- 1 Exocet Sudoku
- 2 Order in Strategy List
- 3 Credits
- 4 The Exocet Pattern
- 5 Pattern Inferences
- 6 Double Exocet
If these requirements are satisfied,
- The solution in the first Base Cell corresponds to one of the Target Cells, whereas the solution in the second Base Cell corresponds to the other Target Cell.
- The Mirror Nodes must have the same Base Digits as the Target Cells they are connected with, plus one false digit in the Base Cells.
- In two S Cells, each of the two Base Candidates that will answer the Base Cells must be true.
The following eliminations are possible with this pattern:.’
Exocet Sudoku Rule 1
A Base Candidate with only one S Cell cover home can’t be a solution in any Base Cell or Target Cell.
A Base Candidate with one cover house would have to be the solution in the S Cell in the CLb Cross-Line if it was the solution in a Base Cell. This would make it the solution in both Target Cells and prevent another Base Candidate from being the solution in a Target Cell, which is impossible.
As a result, such a Base Candidate can be excluded from the Base and Target Cells.
Exocet Sudoku Rule 2
A Base Candidate cannot be a solution in a Target Cell unless it is true simultaneously in at least one Target Cell and its associated Mirror Node.
Since this candidate’s only alternatives in this Square are the Cells in this Mirror Node, it must be the solution in the connected Mirror Node if it is the solution in both a Base Cell and a Target Cell.
Exocet Sudoku Rule 3
In a Target Cell, any non-Base Candidate is false.
In a Target Cell, the answer must be a Base Candidate.
Exocet Sudoku Rule 4
A Base Candidate must be true in another Target Cell is false in Target Cell.
Candidates must be present in each of the Target Cells.
Exocet Sudoku Rule 5
If a Base Candidate has a Cross-Line as an S Cell cover house, the Target Cell in that Cross-Line must be false.
The complete Column (or Row when the Exocet pattern is column-oriented), including the CLb, CL1, or CL2 S Cells, is referred to as a Cross-Line.
Consider a pattern in which CL2 serves as the cover home for a certain Base Candidate. This means that this candidate must be true in no more than one cell in the CLb and CL1 S Cells to meet the pattern criteria.
This candidate would be true in one of the Base Cells and hence in CLb if true in T2. This solution in CLb would force the candidate to be the solution in T1 by removing it from CL1. The pattern would be invalidated if the same candidate was the answer in both T1 and T2.
Candidate 6 would be a genuine Base Candidate if it were true in C7, a Target Cell. Likewise, it would be true in J3 and B4 if true in A1 or A2. However, because B4 is a Target Cell, it requires a Base Candidate other than 6 as a solution. As a result, Candidate 6 cannot be the answer in C7.
Exocet Sudoku Rule 6
In a Target Cell, any Base Candidate that cannot be true in the Mirror Node linked with it is false.
Mirror Node are the only alternatives available for the candidate in this type of Square.
Exocet Sudoku Rule 7
If one Mirror Node Cell can only include non-Base Candidates, the second Mirror Node Cell can only contain Base Candidates from the related Target Cell.
The Base Candidate that is the solution in a Target Cell must also be the solution in one of the Mirror nodes Cells with which it is associated.
Exocet Sudoku Rule 8
If a Mirror Node has only one non-Base Digit value, it is true in that Mirror Node but false in the cells in its immediate vicinity.
A Base Digit and a non-Base Digit must be present in each of the two Cells.
Exocet Sudoku Rule 9
If a locked digit is present in a Mirror Node, all other digits of the same kind (base or non-base) are false.
If a Mirror Node has a locked digit, the answer in one of the Mirror Node’s Cells must be that locked digit.
Because a Mirror Node’s two Cells must each include a Base Digit and a non-Base Digit, all other Base Digits in the Mirror Node can be removed. In the Mirror Node, however, if it is a non-Base Digit, all other non-Base Digits can be deleted.
The 5th candidate must be the solution in one of these Cells because it is locked in C8 and C9. Because these Cells are also Target Cell B4’s Mirror Cells, one must have Candidate 6 or Candidate 8 as its answer. As a result, Candidate 4 cannot answer cell 8 or cell 9.
Exocet Sudoku Rule 10
In all cells in full view of either both Base Cells or both Target Cells, a known Base Digit is false.
A known Base Digit is a digit that we know is the correct answer in one of the Base Cells. As a result, it may be removed from any cells that view both Base Cells and Target Cells.
Candidate 5 must be the answer in either A1 or A2; therefore, it may be ruled out in any Cell that sees both cells. Likewise, it must be the solution in either B4 or cell 7, so it may be removed from any Cells that see both of these Cells. Candidate 8 follows the same logic.
Exocet Sudoku Rule 11
A Base Digit, which only occurs once in the Escape Cells, is false in the non-S cells.
