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stef
Joined: 23 Dec 2007
Posts: 2
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 Posted: Sun Dec 23, 2007 8:34 pm Post subject: a little help please |
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Hi there gurus,
Wow, it has been so long since I have picked up a Sudoku and have forgotten the way to sucess.  I was wondering if anyone can give me a hint to solve this puzzle I am working on. I am sure you are giggling in your seats at how easy this looks but I am stuck! How easy I forget!Thanks in advance!
Stef
[Edit by Keith: This is the starting grid:
| Code: | +-------+-------+-------+
| . . . | . 8 . | . 4 3 |
| . 5 6 | . . . | 9 . 2 |
| . . . | . . 2 | . 6 . |
+-------+-------+-------+
| . . 5 | . . 3 | . . . |
| 4 . . | 2 . 9 | . . 1 |
| . . . | 4 . . | 2 . . |
+-------+-------+-------+
| . 8 . | 3 . . | . . . |
| 9 . 4 | . . . | 5 1 . |
| 2 6 . | . 7 . | . . . |
+-------+-------+-------+ |
end Edit]
| Code: | +-----------+-----------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 34 47 | 9 78 2 |
| 1378 4 38 | 179 39 2 | 178 6 5 |
+-----------+-----------+----------------+
| 68 2 5 | 78 1 3 | 4678 789 4689 |
| 4 7 38 | 2 56 9 | 368 358 1 |
| 368 1 9 | 4 56 78 | 2 3578 68 |
+-----------+-----------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+-----------+----------------+ |
[Edited by keith to add code tags]
Play this puzzle online at the Daily Sudoku site[/img][/list][/list][/code] |
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sdq_pete
Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL
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| Posted: Sun Dec 23, 2007 9:40 pm Post subject: |
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Stef,
For what it's worth, my own solver (which employs the techniques normally required to solve the puzzles on this site) was unable to solve the puzzle from the position you gave. The solver on this site also said "too hard".
Maybe others can offer other techniques. It might also be useful if you post the starting position for this puzzle, just to make sure the position you had reached is correct so far.
Peter |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Dec 23, 2007 10:21 pm Post subject: |
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Hi Stef,
| Code: | +-----------+-----------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 34 47 | 9 78 2 |
| 1378 4 38 | 179 39 2 | 178 6 5 |
+-----------+-----------+----------------+
| 68 2 5 | 78 1 3 | 4678 789 4689 |
| 4 7 38 | 2 56 9 | 368 358 1 |
| 368 1 9 | 4 56 78 | 2 3578 68 |
+-----------+-----------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+-----------+----------------+ |
There's an XYZ-Wing pivoted in r5c7 and a W-Wing on 68 in boxes 4 and 6. Unfortunately, it didn't get me too far. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Mon Dec 24, 2007 12:02 am Post subject: |
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Stef,
If you aren't familiar with the term W-Wing, then, in this case, the same thing can be seen as a 4-cell XY Chain of {68}-{87}-{78}-{86} via the {78} pair in Box 4.
After that, the puzzle can be solved with a single (longer) XY Chain. (The XYZ Wing wasn't required for this solution path.) As an alternate to the long XY Chain, there is a type of UR elimination that accomplishes the same thing. (This UR elimination can solve the puzzle in a single step without using the XYZ Wing or the W-Wing.)
As tough puzzles go, this one isn't so bad. Pete's solver must be set on a sensitive setting. |
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Steve R
Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England
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| Posted: Mon Dec 24, 2007 12:23 am Post subject: |
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Marty’s W-Wing relies on the fact that only two cells in box 5 are open to 8. They are r4c4 and r6c6. One must contain 8 so at least one of r4c1 and r6c9 will contain 6. 6 can therefore be eliminated from r4c7, r4c9 and r6c1. This leaves:
| Code: | +-----------+-----------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 34 47 | 9 78 2 |
| 1378 4 38 | 179 39 2 | 178 6 5 |
+-----------+-----------+----------------+
| 68 2 5 | 78 1 3 | 478 789 489 |
| 4 7 38 | 2 56 9 | 368 358 1 |
| 38 1 9 | 4 56 78 | 2 3578 68 |
+-----------+-----------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+-----------+----------------+ |
Unless you use the unuqueness rectangle r13c17 as Asellus suggests I too think you will need a chain at some stage. You may as well use it now. One possibility is:
r3c5 = 3 ==> r2c5 = 4 ==> r2c6 = 7 ==> r6c6 = 8 ==> r6c1 = 3 ==> r5c3 = 8 ==> r3c3 = 3 ==> r3c5 ≠ 3.
