The New Sudoku Players' Forum

by **ronk** » Thu Mar 29, 2007 11:54 am

Mike Barker wrote:I've just implemented Obi-Wahn's "endo fin" approach and was checking things out. It turns out the NoFish7 actually is a fish with 1's. It just happens to be an Endofin Mutant Whale! Here she blows:

NoFish7
Endofin Mutant Whale: r368c26b5/r4c37b12,endofin=r6c4,fins=r8c45,r79c6: r3c1457|r6c344|r8c3457|r24c2|r1279c6|r4c45 => r9c4<>1

Congratulations on your implementation and on finding that fish.

Since you only have 5 sectors in the cover, you can add b8 to it and be left with only the endofin. (I'm a bit surprised Obi-Wahn's solver missed that.)

by **Obi-Wahn** » Fri Mar 30, 2007 9:19 am

I must admit that I've built in a bug in my program with some of the later changes, that wasn't present in my first attempt. With this bug my program simply skipped some possible combinations of base sectors and thus didn't find all Ultimate Fish anymore.

I've corrected this bug some time ago but forgot to mention that some of my NoFish examples actually contained Fish. I beg your pardon. This applies to NoFish14 and NoFish21 (for which I only published the initial states as a single line) which are solvable with Ultimate Fish.

For NoFish7 this only applies to the pattern of 1's (thanks a lot Mike), but it doesn't solve the entire puzzle.

[edit] This threads seems to be kind of a reference for single digit pattern exclusions that can not easily be explained. I have now automated the generation of diagrams, so here are some more patterns I didn't post before:

Code: Select all: NoFish13 .---------------.---------------.---------------. | 5 9 23 | 23 7 1 | 68 68 4 | | 8 1 4 | 9 6 23 | 23 5 7 | | 7 23 6 | 4 8 5 | 23 9 1 | :---------------+---------------+---------------: | 3 268 258 | 7 1 9 | 48 248 256 | | 4 78 9 | 235 235 6 | 1 78 235 | | 1 267 257 | 8 345 234 | 9 237 2356| :---------------+---------------+---------------: | 6 5 37 | 1 9 234 | 47 234 8 | | 9 348 38 | 6 234 7 | 5 1 23 | | 2 347 1 | 35 345 8 | 467 346 9 | '---------------'---------------'---------------' . . 3 | 3 . . | . . . . . . | . . 3 | 3 . . . 3 . | . . . | 3 . . ---------+---------+--------- . . . | . . . | . . . . . . | 3 3 . | . . 3 . . . | . 3 3 | . -3 3 ---------+---------+--------- . . 3 | . . 3 | . 3 . . 3 3 | . 3 . | . . -3 . 3 . | 3 3 . | . 3 . NoFish16 .---------------.---------------.---------------. | 279 1 279 | 5 3 279 | 4 6 8 | | 4 2679 5 | 2679 1279 8 | 129 27 3 | | 8 2679 3 | 269 129 4 | 1259 257 17 | :---------------+---------------+---------------: | 6 3 4 | 27 257 1 | 8 257 9 | | 5 279 1279| 3 8 6 | 12 4 17 | | 27 8 127 | 4 2579 279 | 125 3 6 | :---------------+---------------+---------------: | 279 5 279 | 8 279 3 | 6 1 4 | | 3 4 8 | 1 6 5 | 7 9 2 | | 1 279 6 | 279 4 279 | 3 8 5 | '---------------'---------------'---------------' 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 | . . . NoFish17 .------------------.------------------.------------------. | 3 4 7 | 56 2 56 | 9 1 8 | | 6 5 1 | 9 8 7 | 2 4 3 | | 9 8 2 | 1 4 3 | 5 7 6 | :------------------+------------------+------------------: | 8 69 34569| 2 7 56 | 1 356 459 | | 2 1 356 | 4 36 9 | 8 356 7 | | 45 7 3569 | 356 1 8 | 46 2 59 | :------------------+------------------+------------------: | 1 36 48 | 368 9 2 | 7 56 45 | | 47 369 69 | 367 5 1 | 346 8 2 | | 57 2 58 | 78 36 4 | 36 9 1 | '------------------'------------------'------------------' . . . | 6 . 6 | . . . . . . | . . . | . . . . . . | . . . | . . . ---------+---------+--------- . -6 6 | . . 6 | . 6 . . . 6 | . 6 . | . 6 . . . 6 | 6 . . | 6 . . ---------+---------+--------- . 6 . | 6 . . | . 6 . . 6 -6 | 6 . . | 6 . . . . . | . 6 . | 6 . . NoFish18 .------------------.------------------.------------------. | 1 23 2356 | 4 78 2367 | 367 359 3689 | | 2356 4 8 | 123 9 2367 | 1367 135 136 | | 7 9 36 | 5 18 36 | 2 4 18 | :------------------+------------------+------------------: | 8 5 37 | 6 2 1 | 9 37 4 | | 23 6 1237 | 9 4 8 | 5 1237 1237 | | 4 12 9 | 7 3 5 | 16 8 126 | :------------------+------------------+------------------: | 9 123 56 | 123 56 4 | 8 1237 1237 | | 235 8 12345| 123 157 2379 | 134 6 1239 | | 236 7 12346| 8 16 239 | 134 1239 5 | '------------------'------------------'------------------' . . . | . . . | . . . . . . | 1 . . | 1 1 1 . . . | . 1 . | . . 1 ---------+---------+--------- . . . | . . . | . . . . . 1 | . . . | . 1 1 . 1 . | . . . | 1 . 1 ---------+---------+--------- . 1 . | 1 . . | . 1 1 . . 1 | 1 1 . | 1 . 1 . . 1 | . -1 . | 1 1 .

