The New Sudoku Players' Forum

[champagne]

FWIW, I think it is a 4 digit Exocet in the general sense. There's nothing in the definition (such as it is) that says "Oh, by the way, if one of the base cell digits would be forced into both target cells if it were true in a base cell, then it isn't an Exocet".
As for JExocet, I guess the bottom line is that it's David's definition, and if he says it isn't, then it isn't. To me, since the the 2's in the "swordfish columns", don't appear more than 2 rows (outside the base band), it should qualify a JExocet as well.

Leren: Nice find, by the way !

It is an Exocet and it comes on my side in the code I use to detect JExocets, but as says blue, no reason to fight on definitions.
And as "2" in the base forces "2" in both targets, "2" can not exist in the base.

r7c2=7
r7c1<>2

[dobrichev]

Nevertheless, there may remain something interesting to dig: do these puzzles have any special intrinsic property?

Exactly.
Even after nobody from the experts came with answer "all they have XXX not broken by YYY", the exercise was fun.
Thanks! Enjoy sudoku!

[storm_norm22]

Nevertheless, there may remain something interesting to dig: do these puzzles have any special intrinsic property?

Exactly.
Even after nobody from the experts came with answer "all they have XXX not broken by YYY", the exercise was fun.
Thanks! Enjoy sudoku!

we shall !!

[Leren]

JC Van Hay wrote : "Exocet" : {2789C3 2789C5 2789C7 7N12}

Pardon my ignorance but I'm not understanding this - it looks like a Rank 0 logic structure in Exocet format. Are these the 14 Truth sets in which case what are the link sets ? If not perhaps you could explain a bit further.

Interestingly most, but not quite all, of your eliminations followed from the Exocet I found, so there is some subtle difference between the two "Exocet" approaches.

Leren

[David P Bird]

I think I must retract my retraction! This kept me awake last night when I produced this line of reasoning:

1. The base cells, must hold two of the base digits (ab) which will makes them false in JExocet band,crossline1
2. By selection crosslines 2 & 3 can each only hold one of the base digits in the JExocet band - in the target cells
3. This forces the parallel bands,crosslines123 to hold at least 4 truths for (a) & (b)
4. If these cells are restricted to a single truth for (a) they must therefore hold three truths for (b).
5. When no selection for (b) allows this, the base cells can't hold (a) and it can be eliminated from them.

Congratulations on the find Leren, and thanks a lot for bringing it up.

As Blue says it's all in the definition, and it obviously needs revising. The JExocet thread is too long for me find the chapter and verse on this just now, but I'll tackle it when I have time.

David

[denis_berthier]

Nevertheless, there may remain something interesting to dig: do these puzzles have any special intrinsic property?

Exactly.
Even after nobody from the experts came with answer "all they have XXX not broken by YYY", the exercise was fun.

Maybe you're the only one who can tweak your program to check that there is indeed no 2-value solution, whichever sequence of choices you make in DFS for those 39 puzzles. If we were sure it isn't only "an artefact of the sequence of trials" (taking your words), we'd be more inclined to try deeper analyses.

The special thing I found in this puzzle is that my solver, which recognises only singles, needs T&E from 3-position candidate in a house.
There are no such puzzles in the list of 800 K hardest - it is always possible to try for several times from a 2-value cell or 2-position candidate and solve with direct eliminations.

That's an aspect of the question I had overlooked in my first answer. Requiring 3-value 2D cells might suggest that the puzzles are "harder" in some sense. But you're saying that the 800,000 known hardest ones (wrt to SER) can be dealt with using only 2-value.
I computed the SER of your 39:

Hidden Text: Show

Code: Select all

10.4
10.4
9.3
9.7
9.6
9.6
9.6
9.6
9.0
9.0
9.6
9.6
9.6
9.6
9.7
9.7
9.7
9.7
9.7
10.4
9.0
8.9
9.7
9.7
9.6
9.7
9.7
9.7
9.6
9.7
9.5
9.7
9.5
9.0
10.4
9.7
9.5
9.5
9.5


It appears that they are all in what I've defined as the grey zone http://forum.enjoysudoku.com/the-sudoku-grey-zone-t31143.html. Moreover:

- 6 can be solved by braids (# 3 9 10 21 22 34)
- 15 require g-braids (# 5 6 7 8 11 12 13 14 25 29 31 33 37 38 39)
- the remaining 18 can be solved by B2-braids (among these, 14 can be solved by S2-braids but no more can be solved by allowing S3-braids or S4-braids)
(These classifications are intrinsic, pure logic, properties of the puzzles - more precisely of their classes of essential equivalence).

[eleven]

Just to say it, the exocet is not needed in champagne's puzzle.
After w-wing 46, there is a UR 46 with x-wing in r78c68, which leaves 6 in r7c6 and r8c8.

Code: Select all

+-------------------------+-------------------------+-------------------------+
| 23789  #56      2789    |#346789  789     349     | 2789   #45      1       |
| 1      #56      789     |#46      789     2       | 789     3      #45      |
| 3789    237     4       | 3789    5       1       | 6       29      2789    |
+-------------------------+-------------------------+-------------------------+
| 4       8       1       | 239     6       39      | 5       7       239     |
| 237     237     5       | 239     1       8       | 4       29      6       |
| 23      9       6       | 5       4       7       | 1       8       23      |
+-------------------------+-------------------------+-------------------------+
| 2789    27      3       | 1       2789   *46      | 2789  *#456    #45      |
| 5       1       2789    | 4789    2789   *469     | 3      *46      2789    |
| 6       4       2789    | 789     3       5       | 2789    1       2789    |
+-------------------------+-------------------------+-------------------------+

Then the 8-cell-DP 456 eliminates 46 from r1c4.

