View previous topic :: View next topic |
Author |
Message |
Glassman
Joined: 21 Oct 2005 Posts: 50 Location: England
|
Posted: Tue Jun 19, 2007 11:55 am Post subject: June 19 2007 VH |
|
|
Having trouble with this. I solved it and proved uniqueness by starting at the derived end of the only non-trivial pair on the grid. Whichever way around I started this pair, the cell in between came out with the same value.
I could not find a way of solving this without resorting to trial and error, and now cannot find a way retrospectively.
I would welcome enlightenment.
Glassman |
|
Back to top |
|
|
Earl
Joined: 30 May 2007 Posts: 677 Location: Victoria, KS
|
Posted: Tue Jun 19, 2007 12:49 pm Post subject: June 19 |
|
|
I solved it by the interconnection of the conjugate pairs of <1> in r3c5- r3c7 and r7c5-r7c8, and r3c7-r8c7. If either r3c5 or r3c7 is 1, r7c8 must be 1. The rest is simple elimination.
Is this called a skyscraper?
Earl |
|
Back to top |
|
|
PouLeeps
Joined: 19 Jun 2007 Posts: 6 Location: Lismore, Australia
|
Posted: Tue Jun 19, 2007 1:19 pm Post subject: |
|
|
Hi all,
I'm very new to Sudoku. I'm stuck at this point. Thanks.
[code]
+--------------+------------+--------------+
| 16 2 59 | 17 1579 3 | 4 167 8 |
| 168 368 389 | 2 179 4 | 5 1367 67 |
| 4 35 7 | 6 15 8 | 13 2 9 |
+--------------+------------+--------------+
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 58 58 | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
+--------------+------------+--------------+
| 68 7 38 | 4 18 9 | 2 136 5 |
| 9 3468 1 | 37 2 5 | 38 367 467 |
| 5 348 2 | 137 178 6 | 138 9 47 |
+--------------+------------+--------------+
How do I align the columns? |
|
Back to top |
|
|
Mesmin
Joined: 01 May 2007 Posts: 12 Location: Ontario
|
Posted: Tue Jun 19, 2007 2:04 pm Post subject: |
|
|
PouLeeps wrote: | Hi all,
I'm very new to Sudoku. I'm stuck at this point. Thanks.
Code: |
+--------------+------------+--------------+
| 16 2 59 | 17 1579 3 | 4 167 8 |
| 168 368 389 | 2 179 4 | 5 1367 67 |
| 4 35 7 | 6 15 8 | 13 2 9 |
+--------------+------------+--------------+
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 58 58 | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
+--------------+------------+--------------+
| 68 7 38 | 4 18 9 | 2 136 5 |
| 9 3468 1 | 37 2 5 | 38 367 467 |
| 5 348 2 | 137 178 6 | 138 9 47 |
+--------------+------------+--------------+
|
How do I align the columns? |
All you need to do is include the [*/code*] tag. (Don't put the *s in, but I couldn't make it show up in the post without them.
The first step from here would be a X-wing on 6s (cols 2 and 9). There is, I think, one more X-wing and an XY-wing before the puzzle falls apart. |
|
Back to top |
|
|
Steve R
Joined: 24 Oct 2005 Posts: 289 Location: Birmingham, England
|
Posted: Tue Jun 19, 2007 2:10 pm Post subject: |
|
|
This is the sticking point:
Code: | +-----------------------+
| . 2 . | . . 3 | 4 . 8 |
| . . . | 2 . 4 | 5 . . |
| 4 . 7 | 6 . 8 | . 2 9 |
-------------------------
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 . . | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
-------------------------
| . 7 . | 4 . 9 | 2 . 5 |
| 9 . 1 | . 2 5 | . . . |
| 5 . 2 | . . 6 | . . . |
+-----------------------+ |
Only two cells are open to 1 in rows 3 and 7:
Code: | +-----------------------+
| . 2 . | . . 3 | 4 . 8 |
| . . . | 2 . 4 | 5 . . |
| 4 . 7 | 6 a 8 | b 2 9 |
-------------------------
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 . . | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
-------------------------
| . 7 . | 4 c 9 | 2 d 5 |
| 9 . 1 | . 2 5 | . . . |
| 5 . 2 | . . 6 | . . . |
+-----------------------+ |
Cells a and c cannot both contain 1 so it must be in b or d. This eliminates 1 from r9c7. In the seventh column just b remains available.