by **DanG** » Mon Apr 23, 2007 5:19 pm

Obi-Wahn wrote:This threads seems to be kind of a reference for single digit pattern exclusions that can not easily be explained. I have now automated the generation of diagrams, so here are some more patterns I didn't post before:
............

...instead there are some Broken Wing (BW) patterns there. Also you did not mentioned using BW, you always showed some valid exclusions. Does your solver do that or you do them manually? :?:

Dan

by **Obi-Wahn** » Mon Apr 23, 2007 6:14 pm

In all the examples above, where I didn't mention it, there's no Ultimate Fish or Broken Wing pattern without a remote fin or guardian respectively, that my solver could recognize.
The exclusions where identified by my solver using a technique that SudoCue calls template check/nishio. It only requires information about the pattern of all candidates of a single digit but uses brute force to generate all possible solutions for this digit. Any candidate that isn't part of at least one solution can be eliminated.
My goal was to explain all these exclusions with a pattern method without using chains, but neither Ultimate Fish in its most general form nor Broken Wings will do the trick entirely.

I couldn't identify a Broken Wing pattern in the last example that uses only guardians directly seen by the exclusion candidate. However, if you allow remote guardians you can almost always find a BW pattern (but that requires an AIC chain to explain the connection between the remote guardian and the exclusion cell in my POV).

by **daj95376** » Tue Apr 24, 2007 6:55 am

Obi-Wahn wrote:I couldn't identify a Broken Wing pattern in the last example that uses only guardians directly seen by the exclusion candidate.

Trying to replace remote guardian cells with one that sees the elimination cell. Does this seem logically correct?

Code: Select all: NoFish18: Traditional guardian cells (?) (*) School of Turbots containing Broken Wing as sub-pattern (#) Guardian cells preventing SoT/BW [r9 c378 ] => ![r9c5] [r2 c 78 ] => ![r3c9] => [r3c5] => ![r9c5] (remote elimination) [r5678c 9] => ![r3c9] => [r3c5] => ![r9c5] (remote elimination) ^-----------------------------------^ | 1 . . | . . . | . . . | | . . . | 1 . . | #1 #1 1 | | . . . | . 1 . | . . 1 | |-----------+-----------+-----------| | . . . | . . 1 | . . . | | . . *1 | . . . | . *1 #1 | | . *1 . | . . . | *1 . #1 | |-----------+-----------+-----------| | . *1 . | #1 . . | . *1 #1 | | . . *1 | #1 #1 . | *1 . #1 | | . . #1 | . -1 . | #1 #1 . | ^-----------------------------------^

