1.8..68.1...3...2.8......6..2.85..4...3
.6..98.4.31.......5.8....3...1..6.........4.....1825.....245..7...9..6.1..7...2..
I think most people would first spot a BUG+1 and a BUG+2.

Mike Barker wrote:#26 9-node XY-chain
....126.7.59....32.......8.7..........84...7...58.912..9.7582....6.4...5.4.......
BUG+1

Mike Barker wrote:#42 BUG+1 (8-node XY-chain)
..8...2..9.......72.7....934...9...6....2.........31.5.....8....5.43.....6...7.84
Code: Select all
+-------------+--------------+-------------+
|  5   34   8 |  39   7   49 |   2   6   1 |
|  9   13   6 |  23  48   12 |  48   5   7 |
|  2   14   7 |  18 *56  *56 |  48   9   3 |
+-------------+--------------+-------------+
|  4   28  35 |  18   9   15 |   7  23   6 |
|  1    7  35 | *56   2 -456 |   9  34   8 |
|  6  289  29 |   7  48    3 |   1  24   5 |
+-------------+--------------+-------------+
|  7   29   4 | *56 *56    8 |   3   1  29 |
|  8    5   1 |   4   3   29 |   6   7  29 |
|  3    6  29 |  29   1    7 |   5   8   4 |
+-------------+--------------+-------------+
A nice BUG-Lite+1, but a nice BUG+2 too.

Mike Barker wrote:#81,#82 5-node XY-chain
......56.9.....2...8..2....2.9..4..53....9..71....2.36...46....4......1....5.1..3
1.9......6..58.......72..4....37...2......4.7..31...9.8.24...............5...29.1
BUG+1

P.S. In the quotes, I changed the "elimination type" code to puzzle numbers.
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Postby RW » Thu Jun 29, 2006 6:40 pm

Thank you again Mike for the puzzles, finally I had time to check them. I've added the puzzles that clearly passed the test to the list. Some are added in different categories than the ones you mentioned (mostly BUGs and BUG-lights) if I found some move to solve the puzzle that IMO is easier than the one you mentioned. As a difficulty rating for different techniques I mostly use the amount of cells involved in the pattern and techniques that only involve bivalue cells were rated easier than techniques that involve multivalue cells (and I tend to rate uniqueness based techniqes as easier than some other techniques).

The puzzles that were not added at all were puzzles that either could be solved by the "non-advanced" techniques alone (listed in the first post) or puzzles that could be solved with simpler techniques than the mentioned one in several steps. An example, your last TUVWXYZ-wing puzzle:

Code: Select all
....4..6...53.9....97............4.991.2.....58..17....7.6......2...37..8.......2
 *-----------------------------------------------------------*
 | 1     3     8     | 7     4     2     | 9     6     5     |
 | 6     4     5     | 3     8     9     | 12   *27   *17    |
 | 2     9     7     | 1     5     6     | 38    348   348   |
 |-------------------+-------------------+-------------------|
 | 7     6     2     | 58    3     58    | 4     1     9     |
 | 9     1     3     | 2     6     4     | 58    578   78    |
 | 5     8     4     | 9     1     7     |-236  *23   *36    |
 |-------------------+-------------------+-------------------|
 | 3     7     19    | 6     2     58    | 158   4589  148   |
 | 4     2     16    | 58    9     3     | 7     58   *16    |
 | 8     5     69    | 4     7     1     | 36    39    2     |
 *-----------------------------------------------------------*


As the name suggests, a TUVWXYZ-wing makes use of 7 cells. I found a 5-cell XY-chain to eliminate '3' from r6c7. If this had solved the puzzle, I'd added it as a 5-cell XY-chain. As it still requires a XY-wing after the chain, I didn't add the puzzle anywhere. I'm sure nobody will fully agree on all desicions I made, feel free to comment.

One of your puzzles had a very nice BUG-lite patterns of this type:

Code: Select all
ab .  . |ab .  . |ab .  .
ab .  . |ab .  . |ab .  .
ab .  . |ab .  . |ab .  .

Two digits 'ab' cannot be in the same column of three adjacent boxes.


