Para,
The Sudocue program allows you to enable or disable the various solving techniques it can use in its solution. When a new puzzle is loaded into Sudocue, it will report to you if it is unable to solve the puzzle using only the currently enabled techniques. Thus, if you disable the Medusa techniques and Sudocue does not report an inability to solve the puzzle, then you can be sure they are not needed. To change the set of enabled techniques, from the menu choose Tools, then Options, then Solver. I don't remember exactly when they began, but I feel safe in saying that none of the puzzles in the Archive before Oct 2006 require Medusa techniques.
From the position you posted, I used an ALS XZ rule elimination followed by a 4 cell XY chain to complete the solution, without need of any of the Medusa techniques. (In case you're not yet familiar with the ALS XZ technique, refer to the Solving Guide on this site.) I had not run the solver on this puzzle, but after seeing your post, I ran it with the ALS XZ technique enabled and the Medusa techniques disabled. In your posted position (shown below), it found the elimination of 6 from r1c2 which you mentioned, using two fairly large ALS's -- r1c345678 and r3c3789 -- with 3 as the "restricted common" digit.
Code: Select all
.------------------.------------------.------------------.
| 1 B36 256 | 478 2467 2678 | 2578 2-357 9 |
| 59 8 4 | 79 27 3 | 1257 6 127 |
| 39 7 B26 | 1 5 2689 |A28 A234 A2348 |
:------------------+------------------+------------------:
| 6 12 9 | 5 17 4 | 3 8 127 |
| 38 123 7 | 89 136 689 | 4 129 5 |
| 358 4 15 | 2 137 789 | 179 179 6 |
:------------------+------------------+------------------:
| 47 16 168 | 3 9 5 | 12678 1247 12478|
| 47 5 138 | 6 247 27 | 189 139 138 |
| 2 9 36 | 47 8 1 | 567 3457 347 |
'------------------'------------------'------------------'
To my human eye, the ALS in r3c789 -- marked with "A" in the diagram, was more readily apparent. It can be used with the ALS {r1c2,r3c3} -- marked with "B" -- to eliminate 3 from r1c8, using 2 as the "restricted common" digit. (Since r1c2 and r1c8 are strongly linked for digit 3, this immediately implies r1c2=3, as does your and Sudocue's elimination of 6 from r1c2).
This position is reached after either elimination is followed up with basic techniques:
Code: Select all
.------------------.------------------.------------------.
| 1 3 26 | 47 2467 8 | 5 27 9 |
| 5 8 4 | 9 A27 3 | 127 6 1-2-7|
| 9 7 26 | 1 5 B26 | 8 34 #34 |
:------------------+------------------+------------------:
| 6 12 9 | 5 1-7 4 | 3 8 #27 |
| 3 12 7 | 8 16 C69 | 4 29 5 |
| 8 4 5 | 2 3 D79 | 179 179 6 |
:------------------+------------------+------------------:
| 47 6 *18 | 3 9 5 | 127 1247 *12478|
| 47 5 *18 | 6 247 27 | 19 139 *138 |
| 2 9 3 | 47 8 1 | 6 5 #47 |
'------------------'------------------'------------------'
Here there is a short XY chain, in cells A (r2c5), B, C, D in the diagram, which eliminates candidate 7 from r4c5:
(7=2)r2c5 - (2=6)r3c6 - (6=9)r5c6 - (9=7)r6c6 => r4c5 <> 7
The solution is easily completed after this elimination. This is really not the reason for my response, however.
The solution path found by the Sudocue solver is more complex, but it does find a very interesting uniqueness elimination in the position above. Cells r78c39 (marked with "*" in the diagram) form the potential non-unique rectangle, with surplus candidates 2,3,4,7 on one side of the rectangle, in column 9. These combine with cells r349c9 (marked with "#" in the diagram) to form, in effect, a naked quad in column 9, which eliminates 2 and 7 from r2c9. This is termed a "unique subset" pattern in the Solving Guide, in this case a "unique quad." Alongside this example, my discovery of a "unique triple" described in
this post looks rather pale.
Another way to view the above is to note that r78c9 are strongly linked for digit 8; therefore neither cell can be 1 since that would force the other to 8, forming the non-unique rectangle. This leaves only r2c9 available for candidate 1 in column 9. However, this would miss the unique quad pattern.
To GreenLantern: I haven't broken down to using the Medusa techniques, but I think "Medusa wrap" is an aid to locating "nice loops" in the grid, though perhaps not called by that name. In the example in the Solving Guide, Ruud gives an equivalent loop for the conflict revealed by the Medusa wrap. I seldom use formal notation for loops, and I suppose it's time I began. Looking at your nice loop (shown below), shouldn't the link between r1c2 and r3c1 (via candidate 3) be a strong link? Otherwise I don't see the alternation of strong and weak links and I don't see how any inference could be drawn.
Code: Select all
[r3c6]=6=[r3c3]-6-[r1c2]-3-[r3c1]-9-[r3c6] => r3c6<>9
To Ruud: On the page describing
Eureka notation, in the portion under "Strong Inferences" shown below, I believe the second line is in error, if my interpretation of your symbology is correct. I interpret the "∨" symbol to mean logical "or." What's needed is logical "exclusive or." To avoid more possibly confusing symbology, perhaps you could use "<>." as you explain in the following text.
Code: Select all
(P=false => Q=true) & (Q=false => P=true)
(P ∨ Q)
P=Q
A nit: In the introductory paragraph, next to last sentence, there is a "reversible" error.