The contradiction means that r3c5 ≠ 3 and solves the puzzle.
Steve |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Dec 24, 2007 2:40 pm Post subject: |
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Stef,
I have edited your first message to correct the code tags. If you look at the message in edit mode, you can see how it is done.
The following expands on observations made by others in this thread:
The quick solution of your puzzle is via the Type-3 Unique Rectangle in R13C17:
| Code: | +-----------+------------+----------------+
| 17@ 9 2 | 56 8 56 | 17@ 4 3 |
| 1378 5 6 | 17 34 47 | 9 78 2 |
|1378# 4 38%| 179 -39 2 | 178# 6 5 |
+-----------+------------+----------------+
| 68 2 5 | 78 1 3 | 4678 789 4689 |
| 4 7 38 | 2 56 9 | 368 358 1 |
| 368 1 9 | 4 56 78 | 2 3578 68 |
+-----------+------------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+------------+----------------+ |
The deadly pattern is <17> on all four corners. To avoid this, one of the extra candidates <38> in the cells marked # must be true. But, there is a cell % that is <38>. So, in R3, the cells # and % will contain all the occurrences of <38>. You can remove <3> from R3C5, and this solves the puzzle.
If you do not use the UR, things are more difficult. There is an XYZ-wing:
| Code: | +-----------+-----------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 34 47 | 9 78 2 |
| 1378 4 38 | 179 39 2 | 178 6 5 |
+-----------+-----------+----------------+
| 68 2 5 | 78 1 3 | 4678 789 4689 |
| 4 7 38@| 2 56 9 | 368@ 35-8 1 |
| 368 1 9 | 4 56 78 | 2 3578 68@ |
+-----------+-----------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+-----------+----------------+ |
One of the cells @ must be <8>, you can remove <8> from R5C8.
The next sequence is a W-wing:
| Code: | +-----------+-----------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 34 47 | 9 78@ 2 |
| 1378 4 38 | 179 39 2 | 178 6 5 |
+-----------+-----------+----------------+
| 68 2 5 | 78@ 1 3 | 4678 7-89 4689 |
| 4 7 38 | 2 56 9 | 368 358 1 |
| 368 1 9 | 4 56 78#| 2 3578# 68 |
+-----------+-----------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+-----------+-----------+----------------+ |
The cells @ are a W-wing, connected by the strong link # on <7>. You can eliminate <8> in R4C8.
The strong link on <8> in B5 leads to three <68> W-wings, only one of which is useful: R4C1 and R6C9. You can eliminate <6> in R6C1 and R4C79, which solves R4C1 as <6>.
Now what? I tried Medusa coloring, and did not find anything, So, I tried Medusa again, and came up with what you might call Medusa multi-coloring.
| Code: | +----------------+----------------+----------------+
| 17 9 2 | 56 8 56 | 17 4 3 |
| 1378 5 6 | 17 3r4g 4r7g | 9 78 2 |
| 1378 4 3b8 | 179 -39 2 | 178 6 5 |
+----------------+----------------+----------------+
| 6 2 5 | 78 1 3 | 478 79 489 |
| 4 7 3y8 | 2 56 9 | 368 35 1 |
| 3b8y 1 9 | 4 56 7r8g | 2 3578 68 |
+----------------+----------------+----------------+
| 5 8 7 | 3 49 1 | 46 2 469 |
| 9 3 4 | 68 2 68 | 5 1 7 |
| 2 6 1 | 59 7 45 | 348 389 489 |
+----------------+----------------+----------------+ |
In R6, start two Medusa chains - blue/yellow and red/green. <8> is not strongly linked in R6, but one of green or yellow is false; one of blue or red must be true.
Showing only the essential colors, R3C3 has <3b>, and R2C5 has <3r>. R3C5 cannot be <3>, and the puzzle is solved.
I am sure there are other names and approaches for this kind of elimination. [Edit: After posting my message, I see that my chain is exactly the same as Steve's. But, let me add that the coloring also takes out <3> in R2C1, (R6C1 <3b> and R2C5 <3r>), which also solves the puzzle. In a slightly simpler way.]
Keith
PS: I now see that the coloring elimination is the same one that solves the puzzle via the UR. I was not concentrating on that cell. I did the red/green Medusa net, and did not find anything. I then started the blue/yellow coloring in R6C1 because of the argument I made above that connects blue and red. |
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