I've looked for pure patterns like that, but haven't found any really good ones earlier. Your puzzle:

Code: Select all
.9..8..7....3...5265.4.....8.7..31.61........9..8.4.......6.4.778..........2.....
 *--------------------------------------------------------------------*
 | 2      9      1      | 6      8      5      | 3      7      4      |
 | 4      7      8      | 3      9      1      | 6      5      2      |
 | 6      5      3      | 4      7      2      |*89    *189   *189    |
 |----------------------+----------------------+----------------------|
 | 8      24     7      | 9      5      3      | 1      24     6      |
 | 1      34     45     | 7      2      6      |*589   *3489  *3589   |
 | 9      236    256    | 8      1      4      | 7      23     35     |
 |----------------------+----------------------+----------------------|
 | 35     12     29     | 15     6      8      | 4      139    7      |
 | 7      8      46     | 15     34     9      | 2      136    135    |
 | 35     146    469    | 2      34     7      |-589   -13689 -13589  |
 *--------------------------------------------------------------------*
r9c789<>9


Digits '8' and '9' have to go in row 3 in box 3 and row 5 in box 6. '8' has to go in row 9 in box 9, therefore '9' cannot be in that row. Alternatively this could be viewed as a reverse-BUG (r7c3<>9).

The same technique also works in this puzzle:
Code: Select all
[Edit: row corrected]
.78...2....4.9..3..6.4..9..3....6.158...1....61...5...4.............28.9.......27
 *-----------------------------------------------------------*
 | 9     7     8     | 6     3     1     | 2     5     4     |
 | 1     5     4     | 2     9     78    | 67    3     68    |
 | 2     6     3     | 4     5     78    | 9     78    1     |
 |-------------------+-------------------+-------------------|
 | 3     24   *79    |*789   248   6     | 47    1     5     |
 | 8     24    5     |*379   1     34    | 3467 *79    26    |
 | 6     1    *79    |*379   24    5     | 347  -789   28    |
 |-------------------+-------------------+-------------------|
 | 4     8     2     | 1     7     9     | 5     6     3     |
 | 7     3     1     | 5     6     2     | 8     4     9     |
 | 5     9     6     | 38    48    34    | 1     2     7     |
 *-----------------------------------------------------------*
r6c8<>79


Here's a list of some puzzles where I couldn't find your intended moves (not added to the list yet), could you post some grids that show them (as you see, I'm not very familiar with mr Frankenfish):

Code: Select all
11 Franken Swordfish
1........79.....4.....37...51.4..7.9...38.......1..8......2...3.75.......6...4.5.
..8..7964..96...........7.......1.3.7..2.41...6.5.........5....5....2.83.463....7

12 Franken Jellyfish
......5..87.5.4.9..3..9.....6..5...9.8....746.........4.1....2....4..1.7...8.....
.1..3.......29.5.17.....49.4..3.1..6........4.3.9..72...9.6.8..5..4.........1.2..

24 VWXYZ-wing
.763.........9...2....84.....3...16........4.2......8.1......2.6.9.75.....24.9..5

25 UVWYXZ-wing
.4..9...76.85....2..5....8....2..7..41..36........1.3.2..3...1.9...4.........9.2.
.9......4..78.....4..7.21.8..9.5.....6....54..7...1.6..51.....39..1.8.5....5..2.6

33 ALS xz-rule
9..2...8.24.........8.4...9......3.8.......7....591...6...7.......8..6...71..6.54

58 ALS xz-rule (A=3 cells)
7..3...6.....1...4.3...52......649..9.61........8.......3.2..5.2......1..154...7.

19 Three Grouped Strong Links (Grouped Turbot Chain)
1.8.9.....6.......52.4....1.......14...9...8...3..6.9..816.2.......7..6.49..5...2

42 UR+3N/2SL - I can find 2 UR-eliminations, but neither solves the puzzle.
.....49.623.7........5....11.........4....8...5...36.99....8......1..3.7..2..9.4.

50 Advanced BUG-Light Elimination
3...1..59..762....1...4.......97...5..4....7..6....2.4.7......1..5..8.3..91......
(r9c5-5-r7c5, r7c5-8-r7c7, r7c7-6-r7c1, SL:r7c7=5=r9c7, SL:r7c1=8=r9c1): r79c15|r79c7 => r9c5<>6
   ...  And then what?


