Let's build a zoo...

Advanced methods and approaches for solving Sudoku puzzles

Postby gsf » Tue Sep 05, 2006 1:44 pm

Mike Barker wrote:
Code: Select all
Four Grouped Strong Links: r46c4=7=r46c5-7-r23c5=7=r1c46-7-r1c23=7=r2c3-7-r7c3=7=r7c56~7~ => r89c4<>7
+--------------------+--------------------+-----------------------+
|     5  *478  *4678 |  *2378     9  *278 |   1237  23467  123467 |
|    49     3   *479 |      6   *27     1 |      8      5     247 |
|    68     1      2 |      4  *378     5 |     37    367       9 |
+--------------------+--------------------+-----------------------+
|   469  2459   1469 |  *2579  *267     3 |   1257   2467       8 |
|     7  2458   3468 |    258     1    28 |      9   2346    2346 |
|  3689  2589  13689 | *25789 *2678     4 |  12357   2367   12367 |
+--------------------+--------------------+-----------------------+
|   389     6  *3789 |      1 *2378 *2789 |      4     89       5 |
|     2  4789  34789 |    -38     5   789 |      6      1      37 |
|     1   789      5 |    -38     4     6 |    237     89     237 |
+--------------------+--------------------+-----------------------+


this one solves with 2 naked pairs and singles
gsf
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Postby Mike Barker » Tue Sep 05, 2006 2:24 pm

My mistake, I posted the puzzle after the elimination.
Code: Select all
+--------------------+--------------------+-----------------------+
|     5  *478  *4678 |  *2378     9  *278 |   1237  23467  123467 |
|    49     3   *479 |      6   *27     1 |      8      5     247 |
|    68     1      2 |      4  *378     5 |     37    367       9 |
+--------------------+--------------------+-----------------------+
|   469  2459   1469 |  *2579  *267     3 |   1257   2467       8 |
|     7  2458   3468 |    258     1    28 |      9   2346    2346 |
|  3689  2589  13689 | *25789 *2678     4 |  12357   2367   12367 |
+--------------------+--------------------+-----------------------+
|   389     6  *3789 |      1 *2378 *2789 |      4     89       5 |
|     2  4789  34789 |   -378     5   789 |      6      1      37 |
|     1   789      5 |   -378     4     6 |    237     89     237 |
+--------------------+--------------------+-----------------------+
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Postby ronk » Tue Sep 05, 2006 7:06 pm

Mike Barker wrote:(...) the best part is that it is also solved with a Franken Squirmbag (not your everyday "there's a smaller fish which can also make the same elimination" Squirmbag, but I believe an "this proves that Squirmbags exist without a smaller fish elimination" Squirmbag)

Your "franken squirmbag" (N=5 almost constrained sets) ...
Code: Select all
 .  7  7 |  7  .  7 |  7  7  7
 .  . *7 |  . *7  . |  .  . *7
 .  .  . |  . *7  . | *7 *7  .
---------+----------+----------
 .  .  . | *7 *7  . | *7 *7  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . | *7 *7  . | *7 *7 *7
---------+----------+----------
 .  . *7 |  . *7 #7 |  .  .  .
 .  7  7 | -7  .  7 |  .  .  7
 .  7  . | -7  .  . |  7  .  7
 
Base: r23467
Cover: c345 & b36
Fin: r7c6
Exclusions: r89c4

.. has this complementary "franken swordfish" (N=3 almost constrained sets):
Code: Select all
 . *7  7 |  7  . *7 |  7  7  7
 .  .  7 |  .  7  . |  .  .  7
 .  .  . |  .  7  . |  7  7  .
---------+----------+----------
 .  .  . |  7  7  . |  7  7  .
 .  .  . |  .  .  . |  .  .  .
 .  .  . |  7  7  . |  7  7  7
---------+----------+----------
 .  .  7 |  .  7 #7 |  .  .  .
 . *7  7 | -7  . *7 |  .  . *7
 . *7  . | -7  .  . | *7  . *7
 
Base: c26 & b9
Cover: r189
Fin: r7c6
Exclusions: r89c4
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Postby Mike Barker » Wed Sep 06, 2006 12:39 am

I guess its how you define a fish. I've always used the requirement that the base set be "n" rows or columns. The dual for the Squirmbag uses a box and thus, in my accounting, is not a fish. It would be better if even this dual didn't exist (which I believe is what happens in some of the examples here, however, I was happy with even finding this guy given the other constraints of the zoo.
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Postby Mike Barker » Fri Sep 08, 2006 6:49 pm

This latest update includes a puzzle from Mars and a puzzle from Venus. The Martian puzzle is a carnivorous BUG+4X (think of a Type 3/3B UR with 4 non-bivalued cells and the elimination is part of the BUG. For the distaff side there is a 7-cell XY-ring which also includes an XY-wing. It can also be solved with a 3-element nice loop. I guess many would consider a ring to be a really nice loop! I won't post the pencil marks unless asked, because unlike the last set these should be pretty obvious.

Code: Select all
#23 BUG+4X (Type 3/3B)
...5...79.6.9..1.3.7.1...2...8.......5...461..1.....58.9...7........14....3....97 #23.17

#55 7-node XY-ring
4...7.8........5..6....1.42...8.......5.1.4..3.29......7...93.1....46..5....2.... #55.1y(3-element Nice Loop)
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Postby Mike Barker » Sun Sep 17, 2006 8:00 pm

Here are a couple of new additions to the zoo that are pretty cool.