Code: Select all: NoFish18: All guardian cells see elimination cell (*) School of Turbots containing Broken Wing as sub-pattern (#) Guardian cells preventing SoT/BW [r9c378] => ![r9c5] [r3c5 ] => ![r9c5] ^-----------------------------------^ | 1 . . | . . . | . . . | | . . . | 1 . . | 1 1 1 | | . . . | . #1 . | . . 1 | |-----------+-----------+-----------| | . . . | . . 1 | . . . | | . . *1 | . . . | . *1 1 | | . *1 . | . . . | *1 . 1 | |-----------+-----------+-----------| | . *1 . | #1 . . | . *1 1 | | . . *1 | #1 #1 . | *1 . 1 | | . . #1 | . -1 . | #1 #1 . | ^-----------------------------------^

[r3c5] prevents [r3c9] from eliminating [r2c789] and [r5678c9], thus preventing the SoT.

[Edit: Added guardian cells in box 8 as per ronk's suggestion. Thanks.]

by RW » Tue Apr 24, 2007 12:51 pm

daj95376 wrote:
Code: Select all
NoFish18: All guardian cells see elimination cell (*) School of Turbots containing Broken Wing as sub-pattern (#) Guardian cells preventing SoT/BW [r9c378] => ![r9c5] [r3c5 ] => ![r9c5] ^-----------------------------------^ | 1 . . | . . . | . . . | | . . . | 1 . . | 1 1 1 | | . . . | . #1 . | . . 1 | |-----------+-----------+-----------| | . . . | . . 1 | . . . | | . . *1 | . . . | . *1 1 | | . *1 . | . . . | *1 . 1 | |-----------+-----------+-----------| | . *1 . | 1 . . | . *1 1 | | . . *1 | 1 1 . | *1 . 1 | | . . #1 | . -1 . | #1 #1 . | ^-----------------------------------^

[r3c5] prevents [r3c9] from eliminating [r2c789] and [r5678c9], thus preventing the SoT.

You still take in consideration the remote guardian cells (r5678c9). I don't see why this would be any better than confessing that you use a short chain to eliminate all guardians...

RW

by **daj95376** » Tue Apr 24, 2007 3:02 pm

[Withdrawn: mute point]

[r9c5] doesn't cause SoT/BW without help from [r3c9], so [r9c5] can't be expected to 'see' all of the guardian cells by itself. Thus, some (remote) guardian cells can be expected to need a chain back to [r9c5].

by **DanG** » Tue Apr 24, 2007 6:08 pm

Here is a real challenge for us all, because there is no hint for the target cells as on Obi-Wahn's NoFish grids.
GD1..4 may or may not contain an elimination cell(s) but obviously at least one or more of them will.
Please use whatever method you like and rate the difficulty (provided you are honest about it).
After a week or so I will post the whole puzzles.

Code: Select all: GD01 x . . | . x x | . . . . . . | . . . | . . X . . x | x . . | . . . ---------+----------+--------- . x . | x . x | . x . x . x | . x x | x . . x x x | . x . | x . . ---------+----------+--------- x . . | x . . | . x . . . x | . x x | . x . x x x | . x x | x x . GD02 . . . | x x . | . x . . . . | x . x | . . x . . X | . . . | . . . ---------+----------+--------- . x . | . x . | . . x . . . | x . x | x x . x x . | x x x | . . . ---------+----------+--------- . . . | x . x | x . . x x . | x x . | x x . . x . | x . . | . . . GD03 . . . | . . . | . X . . x x | x . . | . . . . . x | . x . | . . . ---------+----------+--------- x . . | . . x | . . x . x . | x . . | . . x . x . | x . x | x . . ---------+----------+--------- . x x | . x . | . . x x . . | . x x | x . . x . . | . . x | x . . GD04 . x . | . . . | . . x . . . | . X . | . . . . x x | . . . | x . x ---------+---------+--------- x . x | . . x | . x x x x . | x . . | . x . x . . | x . x | x . . ---------+---------+--------- x x x | . . x | x . . . x . | x . . | . x . x . . | x . . | . . x

EDIT: No solvers please.
Dan

by **daj95376** » Fri May 18, 2007 8:56 pm

Your week or so is now over three weeks. So, here's a couple computer assisted solutions -- I hope.