And finally a list of the puzzles that didn't make it to the list, feel free to ask why and I'll try to recall it.

Code: Select all
18 Two strong links (Turbot Fish)
6...3.2..3..71..8...7..23.1...4......416.....82....1..4......5.1...739........6..

19 Three strong links (Turbot Chain)
1........746.....2...3..65.971..2.....2....16.....4.......8..2..9...13..58..4....
...64.5..54...3.8......7......89....1...6..3..97...6..9.5.......3..5.1.9......7..

23 WXYZ-wing
.2.13.9.795......4......1..18..7....3.....476...36.2......8..6.5...1.....4......3
.7......9....4.1.61.....28...36.......8423...5.6..8...3.....8...4..8.69....5....1
..3..1..7.9.56.3....6.......82.5........4.9...4.6.8......89...2..5....7982...76..

24 VWXYZ-wing
.8.5.......1......9..1.45..7.2..316.....1.7.5.....93.4........6...8..9...147.....
.......6..93.8......6.49......37....182...7.........1..1..538........67.36..981..

25 UVWYXZ-wing
.72.........52.....8.43.9.6........32..68.4.7..5........63...9.....58....3..1..8.

26 TUVWXYZ-wing
2.....93...57..........3..41..2....5.4....61...7........3..426..68.2...........9.
....4..6...53.9....97............4.991.2.....58..17....7.6......2...37..8.......2

9 Finned X-wing
6..........7...64.....92.1...4..79...3..1.42.......1.6..32....5.4.5......2....... 
1..5.9....4.....788..3..9..7..8..4......6.1...62.7..3.4...5......7...35....1...8. 
.6.7..8.......3..2..2.8..9..1....4.....3...6764.1............5.82..76.......29..4

10 Finned Swordfish
......6....569..7..2....5..3.9.....4....2.1.....4.7.....391..5..4..7...2..1..3.4.
......6....569..7..2....5..3.9.....4....2.1.....4.7.....391..5..4..7...2..1..3.4.
8..5..9.7..1...8..2.........6.......4..6.1...7.3.9..2...697.....7.....8.9...826..

21 XY-wing
...82....7.34.6...5.......79......5..3.5....4...2.4.....9...38.26..7......4..12..
.......5.6.....91.4....9...2..8.16..3.1.6....8..5......2.....87.3..9.52....34....

32 7-node XY-chain
...9..7.5.7.....1..3.4........6....8.6.27.9.4...5.4.7.9.13...6.7....24..4.....5..

9 X-wing
.8..7..9.......81.7.6..4...5.....9...3.92....1..8....64....5..1....1..8....6..4..
.85...9.......9....6.5..1....3....48..1..4.2..5..3.......62...39.......5...7.1...
.....7.8.8.4.6.3......1.....9..36...7....4.5.54....69.........8...7..9...7.45..1.

12 Franken Jellyfish (2 per puzzle)
..1...9......2...54.81.9.7..1..63..8..7.......3..1....2..7..15....6..82.3........
..5......94..7.....165.9..4....9...8.....7..21.3...67...7..4..639.......6..1.5...

10 Franken Swordfish (2 per puzzle)
...3..9.2..7..5..44...9..8....5.3798...........671....7..9..8.5.......2...52...4.


RW
Last edited by RW on Fri Jun 30, 2006 4:07 am, edited 1 time in total.
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Postby ronk » Thu Jun 29, 2006 9:07 pm

RW wrote:One of your puzzles had a very nice BUG-lite patterns of this type:

Code: Select all
ab .  . |ab .  . |ab .  .
ab .  . |ab .  . |ab .  .
ab .  . |ab .  . |ab .  .

Two digits 'ab' cannot be in the same column of three adjacent boxes.

If that's a BUG-Lite, then we need a revised definition here where ...
Jeff wrote:A BUG-Lite is a partial BUG pattern that exhibits similar properties of a BUG where all nodes in the pattern are bivalue and if a candidate exists in a row, column, or box, it shows up exactly twice.