Code: Select all
#23 BUG+4x (Type 2/2B)
82......6.3.....52.6...81.36....3..12...4....1...6.2.....6.4....9.3...47...5....9 #23.18

#56 Jellyfish (basic, finned, big fin, and franken)
..8..6.4.........6..9...71...7..9....3.1...8..4.5...3.2.6..8.......1..9.1...3.... #56.1 (Franken/Big Fin)

#65 11-node XY-chain
..65.....18..4.9.5......3....846.5....2.....4.59.8..6......614..3....6.......7.83 #65.1y
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Postby daj95376 » Sun Sep 17, 2006 11:25 pm

Mike Barker,

Your zoo examples are great, but you have gone overboard with the pound (#) character. It should only be used to indicate comment information follows ... like in ... group headings and trailing comments at the end of a puzzle. Many of your latest additions have the pound character in front of the puzzle as well. This will cause most solvers to skip over them.
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Postby Mike Barker » Mon Sep 18, 2006 5:11 am

My goal in the zoo was to get two examples of each technique which required only singles. Originally as I found simpler puzzles I would delete the more complex ones, but have posted them and not really wanting to loose them, I started comment them out. There is no real reason to do this, so I've uncommented these. I also copied puzzles when one puzzle demonstrated several techniques. This isn't strictly valid for the later techniques so I commented out the duplicates. I've left these commented out.

I've also distinguished between continuous and discontinuous nice loops. For discontinuous loops I've distinguished between those where the end nodes share a house, but a valid link can't be made (a label discontinuity) and those where the end nodes don't share a house (a locations discontinuity). In the first case elminations are within the nodes. In the second they are outside of the nodes. Interestingly label discontinuities seem to dominate. I don't know if this is a characteristic of my solver or a general situation.
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Postby ronk » Sun Sep 02, 2007 10:16 pm

here Mike Barker wrote:
Code: Select all
#65 10-node XY-chain
......1..2......96.53.1..7....74...3...5.1.8.7.9.3.....2.......9.56.4..7.4.8.....

Mike, that's an impressive list of zoo critters. Thanks for posting them.

I've been examining some of the longer XY-chains. For the above, the best I could come up with was 9 XY-nodes plus the elimination cell. Are you counting the elimination cell as a node:?:
Code: Select all
 468    9      68-4   |I34     67     267    | 1      2345   2458
 2      7      1      |H34     8      5      |G34     9      6
 468    5      3      | 9      1      26     | 248    7      248
----------------------+----------------------+---------------------
 5      1     B28     | 7      4      89     | 269    26     3
 34    D36    A24     | 5      69     1      | 7      8      29
 7     C68     9      | 2      3      68     | 45     45     1
----------------------+----------------------+---------------------
 368    2      678    | 1      579    379    | 345689 3456   4589
 9     E38     5      | 6      2      4      |F38     1      7
 1      4      67     | 8      579    379    | 23569  2356   259

    A       B       C       D       E       F       G       H       I
-4-r5c3 -2-r4c3 -8-r6c2 -6-r5c2 -3-r8c2 -8-r8c7 -3-r2c7 -4-r2c4 -3-r1c4-4- 

implies r1c3<>4
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Postby Mike Barker » Sun Sep 02, 2007 10:29 pm

Thanks:)

Although I originally I only counted the number of bivalues, my understanding was for XY-chains the elimination cell should be counted in the size, that way the number of nodes equals the number of links. I think Jeff supported this POV. On the other hand, with nice loops I count the number of "elements" (strong inferences) which I consider to be a better measure than the number of nodes or links.
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Postby ronk » Tue Sep 04, 2007 11:19 am

Mike Barker wrote:Although I originally I only counted the number of bivalues, my understanding was for XY-chains the elimination cell should be counted in the size, that way the number of nodes equals the number of links. I think Jeff supported this POV.

This is like déjà vu all over again." -- Yogi Berra

This topic seemed all too familiar, so I searched and found a prior discussion starting ...
here where ronk wrote:
Ocean wrote:This one has an even shorter xy-chain (lenght 4, from r9c1 via r2c1/r2c4 to r2c8), which eliminates the '5' from r9c8.

I've learned to count the "discontinuity" as well, so your chain is length 5 to me, and it's length 5 whether counting cells or links.

It appears for "length" that you are counting only the bi-valued cells. Is that correct?

So while you've changed in one direction, I've changed in the opposite.:D

For discontinuous loops, I now recognize that chain length and loop length are two different measures. When someone writes "10-node XY-chain", reference to chain length seems to be implied.

Jeff was a strong nice loop proponent, so his use length to mean loop length is not surprising. I think some also use the term cycle length. But ever since ...
gsf wrote:discontinuous cycle is an oxymoron
... I view cycle length as inappropriate for discontinuous loops.

Mike Barker wrote:On the other hand, with nice loops I count the number of "elements" (strong inferences) which I consider to be a better measure than the number of nodes or links.

Which is different than Stephen Kurzhals's count of "native strong inferences", at least when ALSs are involved, but I'm leaning in the same direction as you.
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Postby Steve R » Tue Sep 04, 2007 4:59 pm

When I went to school we were taught to say the length of a chain was, say, 20 feet, 20 yards or 20 links.

If we said its length was 20 we were thrashed.

Steve
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