Code: Select all: Puzzle GD01: (*) illegal pattern (#) direct guardian cells (@) remote guardian cells ^-----------------------------------^ | *x . . | . x x | . . . | | . . . | . . . | . . +x | | . . *x | *x . . | . . . | |-----------+-----------+-----------| | . x . | #x . x | . -x . | | @x . @x | . x x | x . . | | @x x @x | . x . | x . . | |-----------+-----------+-----------| | *x . . | *x . . | . #x . | | . . *x | . x x | . x . | | #x #x #x | . x x | -x x . | ^-----------------------------------^

Code: Select all: Puzzle GD03: (*) illegal pattern (#) direct guardian cells (@) remote guardian cells ^-----------------------------------^ | . . . | . . . | . +x . | | . x x | x . . | . . . | | . . x | . x . | . . . | |-----------+-----------+-----------| | *x . . | . . #x | . . *x | | . x . | -x . . | . . #x | | . x . | x . x | x . . | |-----------+-----------+-----------| | . *x *x | . @x . | . . *x | | *x . . | . x x | x . . | | *x . . | . . x | x . . | ^-----------------------------------^

by **DanG** » Sun May 20, 2007 7:13 am

Thank You daj95376 for showing some BWs. I had hoped somebody would spot them manually.

Certainly my solution does not count because I knew the CECs, but as promised here is my approach by using SoPT.

Code: Select all: School of Perfect Turbots (SoPT size 5). / . x | . / x | . . . x . / | . x / | . . . . . . | . . . | . . . < ---------+----------+--------- x . / | . / x | . . . . . . | . . . | . . . < / . x | . x / | . . . ---------+----------+--------- . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ^ ^ "/" cell with NO "x" candidate. "<" and "^" marks location of "corridors"

We may call the 4 boxes containing SoPT the SoPT habitat (here b1245), and the other boxes adjacent to SoPT the SoPT neighborhood (here b3678).
The "<" and "^" marks along the grid sides show the location of the 4 "corridors".
If instead of SoPT would be a valid pattern ( i.e. double tier X-wing), the corridors inside that pattern will be empty and the X placement in the corridors will take place only in the neighboring boxes. Therefore SoPT does not exist when all "x" candidates are restricted to its 4 rows and 4 columns! A SoPT needs some degree of freedom outside its habitat.. in the neighboring boxes. As we may see later, at least one corridor is used for repairing SoPT and at least one SoPT line (row/col) is released for neighboring boxes use.
There are some variants of the basic SoPT due to "splitting" of one or more of the turbot cells "tx".

Code: Select all: / . tx | . / tx | . . . tx . / | . tx / | . . . . . . | . . . | . . . < ---------+----------+--------- tx . / | . / tx | . . . . . . | . . . | . . . < / S tx | . tx / | . . . ---------+----------+--------- . x S | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ^ ^ SoPT cells marked with "t" "S" pair of splitting cells from a "tx"

Here r6c3 cell splits into two "S" candidates which go together (either true or false) as on a X-Wing. r7c2 completes the pattern into a simple dead end, but any strong link into b7,c23 will do. The splitting cells "S" migrate one into same box corridor as tx, say row/column, the other one outside SoPT habitat on corresponding column/row.
We may (or may not) have turbot cells splitting invading every corridor. Sometime when such split-cells occur, the corresponding turbot cell "tx" could be missing "Sashimi style":

Code: Select all: / S tx | . / tx | . . . tx . / | . t. / | . x . . . . | . S . | . S . < ---------+----------+--------- t. . / | . / tx | x . . S . . | . . S | S . . < / S t. | . tx / | . . . ---------+----------+--------- . . S | . . . | . . x . . . | . . . | . . . . x . | . . . | . . x ^ ^

With no other "x" candidates within/around the pattern, the SoPT and all its variants (with "S" cells) are invalid patterns because trying to place the X number in any of the pattern cell result in one empty sector. Certainly the pair of "S" are NOT guardians, simply because they cannot repair SoPT.