In your exemplar, each candidate shows up exactly three times in each row, column, and box. In the absence of such a redefinition then, I view your example as a selective overlay of two (1st and 4th, 1st and 5th, e.g.) of the following BUG-Lites that do fit the definition.
Code: Select all
1:
ab .  . |ab .  . |.  .  .
ab .  . |.  .  . |ab .  .
.  .  . |ab .  . |ab .  .

2:
ab .  . |ab .  . |.  .  .
.  .  . |ab .  . |ab .  .
ab .  . |.  .  . |ab .  .

3:
ab .  . |.  .  . |ab .  .
ab .  . |ab .  . |.  .  .
.  .  . |ab .  . |ab .  .

4:
ab .  . |.  .  . |ab .  .
.  .  . |ab .  . |ab .  .
ab .  . |ab .  . |.  .  .

5:
.  .  . |ab .  . |ab .  .
ab .  . |ab .  . |.  .  .
ab .  . |.  .  . |ab .  .

6:
.  .  . |ab .  . |ab .  .
ab .  . |.  .  . |ab .  .
ab .  . |ab .  . |.  .  .


RW wrote:..8...2..9.......72.7....934...9...6....2.........31.5.....8....5.43.....6...7.84

That starting grid doesn't match the candidate grid that follows.

[edit: corrected the last grid]
Last edited by ronk on Thu Jun 29, 2006 7:32 pm, edited 1 time in total.
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Postby RW » Thu Jun 29, 2006 10:14 pm

ronk wrote:In the absence of such a redefinition then, I view your example as a selective overlay of two (1st and 4th, 1st and 5th, e.g.) of the following BUG-Lites that do fit the definition.


In the absence of a definition, I don't care and keep solving puzzles. And btw, it's a non-selective overlay of all 6 patterns.

ronk wrote:That starting grid doesn't match the candidate grid that follows.


??? Splitting the row gives
Code: Select all
.9. .8. .7.
... 3.. .52
65. 4.. ...

8.7 ..3 1.6
1.. ... ...
9.. 8.4 ...

... .6. 4.7
78. ... ...
... 2.. ...
which seems to match the candidate grid very well.

RW
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Postby Ocean » Thu Jun 29, 2006 11:32 pm

Great job finding instructive puzzles, Mike! Gives this thread a very welcomed diversity.

Also: Good job with verifying all the puzzles, RW!

Just a comment to this:
RW wrote:An example, your last TUVWXYZ-wing puzzle:
Code: Select all
....4..6...53.9....97............4.991.2.....58..17....7.6......2...37..8.......2
 *-----------------------------------------------------------*
 | 1     3     8     | 7     4     2     | 9     6     5     |
 | 6     4     5     | 3     8     9     | 12   *27   *17    |
 | 2     9     7     | 1     5     6     | 38    348   348   |
 |-------------------+-------------------+-------------------|
 | 7     6     2     | 58    3     58    | 4     1     9     |
 | 9     1     3     | 2     6     4     | 58    578   78    |
 | 5     8     4     | 9     1     7     |-236  *23   *36    |
 |-------------------+-------------------+-------------------|
 | 3     7     19    | 6     2     58    | 158   4589  148   |
 | 4     2     16    | 58    9     3     | 7     58   *16    |
 | 8     5     69    | 4     7     1     | 36    39    2     |
 *-----------------------------------------------------------*

As the name suggests, a TUVWXYZ-wing makes use of 7 cells. I found a 5-cell XY-chain to eliminate '3' from r6c7. If this had solved the puzzle, I'd added it as a 5-cell XY-chain. As it still requires a XY-wing after the chain, I didn't add the puzzle anywhere. I'm sure nobody will fully agree on all desicions I made, feel free to comment.

