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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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 Posted: Fri Jun 30, 2006 5:02 pm Post subject: Rectangle question |
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Just a very general question: is there any potential to do anything when just one corner contains only the two deadly candidates? If yes, what should be looked for?
Or are we better off just doing the other usual things until and if a second corner is reduced to the two candidates and the rectangle can now be categorized as Type, 1, 2, etc? |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Fri Jun 30, 2006 7:45 pm Post subject: |
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I am not very firm with the uniqueness types.
But when i am stuck, i try to spot potential uniqueness pairs (with maybe having extra candidates in all 4 cells) and then check for strong links for the 2 numbers. If there are any, i look, if starting with one number a deadly pattern is forced. So i found some eliminations, but they did not help much so far. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Jun 30, 2006 8:27 pm Post subject: UR with one pair |
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Marty,
First, I agree completely with what ravel says.
The short answer to your question is "yes", but you need to have some strong links. Here is a simple example:
and suppose this is also an X-wing on <1>. The elimination is: <125> cannot be <2>!
If <125> is <2> it is not <1>, so <124> and <123> are both <1>, which forces the deadly solution since <12> must then be <2>.
I think this kind of pattern is very common, but the reduction is often not very critical.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Jun 30, 2006 8:52 pm Post subject: |
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| As always, thanks to both of you for the tips. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 01, 2006 7:52 pm Post subject: An example |
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Marty,
This puzzle is not only fun to solve, it has an example that illustrates the answer to your question.
| Code: | Puzzle: MM063006 Diabolical
+-------+-------+-------+
| . . 1 | 8 . 7 | 3 . . |
| . . . | . 2 . | . 1 6 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 5 | . . . | 8 . . |
| 2 . . | . . . | . . 7 |
| . . 9 | . . . | 1 . . |
+-------+-------+-------+
| . . . | 1 . 2 | 7 . . |
| 8 5 . | . 7 . | . . . |
| . . 6 | 5 . 4 | 9 . . |
+-------+-------+-------+
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Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jul 01, 2006 9:56 pm Post subject: Re: An example |
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| keith wrote: | Marty,
This puzzle is not only fun to solve, it has an example that illustrates the answer to your question.
| Code: | Puzzle: MM063006 Diabolical
+-------+-------+-------+
| . . 1 | 8 . 7 | 3 . . |
| . . . | . 2 . | . 1 6 |
| . . . | 3 . 6 | . . . |
+-------+-------+-------+
| . . 5 | . . . | 8 . . |
| 2 . . | . . . | . . 7 |
| . . 9 | . . . | 1 . . |
+-------+-------+-------+
| . . . | 1 . 2 | 7 . . |
| 8 5 . | . 7 . | . . . |
| . . 6 | 5 . 4 | 9 . . |
+-------+-------+-------+
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Keith |
Keith, is there any chance something is missing? The puzzle is symmetrical except for lack of a given in r3c3. I know you're pretty accurate, but I thought it best to double-check before I start. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jul 01, 2006 10:15 pm Post subject: Good catch! |
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Marty,
I did not notice the asymmetry! The original puzzle is here:
http://www.sudoku.org.uk/DailySudoku.asp?day=30/06/2006
and I believe I have posted the same one. The missing symmetrical clue is <4>, I do not believe it changes the path to the solution at all.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jul 02, 2006 3:25 am Post subject: |
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I'm not sure whether that asymmetry was deliberate or not, as the few other asymmetrical puzzles I've seen have been VERY asymmetrical, not like this.
At any rate, I did what I could with the basic stuff, plus I found two X-Wings. I did see a 49 rectangle with just one corner containing only the two candidates, but I couldn't do anything with it, even though there was a strong link on the "9."