The argument is (much) the same as Earl’s above.
You can also align the grid by selecting it and then clicking the “Code” button.
Steve |
|
Back to top |
|
|
David
Joined: 02 Jun 2006 Posts: 58 Location: Bedford, UK
|
Posted: Tue Jun 19, 2007 2:39 pm Post subject: |
|
|
I think the fastest route to solving this one is the option chosen by Earl. Yes, it is called a 'skyscraper', although I normally refer to it as 'strong links' |
|
Back to top |
|
|
Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
|
|
Back to top |
|
|
sdq_pete
Joined: 30 Apr 2007 Posts: 119 Location: Rotterdam, NL
|
Posted: Tue Jun 19, 2007 4:56 pm Post subject: |
|
|
Steve R wrote: |
Only two cells are open to 1 in rows 3 and 7:
Code: | +-----------------------+
| . 2 . | . . 3 | 4 . 8 |
| . . . | 2 . 4 | 5 . . |
| 4 . 7 | 6 a 8 | b 2 9 |
-------------------------
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 . . | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
-------------------------
| . 7 . | 4 c 9 | 2 d 5 |
| 9 . 1 | . 2 5 | . . . |
| 5 . 2 | . . 6 | . . . |
+-----------------------+ |
Cells a and c cannot both contain 1 so it must be in b or d. This eliminates 1 from r9c7. In the seventh column just b remains available.
|
For what it's worth, I found myself in the following situation and broke the deadlock by a very similar argument:
Code: |
+------------+-----------+-----------+
| 16 2 59 | 17 59 3 | 4 167 8 |
| 18 368 389 | 2 179 4 | 5 137 67 |
| 4 35 7 | 6 15 8 | 13 2 9 |
+------------+-----------+-----------+
| 2 9 6 | 8 4 1 | 7 5 3 |
| 7 58 58 | 9 3 2 | 6 4 1 |
| 3 1 4 | 5 6 7 | 9 8 2 |
+------------+-----------+-----------+
| 68 7 38 | 4 18 9 | 2 136 5 |
| 9 46 1 | 37 2 5 | 8 37 46 |
| 5 348 2 | 137 178 6 | 13 9 47 |
+------------+-----------+-----------+
|
Play this puzzle online at the Daily Sudoku site
R3C7 = 13. If it is 3 it leads to 1 at R3C5 and to 1 at R1C4. Ergo R3C7 must be 1.
Peter |
|
Back to top |
|
|
cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
|
Posted: Tue Jun 19, 2007 7:28 pm Post subject: |
|
|
I eventually solved it with skyscrapers on 1s in col 4 and 7. Then on 3s in col 4 and 7. Then with an xy wing using nos 1-8-6 in R2 & R7, Col 1 and R7C8 which eliminated the 1 from R2C8. I probably got lucky - but I think it was brilliant. |
|
Back to top |
|
|
Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
|
Posted: Tue Jun 19, 2007 9:03 pm Post subject: Color Wrap |
|
|
Starting from Peter's position, I applied the X-Wing on <7> in R1 and R8. This leaves 13 and 67 pairs in Box 3.
Next, color wrapping <1> starting at R2C8 produces opposite polarity for the <1>s in R3C7 and R7C5, eliminating the <1> at R3C5.
Essentially the same solution as others have posted, I believe. The term "Skyscraper" used on this board seems to apply both to what I learned as the simplest forms of Color Wraps and Color Wings (without extended wrapping). |
|
Back to top |
|
|
cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
|
Posted: Tue Jun 19, 2007 10:50 pm Post subject: |
|
|
Geez Mate! - Color Wraps and Color Wings (without extended wrapping).
No offense, but I actually think there is far too much "terminolgy" on this site. When I first joined there was Swordfish and colouring and all kinds of other stuff. Never did get to find out what it all meant. But since, I have learned that the only things I need to solve the "very hards" are Skyscrapers (probably called x wings). - xy wings and xyz wings.
I believe there is a need to simplify and standardise terminology. |
|
Back to top |
|
|
Marty R.