This alternative chain solves the puzzle:
Code: Select all
....4..6...53.9....97............4.991.2.....58..17....7.6......2...37..8.......2
 *-----------------------------------------------------------*
 | 1     3     8     | 7     4     2     | 9     6     5     |
 | 6     4     5     | 3     8     9     | 12    27    17    |
 | 2     9     7     | 1     5     6     | 38    348   348   |
 |-------------------+-------------------+-------------------|
 | 7     6     2     | 58    3     58    | 4     1     9     |
 | 9     1     3     | 2     6     4     | 58    578   78    |
 | 5     8     4     | 9     1     7     | 236  -23   *36    |
 |-------------------+-------------------+-------------------|
 | 3     7     19    | 6     2     58    | 158   4589  148   |
 | 4     2    *16    | 58    9     3     | 7     58   *16    |
 | 8     5    *69    | 4     7     1     | 36   *39    2     |
 *-----------------------------------------------------------*

It involves the same number of cells, but it's an xy-chain (the previous was an xy-ring), "cycle-length" is 6 if the discontinuity cell r6c8 is counted. There is even a third alternative chain (same length) that also solves the puzzle (by eliminating the '3' in r9c8). Both the latter chains solve the puzzle with one single extreme technique.

I don't know if the xy-ring is regarded easier than an equally sized xy-chain (and therefore higher priority), or if the somewhat artificially defined counting defines the ring as shorter than other chains. But since the same number of cells are involved, they could also be regarded as equal alternatives, and the puzzle could be put in the "xy-chain (6)" category.
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Postby ronk » Thu Jun 29, 2006 11:51 pm

RW wrote:In the absence of a definition, I don't care and keep solving puzzles. And btw, it's a non-selective overlay of all 6 patterns.

Keepin' on keepin' on is a good thing but, if it's actually an overlay of BUG-Lite patterns, it's helpful to others to describe things as they are. And I described it as a selective overlay of two BUG-Lite patterns so that others would know it was sufficient to detail only two ... not that I didn't know an overlay of all six also worked.

RW wrote:
ronk wrote:That starting grid doesn't match the candidate grid that follows.

??? Splitting the row gives (...) which seems to match the candidate grid very well.

Sorry, I meant to post the second one.
Code: Select all
..8...2..9.......72.7....934...9...6....2.........31.5.....8....5.43.....6...7.84
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Postby Mike Barker » Fri Jun 30, 2006 2:21 am

Here is what I was thinking. I've been continuing to modify my solver to choose simpler techniques so not all passed through a retest:

Code: Select all
24 VWXYZ-wing
.763.........9...2....84.....3...16........4.2......8.1......2.6.9.75.....24.9..5
+-------------------+---------------------+------------------+
|  4589     7     6 |       3   25     12 |    48   159   18 |
|  3458   138  1458 |    1567    9    167 |  3478   135    2 |
|   359     2   #15 |     157    8      4 |    37  1359    6 |
+-------------------+---------------------+------------------+
|  4578   *89     3 |    5789  245    278 |     1     6   79 |
|   578 *1689  *158 |  156789  356  13678 |     2     4  379 |
|     2  *169   -14 |    1679  346   1367 |     5     8  379 |
+-------------------+---------------------+------------------+
|     1     5     7 |      68   36    368 |     9     2    4 |
|     6     4     9 |       2    7      5 |    38    13   18 |
|    38    38     2 |       4    1      9 |     6     7    5 |
+-------------------+---------------------+------------------+

25 UVWXYZ-wing
.4..9...76.85....2..5....8....2..7..41..36........1.3.2..3...1.9...4.........9.2.
+---------------------+-------------------+--------------------+
|    13      4      2 |   168      9   38 |   1356   56      7 |
|     6    379      8 |     5     17  347 |   1349   49      2 |
|   137    379      5 |  1467      2  347 |  13469    8   3469 |
+---------------------+-------------------+--------------------+
|  *358  *3568   *369 |     2    #58 -458 |      7  469      1 |
|     4      1    *79 |   789      3    6 |      2   59    589 |
|   578      2   *679 |  4789    578    1 |   4689    3   4689 |
+---------------------+-------------------+--------------------+
|     2   5678    467 |     3   5678  578 |  45689    1  45689 |
|     9   3568    136 |    18      4    2 |   3568    7   3568 |
|  3578  35678  13467 |   178  15678    9 |  34568    2  34568 |
+---------------------+-------------------+--------------------+