I couldn't do anything else either, but there was an X-Wing on "9s" that didn't eliminate anything, but I started a chain with them and solved the puzzle that way. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jul 02, 2006 7:48 am Post subject: My observations |
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Marty,
Starting from here:
| Code: | +-------------------------+-------------------------+-------------------------+
| 4569 2469 1 | 8 459 7 | 3 2459 2459 |
| 34579 34789 3478 | 49 2 59 | 45 1 6 |
| 4579 24789 2478 | 3 1459 6 | 245 245789 24589 |
+-------------------------+-------------------------+-------------------------+
| 13467 13467 5 | 24679 13469 139 | 8 23469 2349 |
| 2 13468 348 | 469 1345689 13589 | 456 34569 7 |
| 3467 34678 9 | 2467 34568 358 | 1 23456 2345 |
+-------------------------+-------------------------+-------------------------+
| 349 349 34 | 1 3689 2 | 7 34568 3458 |
| 8 5 234 | 69 7 39 | 246 2346 1234 |
| 137 1237 6 | 5 38 4 | 9 238 1238 |
+-------------------------+-------------------------+-------------------------+ |
the usual stuff gets you to an X-wing on <5>, and then one on <6>, when you are here:
| Code: | +-------------------+-------------------+-------------------+
| 6 2 1 | 8 45 7 | 3 459 49 |
| 3 8 7 | 49 2 59 | 45 1 6 |
| 5 9 4 | 3 1 6 | 2 7 8 |
+-------------------+-------------------+-------------------+
| 147 1367 5 | 27 3469 13 | 8 23469 2349 |
| 2 136 8 | 46 34569 135 | 456 34569 7 |
| 47 367 9 | 27 3456 8 | 1 23456 234 |
+-------------------+-------------------+-------------------+
| 9 4 3 | 1 68 2 | 7 68 5 |
| 8 5 2 | 69 7 39 | 46 346 1 |
| 17 17 6 | 5 38 4 | 9 238 23 |
+-------------------+-------------------+-------------------+ |
After you clear the X-wings, you have
| Code: | +-------------------+-------------------+-------------------+
| 6 2 1 | 8 45 7 | 3 459 49 |
| 3 8 7 | 49 2 59 | 45 1 6 |
| 5 9 4 | 3 1 6 | 2 7 8 |
+-------------------+-------------------+-------------------+
| 147 1367 5 | 27 3469 13 | 8 23469 2349 |
| 2 13 8 | 46 349 135 | 456 349 7 |
| 47 367 9 | 27 3456 8 | 1 23456 234 |
+-------------------+-------------------+-------------------+
| 9 4 3 | 1 68 2 | 7 68 5 |
| 8 5 2 | 69 7 39 | 46 34 1 |
| 17 17 6 | 5 38 4 | 9 238 23 |
+-------------------+-------------------+-------------------+ |
and an XY-wing which says R2C7 is not <4> solves the puzzle.
However, note the Unique Rectangle elimination:
(Edited to fix incorrect elimination.)
R4C2 is not <7>. It forces the deadly solution in R49C12, because of the candidates <47> in R6C1.
As a pencil & paper man, I am finding these reductions (UR + strong links) to be very common but (as in this case) not very essential.
Keith
Last edited by keith on Sun Jul 02, 2006 4:29 pm; edited 1 time in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jul 02, 2006 4:03 pm Post subject: |
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Keith,
I presumably used the same X-Wings, as mine were also on 5 and 6.
Couple of things I'm not seeing:
1) How a "4" in r6c8 forces a deadly pattern
2) The XY-Wing which eliminates the "4" from r2c7 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jul 02, 2006 4:36 pm Post subject: |
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| Marty R. wrote: | Keith,
I presumably used the same X-Wings, as mine were also on 5 and 6.
Couple of things I'm not seeing:
1) How a "4" in r6c8 forces a deadly pattern
2) The XY-Wing which eliminates the "4" from r2c7 |
Marty,
1) You are correct. I have fixed my original post. (It was late.)
2) The XY-wing is rooted in R8C4; Either R8C7 or R2C4 is <4>.