It can be solved with "basic advanced" patterns then.

[champagne]

Just to say it, the exocet is not needed in champagne's puzzle.
After w-wing 46, there is a UR 46 with x-wing in r78c68, which leaves 6 in r7c6 and r8c8.
Then the 8-cell-DP 456 eliminates 46 from r1c4.

As usual, especially at that level, you have many ways to solve a puzzle.
Your UR is not classical.. well done for anybody (including me) accepting uniqueness effects.

The exocet appearing later if you start from mladen's puzzle is interesting as example of that pattern in such puzzles.

[daj95376]

After basics + a Skycraper 1r34 I reached the following grid.

Code: Select all

                 v                v                v
*-----------------------------------------------------------------------*
| 23789  56     2789    | 346789 789    3469    | 2789   45     1       |
| 1      56     789     | 46     789    2       | 789    3      45      |
| 23789  237    4       | 3789   5      1       | 6      29     2789    |
|-----------------------+-----------------------+-----------------------|
| 4      8      1       | 239    6      39      | 5      7      239     |
| 237    237    5       | 239    1      8       | 4      29     6       |
| 23     9      6       | 5      4      7       | 1      8      23      |
|-----------------------+-----------------------+-----------------------|
|B789-2 B7-2    3       | 1      2789   46      | 2789   456    45      |
| 5      1      2789    | 46789 T789-2  469     | 3      46     2789    |
| 6      4      2789    | 789    3      5       |T789-2  1      2789    |
*-----------------------------------------------------------------------*
                 ^               ^                 ^

I found a four digit JExocet (2789) r7c1 r7c2 r8c5 r9c7 except that there is only 1 truth for digit 2 in the cross columns.

Putting 2 in a base cell forces 2 into both Target cells and therefore a contradiction in whichever other digit is in the base cells, so 2 can be removed from the base cells.

The pattern then reduces to a 3 digit JExocet (789) and 2 can be removed from the target cells.

The puzzle then solves with 3 more skyscrapers.

This Exocet pattern (a digit with 1 truth in the cross rows can be removed from the base cells) was previously proposed by David P Bird. He then claimed to have found a counterexample and withdrew the proposal, but the counterexample doesn't look valid to me. Details can be found in the JExocet Definition thread.

_

Leren, congratulations on your discovery.

FWIW, the value in target cell r8c5 must also be the value in r9c9. So, you can perform -2r9c9 as well. It doesn't make a big difference in the outcome, but it does help.

Now, I need to go back through my program and include a test for your scenario.

_

[champagne]

Leren, congratulations on your discovery.

FWIW, the value in target cell r8c5 must also be the value in r9c9. So, you can perform -2r9c9 as well. It doesn't make a big difference in the outcome, but it does help.

_

r7c12 r8c7r8c9 is also an exocet, as each time the corresponding cell (here r9c8) is assigned, so you are right.

Now, I need to go back through my program and include a test for your scenario.

_

If you have the code to find Jexocets, it not so expensive to try to find a new one at each cycle.
These are the most interesting for players.
(knowing that with my own code, this is a JExocet)

[JC Van Hay]

Leren, you deserve a lot of congratulations for your analysis of the exocet.

On my side, I switched too fast to the usual way I am solving a puzzle with an exocet : by solving the base cells.
Furthermore, I unfortunately didn't find useful to use Xsudo until I saw your analysis.

JC Van Hay wrote : "Exocet" : {2789C3 2789C5 2789C7 7N12}

Pardon my ignorance but I'm not understanding this - it looks like a Rank 0 logic structure in Exocet format. Are these the 14 Truth sets in which case what are the link sets ? If not perhaps you could explain a bit further.

Interestingly most, but not quite all, of your eliminations followed from the Exocet I found, so there is some subtle difference between the two "Exocet" approaches.

Leren

Meaning of " "Exocet" : {2789C3 2789C5 2789C7 7N12} :=> 52 eliminations" : (Xsudo software says that) the solutions of the 14 truths/base sets/native SIS/constraints exclude 52 candidates.
This can also be done, partially or not, manually as in the following analysis, where the solutions of the 14 native SIS are classified according to the solutions of the base cells of the exocet :

3 Singles (UP27); Skyscraper(1R34) => +1r4c3; 8 Singles (UP35)

Exocet (2789)r7c12 :

r7c12=2 -> +2r8c5
r7c12=7 -> -7r7c57,-7r89c3,7r8c5=XW(7r12c35)-7r12c7=7r9c7; 7r8c5==7r9c7
r7c1 =8 -> -8r7c57,-8r89c3,8r8c5=XW(8r12c35)-8r12c7=8r9c7; 8r8c5==8r9c7
r7c1 =9 -> -9r7c57,-9r89c3,9r8c5=XW(9r12c35)-9r12c7=9r9c7; 9r8c5==9r9c7
|
V
r7c12=2a -> +2r1c3,+2r8c5,+ar9c7; 2c7={} :=> -2r7c12
r7c12=7a, r8c5=7 or a; r7c5=2, r1c7=2; UP49

XWing(7R38)-(7=8)r9c4; UP50
Kite(8R3C7)-(8=9)r7c1; UP70
Skyscraper(4R28)-(4=5)r1c8,r7c9; UP81

Note : linksets/cover sets : forget them or, at least, use them very carfully ! They are giving headaches and could lead to false logic !

Best Regards, JC.

[JC Van Hay]

Then the 8-cell-DP 456 eliminates 46 from r1c4.

It can be solved with "basic advanced" patterns then.

I do like your solution. "Whale" done!