33 ALS xz-rule
9..2...8.24.........8.4...9......3.8.......7....591...6...7.......8..6...71..6.54
+--------------------+--------------------+----------------+
|     9  1356   3567 |     2   135    357 |    4    8  135 |
|     2     4    357 |  1379  1358  35789 |  157    6  135 |
|  1357   135      8 |     6     4    357 |  157    2    9 |
+--------------------+--------------------+----------------+
|   145  1259   2459 |    47     6    247 |    3   19    8 |
|   #14  1269   2469 |   #34    38   2348 | #159    7  #15 |
|   378    38     37 |     5     9      1 |    2    4    6 |
+--------------------+--------------------+----------------+
|     6  3589   3459 |  1349     7   3459 |  189  139    2 |
|   345  2359  23459 |     8   135   3459 |    6  139    7 |
|    38     7      1 |   *39     2      6 |  -89    5    4 |
+--------------------+--------------------+----------------+

58 ALS xz-rule (A=3 cells)
7..3...6.....1...4.3...52......649..9.61........8.......3.2..5.2......1..154...7.
+---------------------+-------------------+---------------------+
|     7  24589  12489 |     3   #48   #28 |    158     6    158 |
|  *568  *2568    *28 | -2679     1 #2678 |   3578   389      4 |
|  1468      3    148 |   679  #478     5 |      2    89    178 |
+---------------------+-------------------+---------------------+
|  1358   2578   1278 |   257     6     4 |      9   238  13578 |
|     9  24578      6 |     1   357   237 |   3578  2348   3578 |
|  1345   2457   1247 |     8  3579  2379 |  13567   234  13567 |
+---------------------+-------------------+---------------------+
|   468  46789      3 |    67     2     1 |    468     5    689 |
|     2  46789   4789 |   567  3578  3678 |   3468     1   3689 |
|    68      1      5 |     4   389  3689 |    368     7      2 |
+---------------------+-------------------+---------------------+

42 UR+3N/2SL
.....49.623.7........5....11.........4....8...5...36.99....8......1..3.7..2..9.4.
+-------------------+-----------------+---------------+
|   578  178   1578 |  238  1238    4 |    9  237   6 |
|     2    3     16 |    7     9   16 |   45    8  45 |
|  4678    9   4678 |    5  2368   26 |   27  237   1 |
+-------------------+-----------------+---------------+
|     1    2    369 |  689   568 -567 |   47  *57  34 |
|    36    4    369 |  269    15 -157 |    8 *157  23 |
|    78    5     78 |   24   124    3 |    6   12   9 |
+-------------------+-----------------+---------------+
|     9   17  13457 |   34  3457    8 |  125    6  25 |
|   458   68    458 |    1  2456  256 |    3    9   7 |
|   357  167      2 |   36  3567    9 |   15    4   8 |
+-------------------+-----------------+---------------+

50 Advanced BUG-Light Elimination
3...1..59..762....1...4.......97...5..4....7..6....2.4.7......1..5..8.3..91......
(r9c5-5-r7c5, r7c5-8-r7c7, r7c7-6-r7c1, SL:r7c7=5=r9c7, SL:r7c1=8=r9c1): r79c15|r79c7 => r9c5<>6
+-------------+---------------+---------------+
|    3   4  2 |   8    1    7 |    6    5   9 |
|    9  58  7 |   6    2   35 |   14   14  38 |
|    1  58  6 |  35    4    9 |  378   28  27 |
+-------------+---------------+---------------+
|    2  13  8 |   9    7    4 |   13    6   5 |
|    5  13  4 |   2   68   16 |    9    7  38 |
|    7   6  9 |  35  358  135 |    2   18   4 |
+-------------+---------------+---------------+
|  *68   7  3 |   4  *56    2 |  *58    9   1 |
|   46   2  5 |   1    9    8 |   47    3  67 |
| *468   9  1 |   7 -356  356 | *458  248  26 |
+-------------+---------------+---------------+


Some new ones. Let me know how to number them so I can number future puzzles:
Code: Select all
39 UR+2rd
14..3...........6....845....2.....9..18......9.6....78.5.7..9..372.1...4..4.....2 ~

56 Nice Loop: r5c7=1=r6c7=8=r6c6-8-r5c6~2~r5c7 => r5c7<>2
.5....3.2.9....7...7.2...8....6.1.....9.3...7..2....64..835....51.8.6..........3. ~