Sorry about the mistake. I'll just have to find another (correct) example!
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jul 02, 2006 8:22 pm Post subject: |
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| Quote: | | 2) The XY-wing is rooted in R8C4; Either R8C7 or R2C4 is <4>. |
They're so much easier to see when the root cells are pointed out.  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sun Jul 02, 2006 9:29 pm Post subject: |
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| Marty R. wrote: |
They're so much easier to see when the root cells are pointed out. |
I think they're much harder to spot when they are spread out, and / or in a rectangle.
Anyway, I am finding that Michael Mepham's online diabolical puzzles are much like the DB Saturday puzzles, but perhaps a little easier. Here is today's:
| Code: | +----------------------+----------------------+----------------------+
| 148 1248 6 | 12478 5 1248 | 3 124789 1248 |
| 148 12458 124 | 9 127 3 | 28 12478 12468 |
| 7 12348 9 | 1248 6 1248 | 28 1248 5 |
+----------------------+----------------------+----------------------+
| 2 169 5 | 178 179 1689 | 4 89 3 |
| 149 7 14 | 123458 1239 124589 | 2589 6 28 |
| 3 469 8 | 245 29 24569 | 1 259 7 |
+----------------------+----------------------+----------------------+
| 5 128 127 | 123 4 12 | 6 1238 9 |
| 1489 12489 124 | 6 1239 7 | 258 123458 1248 |
| 1469 12469 3 | 125 8 1259 | 7 1245 124 |
+----------------------+----------------------+----------------------+
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which can be solved via a couple of X-wings or one (or two) UR's. Choose your poison!.
The Diabolical puzzles are on Friday and Sunday. I have not looked at enough of them to decide if Friday is a different style from Sunday.
http://www.sudoku.org.uk/daily.asp
Best wishes,
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jul 03, 2006 2:59 pm Post subject: A correct example? |
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Marty,
Try this one:
| Code: | Puzzle: DT020306 Diabolical
+-------+-------+-------+
| . 4 . | . 8 . | 5 . . |
| . . . | . 4 3 | 7 6 . |
| . . . | 9 . 1 | . . . |
+-------+-------+-------+
| 2 . 8 | . . 7 | . 9 . |
| . 9 . | . . . | . 1 . |
| . 1 . | 4 . . | 2 . 7 |
+-------+-------+-------+
| . . . | 3 . 9 | . . . |
| . 2 1 | 8 5 . | . . . |
| . . 5 | . 6 . | . 8 . |
+-------+-------+-------+ |
You get to this stage:
| Code: | +----------------+----------------+----------------+
| 37 4 9 | 27 8 6 | 5 23 1 |
| 1 8 2 | 5 4 3 | 7 6 9 |
| 3567 3567 367 | 9 27 1 | 38 4 238 |
+----------------+----------------+----------------+
| 2 35 8 | 16 13 7 | 346 9 3456 |
| 47 9 47 | 26 23 5 | 368 1 368 |
| 356 1 36 | 4 9 8 | 2 35 7 |
+----------------+----------------+----------------+
| 8 67 467 | 3 17 9 | 146 25 25 |
| 369 2 1 | 8 5 4 | 369 7 36 |
| 3479 37 5 | 17 6 2 | 1349 8 34 |
+----------------+----------------+----------------+ |
There is a UR on <38> in R35C79, which is also an X-wing on <8>. The reduction is R5C9 cannot be <3>.
Not very useful. But, notice the strong links on <3> in C38. One (or both) of R1C8 and R3C3 is <3>. So, R3C7 and R3C9 are not <3>, and that solves the puzzle.
There is another budding UR on <39> in R89C17, which is also an X-wing on <9>. I do not know if it will yield anything.
Best wishes,
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Mon Jul 03, 2006 4:11 pm Post subject: Re: A correct example? |
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| keith wrote: |
There is another budding UR on <39> in R89C17, which is also an X-wing on <9>. I do not know if it will yield anything.