A known Base Digit must be the solution in a Cell in the CLb S Cells and a Cell of the S Cells connected with the Target Cell in which it is not the solution. Of course, these two Cells will originate from different Cover Houses. On the other hand, the Exocet pattern mandates that all instances of any Base Digit in the S Cells as a candidate, a provided, or a solved value be restricted to no more than two Cover Houses.
As a result, if a known Base Digit is true in one S Cell in each of the Cover Houses, it may be deleted in all except the S Cells of these Cover Houses.
Candidate 1 cannot be the Target Cells B4 and B7/C7 if it is Base Cells A1 or A2.
It has to be the answer in B3, J4, and E7. This removes E1, E9, J1, J2, and J8. Candidates 2 and 3 follow a similar logic.
Candidate 5 must be true in either E3 and J7 or J3 and E5 since it must be the answer in one of the Base Cells A1 or A2.
Candidate 8 follows a similar logic.
Exocet Sudoku Rule 12
Any digit instance for a known Base Digit that would prohibit two of its S Cells from being true is false.
If all of the combinations of a specific Base Candidate in one Base Cell with all of the other Base Candidates in the other Base Cell result in the development of Deadly Patterns, then that Base Candidate is false.
Deadly Patterns (i.e., four cells forming the corners of a rectangle containing only the same two potential Candidates) are disallowed in a well-behaved Sudoku.
Exocet is a pattern that frequently appears in extremely difficult puzzles with a high candidate density. Other solutions fail because there are few bi-value and bi-location candidates. Exocet works on three or four candidate sets at a time, which is exactly what is required in critical puzzle bottlenecks. My first implementation successfully solved 51 of the 123 weekly “unsolvable” devised by David Filmer. Any known solvable riddles will be replaced with much more difficult challenges.
It’s tough to improve on Phil’s succinct description: When two of the three cells at a box-line intersection have the same three or four candidates, any additional candidates can be deleted from the other two boxes in the same band but on different lines.
Order in Strategy List
My inclination is to place this near the end of the Extremes group of techniques, but I’ve been told that many of the Exocet eliminations overlap with previous methods. I don’t believe I’ve used many of them, but to test and develop, I’m putting it at the beginning of the extremes to give it more practice. According to David Bird, it can go after the essentials, but that will have to wait until additional variants are in place.
A lot of people investigated this method and its numerous versions. Champagne, a forum user, has come up with the moniker. Allan Barker originally noticed the pattern in the “Fata Morgana” puzzle. My primary source is David P Bird’s superb JExocet Compendium, accessible in fourteen downloadable PDFs on the EnjoySudoku Forum, and David has been gracious enough to address inquiries. I’d also want to thank Phil’s Sudoku Solver for providing examples and assistance. Please send me an email if you have any more credits that I haven’t listed.
The Exocet Pattern
Lets start with the pattern.
Pattern Rule 1
In one box, two Base cells (B) are aligned and normally contain three or four possibilities in total. That might be 1,2,3,4 Plus 1,2,3,4 but also 1,2,3+2,3,4 or even 1,2,3+3,4. I haven’t yet come across an instance of two bi-value cells like 1,2+3,4. To be investigated.
Pattern Rule 2
Then we look for two Target cells (T) that have all of the digits in the Base cell (plus any extras). The Targets and the Base Cells are invisible to each other. They have to be in the same Tier or Stack as well (group of 3×3 boxes in a row or column). The uppermost tier is shown in red in the diagram. Given that they must not be seen,’ each Target has just three potential cells.
We seek three Cross-Lines that drop from the Targets and the cell not occupied by the Bases if Bases and Targets are aligned in a Tier (as shown in these pictures). Columns 3, 4, and 7 are highlighted in yellow. The six cells outside the tier are particularly important to us (or stack). S-Cells are the name for these cells.
We’ll go over some of the other cells in the pattern, so let’s get started. A Companion cell is designated with a C in each Target. Each Target has two M1 and M2 Mirror Cells, which are located next to each other on the opposite side of the Target.
Finally, the asterisks are known as Escape cells, and they may be used to store candidates who have been proven to be false in the base.
Pattern Rule 3
Companion Cells must not contain the Base candidates, either as clues or givens, to constitute a true Exocet pattern.
Pattern Rule 4: Exocet Pattern – Cover Lines
There’s one more problem to deal with before we can be positive we’re dealing with an Exocet. I’ve set the Base candidates to 1,2,3 in the graphic. There should be a few of them strewn about in the S-Cells. We don’t want them to show up more than twice. We evaluate the rows where each Base candidate occurs if the Cross-Lines are columns. Cover-Lines are called, and I’ve drawn all of them in the three colors of the three numbers.