63 ALS xz-rule (A=2 cells)
......9.........6742....3...5...4..3...1.2....87.9......2.81.....64...5.......274 ?>
+--------------------+--------------------+-------------------+
|     67   67   1358 |    35  1345    358 |     9  1248  1258 |
|  13589  139  13589 |     2  1345   3589 |  1458     6     7 |
|      4    2   1589 |  5679   156  56789 |     3    18   158 |
+--------------------+--------------------+-------------------+
|   1269    5    *19 |     8    67      4 |   -17  *129     3 |
|    369  369      4 |     1  3567      2 |   578    89   568 |
|   1236    8      7 |  #356     9   #356 |  #145  #124 #1256 |
+--------------------+--------------------+-------------------+
|     57    4      2 |    57     8      1 |     6     3     9 |
|    379  379      6 |     4     2    379 |    18     5    18 |
|  13589  139  13589 |  3569   356   3569 |     2     7     4 |
+--------------------+--------------------+-------------------+
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Postby RW » Fri Jun 30, 2006 8:46 am

ronk wrote:if it's actually an overlay of BUG-Lite patterns, it's helpful to others to describe things as they are.


Yes, but as I've already described it several times in several threads, I'm starting to hope that people understand it already.

ronk wrote:Sorry, I meant to post the second one.


Seems I messed up the copy/pasting, row fixed.

Ocean wrote:I don't know if the xy-ring is regarded easier than an equally sized xy-chain (and therefore higher priority), or if the somewhat artificially defined counting defines the ring as shorter than other chains. But since the same number of cells are involved, they could also be regarded as equal alternatives, and the puzzle could be put in the "xy-chain (6)" category.


The xy-ring is not regarded easier than an equally sized xy-chain. I check all the puzzles manually and didn't spot the xy-chains you mentioned. It is very likely that there are other puzzles in the list with XY-chains that I missed. Seeing the chain that you showed, I can put the puzzle into the "xy-chain" category.

Mike, thank you for the clarifications. The UR I had already seen, but simply missed one of the eliminations it allows. The question about the BUG-lite still remains: then what? Eliminating the '6' doesn't solve the puzzle.

I added the VWXYZ-wing and the ALS-puzzles to the list. I'm still a bit confused with the UVWXYZ-wing. The way I look at it, the elimination is obvious also without considering the cells r456c3. It's just a matter of considering hidden subsets instead of naked. Maybe my POV is not defined as a technique yet.

I'll look at your new puzzles later. The numbering isn't important, I give them numbers in the order I add them to the different categories, just to make it easier for people to refer to a certain puzzle if they have some questions.

RW
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Postby ravel » Fri Jun 30, 2006 9:53 am

RW wrote:The way I look at it, the elimination is obvious also without considering the cells r456c3. It's just a matter of considering hidden subsets instead of naked.

Please explain that (the other 3 marked cells obviously can be filled validly, when r4c6 is 5 or 8). Which hidden subsets ?
[Edit:] Ah, i see. You have 58 in c3, so a 5 and 8 in r4c56 would only leave 1 cell for 58 in box 4. Did you mean that ?
Code: Select all
------------
.42|.9.|..7
6.8|5..|..2
..5|.2.|.8.
------------
...|2..|7.1
41.|.36|2..
.2.|..1|.3.
------------
2..|3..|.1.
9..|.42|.7.
...|..9|.2.
------------
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Postby RW » Fri Jun 30, 2006 6:25 pm

ravel wrote:Ah, i see. You have 58 in c3, so a 5 and 8 in r4c56 would only leave 1 cell for 58 in box 4. Did you mean that ?


Code: Select all
.42|.9.|..7
6.8|5..|..2
..5|.2.|.8.
---+---+---
...|2..|7.1
41.|.36|2..
.2.|..1|.3.
---+---+---
2..|3..|.1.
9..|.42|.7.
...|..9|.2.


Yes, 5 and 8 in box 1 says that at least one of them in box 4 has to be in row 4 (they cannot both be in r6c1). Then when I find that the only possible values in r4c5 are 58, I can pair that cell with r4c12, which has to hold the other of the two, and eliminate 5 and 8 from the rest of the row. I can also eliminate all numbers but 5 and 8 from r6c1, as obviously both 5 and 8 cannot go in r4c12 and leave r4c5 with no possible value.

RW
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