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The 3 in r9c7 could be eliminated, because
r9c7=3 => r8c79<>3 => r8c1=3
But again it does not help. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Mon Jul 03, 2006 8:24 pm Post subject: |
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Keith,
Good puzzles are hard to find. As to the MM that you posted and your comment on them as to how they relate to DB's, they might not be what I'm looking for. But they're certainly an example of the hyperbole ("diabolical") used by puzzle makers.
As to the DT, here is where things came to a halt for me:
| Code: | -------------------------------------------------
|37 4 9 |27 8 6 |5 23 1 |
|1 8 2 |5 4 3 |7 6 9 |
|3567 3567 367 |9 27 1 |348 234 248 |
-------------------------------------------------
|2 35 8 |16 13 7 |346 9 3456 |
|47 9 47 |26 23 5 |368 1 368 |
|356 1 36 |4 9 8 |2 35 7 |
-------------------------------------------------
|8 67 46 |3 17 9 |146 245 2456 |
|369 2 1 |8 5 4 |369 7 36 |
|3479 37 5 |17 6 2 |1349 8 34 |
------------------------------------------------- |
I didn't get quite as far as you did. Looking at it, I don't know why I eliminated the "7" from r7c3. I also have more candidates in r3c789 and r7c89. The 38 rectangle is no longer there because I eliminated the "3" from r3c9 and have a "4" there instead of the "3." And, of course, I don't have the strong link in c8 which helps solve the puzzle.
I'll look again to see if there's any way I can eliminate more candidates. If not, then I'm sure the puzzle can be solved with forcing chains, assuming I haven't made an error. If I have, I'll just get out the eraser and give it another shot.
Update, 25 minutes later: solved with a chain. It's somewhat disappointing that I couldn't eliminate enough to get to the puzzle-solving strong links. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Mon Jul 03, 2006 10:30 pm Post subject: Just a step or two |
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Marty,
In the position you posted, there is a hidden pair <25> in R7 and B9. Then, R3C8 is <4>, and the strong links are there to take out <3> in R3C7.
I am a pattern maker - you seem to be a member of the chain gang! 
Keith |
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David Bryant
Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
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| Posted: Mon Jul 03, 2006 10:34 pm Post subject: A hidden pair |
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| Marty R wrote: | | It's somewhat disappointing that I couldn't eliminate enough to get to the puzzle-solving strong links. |
I sometimes go looking for chains sooner than I ought to. So you're in good (?) company. 
There's a hidden pair {2, 5} in row 7 in the position you posted, Marty. That in turn reveals a {2, 3, 5} triplet in column 8, so you can set r3c8 = 4, and then the "strong links" are apparent. dcb
PS I didn't notice the "fork" that Keith was talking about. But I did find a double-implication chain commencing at r6c3 that solved the puzzle -- looking at it with the benefit of hindsight I see that the chain incorporated the "fork." Sometimes the same feature in a puzzle points different ways for different solvers. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Jul 04, 2006 3:54 am Post subject: |
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It looks like both you guys independently found the hidden pair, since based on time of posts, neither of you saw the other's. I'll have to train myself to be alert; I don't recall ever finding a hidden pair or triple, one reason being that I don't know enough to look for them.
| Quote: | | Looking at it, I don't know why I eliminated the "7" from r7c3. |
Just for the record, it was eliminated via a finned X-Wing.
| Quote: | | That in turn reveals a {2, 3, 5} triplet in column 8, so you can set r3c8 = 4, |
This is one of the useless philosophical questions that I think about: why is r3c8 set to "4"? Is it because of eliminations made from the triplet or is it because it was a hidden single? Maybe hidden single shouldn't be a technique because it's always accompanied by a pair, triple, quad, or whatever.
Oh well, I'd be infinitely better off thinking about how to find hidden pairs than this abstract stuff. |
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