Cover lines are perpendicular to cross-lines, as I previously indicated. Normally, they are; however, we might be flexible to obtain the greatest number of elimination rules. For example, it’s conceivable that the same Base candidate shows twice in the same column. We’d need two cover lines if we were precisely perpendicular, but all we want to do is “cover” the candidates so we can “cover” them vertically in the single-column case. As a result, the cover-line equals the cross-line. This will come in handy later.
If an Exocet pattern is confirmed, the following conclusions might be drawn:
The base digits in the two Target cells must be distinct.
Mirror cells must have the same base digits as their ‘opposite’ Target cells, plus one digit in the base cells that is false.
Each of the two true base digits must be true in two’ S’ cells.
As David puts it, “These are a wealth of eliminations, some of which may be done right now and others which will become accessible as the solution advances. These can be included in AICs as well.”
Note: When we say “true Base digits,” we’re referring to the final result and knowing exactly what those cells contain. At first, we don’t know that, but eliminations here may reveal more, and we may go back through the Exocet checklist.
Elimination Rule 1
Rule 1 of Exocet (untick X-Cycles): Any candidate in a Target cell who is not one of the Base candidates can be eliminated from the start. This eliminates the 4 in B4 and the 2 and 7 in C7.
This example features a slew of Exocet eliminations, but they all depend on a different test known as the Compatible Digit Check. That I haven’t implemented, therefore I’ll disregard them. I’ll return to this example in the next update when I’ve fully grasped this test.
Elimination Rule 2
According to Bird’s criteria, a base candidate with only one ‘S’ cell cover house is invalid and false in the base mini-line and target cells.
Elimination Rule 3
A base number in one target that must be true in the other target is false, according to Bird’s definition. This, to my understanding, means that if previous eliminations have reduced one target to a single-digit ON, it is firmly related and eliminated as a single.
Elimination Rule 4
According to Bird’s criteria, a base candidate with a cross-line as an ‘S’ cell cover house must be false in the target cell in that cross-line.
Elimination Rule 5
“If a mirror node includes only one conceivable non-base digit value, it is true in that node and false in the cells in sight of it,” according to the literature.
I couldn’t get this to function without making some mistakes. “Base digit missing from mirror node or base digits missing in the mirrored target cell” is the best approach that doesn’t result in improper removals.
While requiring the Exocet method at times, these problems are otherwise simple.
They’re excellent practice problems. Klaus Brenner has discovered something.
Very strong elimination sets may be determined from the overlap of two Exocet patterns. Of course, the two Exocets must have the same Base candidates in the current solver implementation. Still, Double Exocet is known to be broader than that, and I aim to be able to take into consideration Exocets that just partially overlap in the future.
Example of a Double Exocet Pattern: Load or: From the Beginning
From Unsolvable #165, here’s an excellent example. Exocet 1 is represented by blue/green cells, whereas Exocet 2 is represented by yellow/orange cells. The base and target cells have been identified and labeled. The Base candidate set for both Exocets is 2,4,5,9, as seen by looking at these cells.
Because the S-Cells for both Exocets are identical, I didn’t bother to color them separately. So instead, I only think of one way to eliminate them on their own:
Elimination rule 1: 8 removed from target cell D9
Double Exocet Rule 1
Rule 1 of the Double Exocet All four target cells are treated as a single unit for the first elimination rule. The same goes for each of the four basic cells. In the second diagram, I’ve colored those cells pink and blue.
Rule 1 states that ‘known’ base digits can be eliminated if they observe all four target cells or base cells. As a result, any of 2,4,5,9 in D1 and D2 can be deleted – pink dashed lines indicate that they can see all of the target cells. Similarly, F5 has all base cells (blue dashed lines). E9 can do the same.
When it comes to base candidates, David Bird’s definition contains “known.” ‘Known’ implies they must fit somewhere in the target+base cells when they would otherwise be confusing. This suggests a larger, partially overlapping definition of Double Exocet. Still, since they overlap in our example is complete, all base possibilities are ‘known.’ I’ll be able to make this requirement more apparent after Exocet is completely developed.
Double Exocet Rule 2
Rule 2 of the Double Exocet We’re not done with this example yet. Next, we’ll look at the significance of S-Cells and their coverings. These were crucial in confirming the existence of the Exocet pattern. Because we have two Exocets with identical base possibilities, the distribution of 2,4,5,9 is severely constrained.
Rule 2 states that non-‘S’ cells in their cover houses can have known base digits deleted.
As a result, we tested to see if 2,4,5,9 appears no more than twice in all S-Cells, yielding our three cover-lines – rows A, B, and J. Our base candidates must be true on someplace along with those S-Cell columns, therefore there is no more room in those rows for them. Again, the Swordfish strategy has a lot of parallels here.
This one step rips the problem apart rather than selecting through a dozen long chaining methods and reveals all of the singles to the conclusion. There’s still a lot to think about with Exocets and Double Exocets, and I’m hoping to understand the finer aspects and different rules to enhance the solver even more.