Joined: 12 Feb 2006 Posts: 5770 Location: Rochester, NY, USA
|
Posted: Wed Jun 20, 2007 1:04 am Post subject: |
|
|
Quote: | But since, I have learned that the only things I need to solve the "very hards" are Skyscrapers (probably called x wings) |
Skyscrapers are not X-Wings, they are the commonest form of what are called "Strong Links."
This is an explanation I made for someone in another thread:
Code: | +---------------+---------------+-------------+
| 259 8 7 | 569 3 69 | 4 1259 129 |
| 59 4 1 | 2 59 8 | 6 3 7 |
| 6 259 3 | 7 1 4 | 25 8 29 |
+---------------+---------------+-------------+
| 1 257 45 | 8 27 3 | 9 247 6 |
| 2379 2379 6 | 4 279 5 | 8 127 123 |
| 23479 2379 8 | 1 6 279 | 23 47 5 |
+---------------+---------------+-------------+
| 457 6 45 | 3 24579 279 | 1 259 8 |
| 8 357 2 | 59 4579 1 | 35 6 349 |
| 34 1 9 | 56 8 26 | 7 25 34 |
+---------------+---------------+-------------+ |
In each of columns 4 and 8 there are only two possibilities for a 9. The columns share one of those possibilities in row 1. Both columns can't have their 9 in row 1, so one of the other possibilities must be a 9. Any cells that see both of those other possibilities can't be a 9. Those cells that see both are r8c9, r7c5 and r7c6. |
|
Back to top |
|
|
Mogulmeister
Joined: 03 May 2007 Posts: 1151
|
Posted: Wed Jun 20, 2007 7:33 am Post subject: |
|
|
Asellus is right - colour wraps/traps/wings are just a different name for a series of techniques which are perhaps slightly better known (eg skyscraper).
In any case, I have to agree with David: these naming conventions are all just variants on strong links (ie conjugate pairs). We know that one must be true and the other false. Colouring is used to highlight different polarities. The colour wrap uses the colours to show up polarities where there is a contradiction or impossibility.
Whatever formation/technique/naming convention you use, the underlying concepts are "strong links".
This was a classic skyscraper (horizontal!) which actually made 3 eliminations - and this, as has been explained, is distinct from an x-wing.
|
|
Back to top |
|
|
Asellus
Joined: 05 Jun 2007 Posts: 865 Location: Sonoma County, CA, USA
|
Posted: Wed Jun 20, 2007 8:59 am Post subject: I See |
|
|
I didn't want to set off a terminology crisis. Being new to this board, I just didn't want to claim "Skyscraper" when I was still not completely certain I had the concept accurately. The responses have shown my understanding to be correct: two parallel strong links ("polarity pairs") sharing a common end, essentially.
Since I was residing in Color Wrap/Wing Land, I saw two different entities in this, depending upon whether (Wrap) or not (Wing) there was also a strong link between the common ends. These have different logics, but produce the same effect when limited to four cells... hence, Skyscraper. And, in C W/W Land, the column/row restriction doesn't matter (any "House" will do, including Boxes), nor does the 4-cell restriction (the strong links can be extended in polarity chains).
But, these restrictions take care of the great majority of useful cases, so... Skyscraper it is!
(Unimportant Notes: A Skyscraper looks like a sort of lopsided X-Wing, which may account for that confusion. Since X-Wing is a species of fish and is unrelated to the XY-and XYZ-Wings, I think it should have a fishy name myself! Perhaps guppy or sardine.) |
|
Back to top |
|
|
cgordon
Joined: 04 May 2007 Posts: 769 Location: ontario, canada
|
Posted: Wed Jun 20, 2007 6:47 pm Post subject: |
|
|
I'm confused here. Are x-wings skyscrapers of equal height? ie squares.
Anyway - I found the Marty R example very helpful. I've been solving the very hards (incl this one) by xyz wings which I find difficult to locate. |
|
Back to top |
|
|
Mogulmeister
Joined: 03 May 2007 Posts: 1151
|
Posted: Wed Jun 20, 2007 9:02 pm Post subject: |
|
|
Quote: | I'm confused here. Are x-wings skyscrapers of equal height? ie squares. |
In a way you're right- x-wings are indeed squares or rectangles but can eliminate candidates at points parallel to all 4 vertices. In a skyscraper the eliminations are made only at the unequal ends. Pictures are best to illustrate the point ! |
|
Back to top |
|
|
|