Where are the Guardians?

Code: Select all: / . tx | . / tx | . . . tx . / | . tx / | . . . . . . | . . . | . . . < ---------+----------+--------- tx . / | . / tx | . . . . . . | . . . | . . . < / . tx | . tx / | . . . ---------+----------+--------- . . . | . . . | . . . G . . | . . . | . . . . . . | . . . | . . . ^ ^

Here G is supposed to be a classical guardian as we know from Rod Hagglund's BW. If G=X, it cancel the two "tx"s on c1 which results in c3 "tx"s = true! It must be another cell inside SoPT habitat doing the repair.

Code: Select all: Type I, guardians: / 1G tx | . / tx | . . . tx 2G' / | . tx / | . . . . . . | . . . | . . . < ---------+----------+--------- tx 2G / | . / tx | . . . . . . | . . . | . . . < / 1G'tx | . tx / | . . . ---------+----------+--------- . . 2G | . . . | . . . 1G . . | . . . | . . . . . . | . . . | . . . ^ ^

Here the external 1G (b7) is paired with internal 1G (b1) or 1G' (b4) and likewise for 2G.. Note since external G takes c1 the internal Gs are shifted into the parallel corridor c2, but align on same line (row/col) with the other sloper's cell. The reverse is true, i.e. placing one of the internal Gs first.
That is to say, the SoPT could be repaired by placing a Guardian inside its habitat in a corridor and releasing one SoPT line (row/col) for its neighboring boxes use.

Code: Select all: Type II, guardians / . tx | . / tx | H1 . . tx . / | . tx / | . H2 . . H . | . . . | . . . < ---------+----------+--------- tx . / | . / tx | . . . . . . | . . . | . . . < / . tx | . tx / | . . . ---------+----------+--------- H1 . . | . . . | . . . . . H2| . . . | . . . . . . | . . . | . . . ^ ^ Type II, guardians H (Hidden cell) guardian H1 or H2 = pairs of external guardians candidates.

The Hidden cell "H" (b1) also repairs SoPT but since it is placed at the intersection of two corridors, one row and one column were released for neighboring boxes use "H1"s or "H2"s.
A particular solution X1,X2,..Xn is a mix of "G","H","t","S" candidates, but never all same letter solution (i.e. G1,G2..Gn).
Note: When Guardian candidates "G" or "H" overlap Split-cells "S", they should be given precedence. When this is the case, "S" cell is omitted till SoPT is unveiled.

Conclusion:
1. Possible Candidate Elimination Cell(s) (CEC) should be where the guardian corridors intersect neighboring box(es).
2. Possible CEC(s) cannot be in the corridors containing only split-cells ("S" here).
3. Guardian cells in corridors are always paired with Guardian cells in neighboring box(es), the later do not belong to any corridor.
4. CEC(s) must be "seen" by either all SoPT internal guardians or all SoPT external guardians (neighboring boxes).
5. The negative logic could be used instead, a template check/nishio.
A particular solution X1,X2,.. which lead to a contradiction, i.e. unveils a SoPT is obviously false.
If we find an unique solution: X1 -AIC-> X2 -AIC-> X3 ... => SoPT
where AIC is an Alternating Inference Chain , then X1 = CEC.
Moreover, if X1,X2.. == X2,X1.. then both X1 and X2 are CEC and so on.

Examples:
In the following examples nG is same with Gn. Preference was given to 1st notation due to more space to the left of "."

Following are Obi-Wahn's NoFish examples with some permutations for hiding the CEC.

Code: Select all: GD01 NoFish4 Filter=5 tx . . | . tx x | . . . . . . | . . . | . . X . . tx | tx . . | . . . ---------+----------+--------- . x . | x . x | . 2X . x . x | . x x | x . . x 3X x | . x . | x . . ---------+----------+--------- tx . . | tx . . | . x . . . tx | . tx x | . x . x x x | . x x | 1X x . < ^ ^ SoPT candidates marked "t" tx . . | . tx 3G | . . . . . . | . . . | . . X . . tx | tx . . | . . . ---------+----------+--------- . x . | 3G . x | . 2X . H . H | . H x | x . . H 3X H | . H . | x . . ---------+----------+--------- tx . . | tx . . | . 1GH . . . tx | . tx x | . 2GH . 2G 1H 1G | . 1G 2H | 1X x . < ^ ^ X1==X2 -> X3 single, the grid becomes: tx . . | . tx S | . . . . . . | . . . | . . X . . tx | tx . . | . . . ---------+----------+--------- . . . | . . . | .-2X . . . . | . S x | . . . . 3X . | . . . | . . . ---------+----------+--------- tx . . | tx . . | . . . . . tx | . tx S | . . . . . . | . . . |-1X . . < ^ ^

.. and c56 pairs of split-cells "S" do not repair SoPT.
CEC = 1X;2X

Code: Select all: GD02 NoFish8 Filter=2 . . . | x tx . | . tx . . . . | x . tx | . . tx . . X | . . . | . . . ---------+----------+--------- . x . | . tx . | . . tx . . . | x . tx | x tx . x x . | -x x x | . . . < ---------+----------+--------- . . . | x . x | x . . x x . | x x . | x x . . x . | x . . | . . . ^ ^

r9 and c1 coloring eliminate r6c4
b2356 contain SoPT marked "t"

Code: Select all: . . . | 3G tx . | . tx . . . . | 2G . tx | . . tx . . X | . . . | . . . ---------+----------+--------- . 1G . | . tx . | . . tx . . . | 2G . tx | S tx . x 1X . | -. S 1G | . . . < ---------+----------+--------- . . . | 4X . 3G | x . . x 2X . | 3X 2G . | x S . . x . | x . . | . . . ^ ^

Either of 1X;2X;3X;4X see guardian corridors r6 and c4 (or external guardians 1G,2G,3G) due to conjugate pairs in r9 and c1
r5c7 and r8c8 are not guardians but rather split-cells "S" from r5c8.
CEC = X1,X2,X3,X4 and the grid becomes:

Code: Select all: . . . | 3G tx . | . tx . . . . | 2G . tx | . . tx . . X | . . . | . . . ---------+----------+--------- . 1G . | . tx . | . . tx . . . | 2G . tx | S tx . x -. . | -. S 1G | . . . < ---------+----------+--------- . . . | -. . 3G | x . . x -. . | -. 2G . | x S . . x . | x . . | . . . ^ ^

Code: Select all: GD03 NoFish16 Filter=7 Rot CCW 90deg, flipped rows: 1,3; 5,6; 7,8 . . . | . . . | . X . . x x | x . . | . . . . . x | . x . | . . . ---------+----------+--------- x . . | . . x | . . x . x . | x . . | . . x . x . | x . x | x . . ---------+----------+--------- . x x | . x . | . . x x . . | . x x | x . . x . . | . . x | x . .

Instead I'll use the original NoFish16 because it shows a triple SoPT for candidate numbers 2, 7 and 9.
Note the SoPT habitat is identical for 2,7 and 9. The only difference is in candidate number positions in the neighboring boxes.

Code: Select all: NoFish16 After SSTS: Filter 2 tx . G1| . . tx | . . . . tx . | G tx . | HS HS . . S . | H S . | x x . ---------+---------+--------- . . . | x G2 . | . x . . G1 x | . . . | x . . S . x | . G2 GH| x . . ---------+---------+--------- tx . G1| . tx . | . . . . . . | . . . | . . 2 . tx . | G2 . tx | . . . Filter 7 tx . SG1| . . tx | . . . . tx . | G tx . | . HS . . S . | H S . | . x x ---------+---------+--------- . . . |-x G2 . | . x . . G1 x | . . . | . . x S . x | . G2 GH| . . . ---------+---------+--------- tx . SG1| . tx . | . . . . . . | . . . | 7 . . . tx . | G2 . tx | . . . Filter 9 tx . G1| . . tx | . . . . tx . | G tx . | HS . . . S . | H S . | x . . ---------+---------+--------- . . . | . . . | . . . . G1 x | . . . | . . . . . . | . G2 GH| . . . ---------+---------+--------- tx . G1| . tx . | . . . . . . | . . . | . 9 . . tx . | G2 . tx | . . . "t" mark of SoPT cells "G" Guardian candidate "H" Hidden-cell guardian candidate "S" Split-cell candidate

Only Filter 7 shows a CEC for r4c4:

Code: Select all: NoFish16 Filter 7 tx . S1| . . tx | . . . . tx . | . tx . | . S2 . . S2 . | . S2 . | . x . ---------+---------+--------- . . . |-X1 . . | . x . . . . | . . . | . . X2 S1 . x | . . . | . . . ---------+---------+--------- tx . S1| . tx . | . . . . . . | . . . | 7 . . . tx . | . . tx | . . .

A solution X1,X2 unveils SoPT with split-cells S1,S2. Therefore CEC=X1
Since r4c4 is a bivalue cell (2,7), a 2 is placed in it. Now the "Filter 2" grid can be examined:

Code: Select all: NoFish16 Filter 2 (with r4c4=2) tx . SG | . . tx | . . . . tx . | . tx . | . S2 . . S2 . | . S2 . | . x . ---------+---------+--------- . . . | 2 . . | . . . . G x | . . . | x . . S . x | . . . | x . . ---------+---------+--------- tx . SG'| . tx . | . . . . . . | . . . | . . 2 . tx . | . . tx | . . .

Since there is only one guardian in b4, we can place a "2" there:

Code: Select all: tx . G | . . t. | . . . . t. . | . tx . | . S2 . . . . | . S2 . | . x . ---------+---------+--------- . . . | 2 . . | . . . . 2 . | . . . | . . . . . . | . . . | 2 . . ---------+---------+--------- tx . G'| . tx . | . . . . . . | . . . | . . 2 . t. . | . . 2 | . . .

and the other "2"s follow: r6c7,r9c6 after which the puzzle unveils itself.

Code: Select all: GD04 NoFish9 Filter 7 Permutate floors 1->3,3->2,2->1 . X4 . | . . . | . . x . . . | . X . | . . . . x x | . . . | X3 . x ---------+---------+--------- x . X6| . . x | . x x x x . | x . . | . x . x . . |-X1 . x | x . . ---------+---------+--------- x x x | . . X2| x . . . x . | x . . | . X7 . X5 . . | x . . | . . x

There is no SoPT that I can spot here, however there is a CEC=r6c4
If r6c4=X1
then r7c6=X2 (single in b8)
r3c7=X3 (single in c7)
r1c2=X4 (single in r1)
r9c1=X5 (single in b7)
r4c3=X6 (single in b4)
r8c8=X7 (single in b9)
b6=empty!
I think daj95376 spotted a Leviathan in NoFish9 here.

by **daj95376** » Sat Sep 08, 2007 3:24 pm

Anyone looking for a Hidden Wing puzzle?

Code: Select all: *-----------------------* | 7 4 . | 8 . . | . . 6 | | . 9 . | . . . | . . . | | . . 8 | 4 7 . | . 9 . | |-------+-------+-------| | . . . | 2 . 7 | 4 . . | | . 5 . | 9 3 4 | . 8 . | | . . 4 | 5 . 1 | . . . | |-------+-------+-------| | . 7 . | . 4 3 | 8 . . | | . . . | . . . | . 2 . | | 5 . . | . . 8 | . 7 4 | *-----------------------*

Code: Select all: # Reduces nicely to this point, but fish only seem to generate [r1c7]<>1 # Where is there a Broken Wing ? # Does its guardian cells lead to [r9c7]<>1 ? *--------------------------------------------------------------* | 7 4 125 | 8 159 259 | 1235 13 6 | | 126 9 1256 | 3 15 256 | 7 4 8 | | 3 16 8 | 4 7 256 | 125 9 12 | |--------------------+--------------------+--------------------| | 89 136 13 | 2 68 7 | 4 156 59 | | 16 5 7 | 9 3 4 | 126 8 12 | | 89 2 4 | 5 68 1 | 369 36 7 | |--------------------+--------------------+--------------------| | 12 7 1269 | 16 4 3 | 8 156 59 | | 4 8 16 | 7 59 59 | 16 2 3 | | 5 136 1369 | 16 2 8 | 169 7 4 | *--------------------------------------------------------------* # alternate approach # [r9c7]= 1 => [r8c7]=6 => [r5c7]<>6 # [r9c7]<>1 => XYZ-Wing => [r5c7]<>6

Code: Select all: *-----------------------------------* | . . 1 | . 1 . | 1 1 . | | 1 . 1 | . 1 . | . . . | | . 1 . | . . . | 1 . 1 | |-----------+-----------+-----------| | . 1 1 | . . . | . 1 . | | 1 . . | . . . | 1 . 1 | | . . . | . . 1 | . . . | |-----------+-----------+-----------| | 1 . 1 | 1 . . | . 1 . | | . . 1 | . . . | 1 . . | | . 1 1 | 1 . . | 1 . . | *-----------------------------------*

by **DanG** » Mon Sep 10, 2007 4:15 am

Code: Select all: *-----------------------------------* | . . 1 | . *1 . | 1 *1 . | | *1 . 1 | . *1 . | . . . | | . *1 . | . . . | 1 . *1 | |-----------+-----------+-----------| | . *1 1 | . . . | . *1 . | | *1 . . | . . . | 1 . *1 | | . . . | . . 1 | . . . | |-----------+-----------+-----------| | 1 . -1 | 1 . . | . 1 . | | . . 1 | . . . | 1 . . | | . 1 -1 | 1 . . | -1 . . | *-----------------------------------* ^ ^ SoPT cells marked "*" 2 corridors marked "^" containing inner (SoPT) guardians.

3 cells marked "-" since each one see either outer and/or inner guardians (due to strong link in r8).

daj95376, where is this puzzle coming from ?

by **daj95376** » Mon Sep 10, 2007 5:42 am

DanG wrote:daj95376, where is this puzzle coming from ?

My puzzle generator created it. I was seeing what would result if I forced it to start with a diagonal exposed from a random grid. This was one puzzle in a bunch of uneventful puzzles.

by **daj95376** » Mon Sep 10, 2007 7:03 pm

I don't recall anyone finding a fish for this elimination. Maybe there's a Broken Wing.

Code: Select all: Puzzle #B026 8: 7..96.1....4..26.3...3.5.2.14......2..7.2.4..9......67.7.6.3...4.62..3....1.94..6 *-----------------------------------------------------------------------------* | 7 23 23 | 9 6 8 | 1 45 45 | | 58 589 4 | 1 7 2 | 6 89 3 | | 6 1 89 | 3 4 5 | 7 2 89 | |-------------------------+-------------------------+-------------------------| | 1 4 358 | 7 358 6 | 9 358 2 | | 358 6 7 | 58 2 9 | 4 1358 15 | | 9 2358 2358 | 4 358 1 | 58 6 7 | |-------------------------+-------------------------+-------------------------| | 258 7 589 | 6 158 3 | 258 1458 14589 | | 4 589 6 | 2 158 7 | 3 1589 158 | | 2358 358 1 | 58 9 4 | 258 7 6 | *-----------------------------------------------------------------------------*

Code: Select all: *-----------------------------------* | . . . | . . 8 | . . . | | 8 8 . | . . . | . 8 . | | . . 8 | . . . | . . 8 | |-----------+-----------+-----------| | . . 8 | . 8 . | . 8 . | | 8 . . | 8 . . | . 8 . | | . 8 8 | . 8 . | 8 . . | |-----------+-----------+-----------| | 8 . 8 | . 8 . | 8 8 8 | | . 8 . | . 8 . | . 8 -8 | | 8 8 . | 8 . . | 8 . . | *-----------------------------------*

by **ronk** » Tue Sep 11, 2007 1:06 am

daj95376 wrote:I don't recall anyone finding a fish for this elimination. Maybe there's a Broken Wing.

It's not a broken wing, but catching the fish is proving to be very difficult.

The New Sudoku Players' Forum

A revival of Broken Wings