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5 JUne difficult -has this technique got a name?
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George Woods



Joined: 28 Mar 2006
Posts: 234
Location: Dorset UK

PostPosted: Tue Jun 05, 2007 1:30 pm    Post subject: 5 JUne difficult -has this technique got a name? Reply with quote

Having reached this position
Code:

+-------+-------+----------+
| . 6 . | . 5 . | 49 2  .  |
| 5 . . | 9 . . | 7  .  .  |
| 9 4 . | 3 . . | 8  .  5  |
+-------+-------+----------+
| 6 5 1 | 2 8 7 | 3  9  4  |
| 8 2 9 | . . 3 | 1  5  7  |
| 3 7 4 | 5 9 1 | .  68 .  |
+-------+-------+----------+
| . . 5 | . . 9 | .  7  1  |
| . . 6 | . . 5 | .  .  .  |
| . 9 . | . 2 . | 5  3  68 |
+-------+-------+----------+

Play this puzzle online at the Daily Sudoku site

I was intreagued by the 68s in Box 6 and 9

whether the 6 in col 7 is in box 6 or 9 it excites an 8 that acts as pincers by denying an 8 to r8c8. and this solves the problem albeit I needed an X wing after this!

Is this a well known type of Wing?
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Tue Jun 05, 2007 3:26 pm    Post subject: Reply with quote

I don't know what it's called, but it's an interesting move! I was stumped at this point I must say. Your logic is a neat way forward. The hint, incidentally, was 7 at R3C5, though in the route adopted by your move this only appears a long way down the line.
To finish, I needed a "sky-scraper" by the way (involving 7's).

Peter
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Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Tue Jun 05, 2007 5:02 pm    Post subject: Reply with quote

As far as I know, it's not a type of wing, but a version of a forcing chain. If r6c7 is a 6 or if r7c7 is a 6, then r8c8 =4. Maybe it can be viewed as a form of an XY-chain, but someone who knows that better than I do should verify that.
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Tue Jun 05, 2007 6:19 pm    Post subject: June 5 Reply with quote

The hint says that r3c5 is 7. Why?
It must be that r1c4, r3c3, or r8c5 is a 7. But how?
Thanks
Earl
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Tue Jun 05, 2007 7:32 pm    Post subject: Reply with quote

Thatís a very nice observation, George! I canít recall the specific pattern being described before.

It seems quite useful. Better still, it is easy to spot: all that has to be done is check whether any two cells with the same two candidates (xy) can be linked via a strong link on x or y.

If you donít object, I shall think of it as a ďW-Wing.Ē

Steve
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Tue Jun 05, 2007 7:43 pm    Post subject: Reply with quote

Earl

Have you used the x-wing for 1 in rows 1 and 9?

If you do this and then identify the pair (13) in row 8, I think you will find that only one cell in the fifth column will admit a 7.

Steve
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sdq_pete



Joined: 30 Apr 2007
Posts: 119
Location: Rotterdam, NL

PostPosted: Tue Jun 05, 2007 8:57 pm    Post subject: Reply with quote

I hadn't spotted the 13 hidden pair - indeed, that gives the 7 in R3C5.

Interestingly, I found another place where George's logic could be applied ("W-wing"). The following is the situation (where the "W-wing" in block 9 has not yet been applied):
Code:

+------------+-------------+-------------+
| 17  6  378 | 148  5   48 | 49   2  39  |
| 5   18 38  | 9    14  2  | 7    46 36  |
| 9   4  2   | 3    7   6  | 8    1  5   |
+------------+-------------+-------------+
| 6   5  1   | 2    8   7  | 3    9  4   |
| 8   2  9   | 46   46  3  | 1    5  7   |
| 3   7  4   | 5    9   1  | 26   68 268 |
+------------+-------------+-------------+
| 24  38 5   | 468  346 9  | 246  7  1   |
| 247 13 6   | 78   13  5  | 249  48 289 |
| 147 9  78  | 1678 2   48 | 2456 3  68  |
+------------+-------------+-------------+

Play this puzzle online at the Daily Sudoku site

Note the 78 in blocks 7 and 8 (similar to the 68 pairs in blocks 6 and 9). In row 7, an 8 appears in blocks 7 and 8 only, as a result of which one of the 78 pairs must be 7 and this eliminates the 7 in R8C1.

Peter
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dulaby



Joined: 02 May 2007
Posts: 13

PostPosted: Tue Jun 05, 2007 9:20 pm    Post subject: Reply with quote

There is a very interesting xy-wing in boxes 1,3 and9(38,36 and 6Cool.
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Tue Jun 05, 2007 10:18 pm    Post subject: "W-wing" Reply with quote

I don't believe George's "W-wing" is valid. There is no polarity between the 68 pair. They could both be 6, for instance, with no 8 elimination.

In sdq_pete's example, the same logic could be used to eliminate the 8s at R9C4 and R9C6. But, R9C4 is, in fact, 8.

Pondering George's 68s led me to an interesting Medusa wrap situation in columns 7,8,9. Assigning a + to the 6 in R6C7 leads to the following:
Code:

-------------------
| 4-9+  *    3+9- |
|  *   14+6  3-6+ |
|  *   16     *   |
-------------------
|  *    *     *   |
|  *    *     *   |
| 26   6+8-  268+ |
-------------------
| 246   *     *   |
| 249- 4-8+  289+ |
|  *    *    68   |
-------------------


Looking at C9, note that there are a 6 and 8 with + polarity. But, this eliminates both candidates from R9C9! Thus, all of the + values can be eliminated. This is VERY helpful in getting to the solution.
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Tue Jun 05, 2007 11:28 pm    Post subject: Reply with quote

Asellus

Here is the grid again:

Code:
+-------+-------+----------+
| . 6 . | . 5 . | 49 2  .  |
| 5 . . | 9 . . | 7  .  .  |
| 9 4 . | 3 . . | 8  .  5  |
+-------+-------+----------+
| 6 5 1 | 2 8 7 | 3  9  4  |
| 8 2 9 | . . 3 | 1  5  7  |
| 3 7 4 | 5 9 1 | .  68 .  |
+-------+-------+----------+
| . . 5 | . . 9 | .  7  1  |
| . . 6 | . . 5 | .  .  .  |
| . 9 . | . 2 . | 5  3  68 |
+-------+-------+----------+


If both r6c8 and r9c9 contain 6, there is no room for 6 in box 3.

George was looking at it from the other direction: the wing is effective because the seventh column must have a 6 in box 6 or box 9.

Steve
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kragzy



Joined: 01 May 2007
Posts: 112
Location: Australia

PostPosted: Wed Jun 06, 2007 12:06 am    Post subject: Reply with quote

Asellus

"They could both be 6, for instance, with no 8 elimination." You've made a simple error here - where would you put the 6 in C6? We all slip up every now and then.

But what is your logic behind the statement "In sdq_pete's example, the same logic could be used to eliminate the 8s at R9C4 and R9C6. "? I can't see it.
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TexCat



Joined: 07 Jul 2006
Posts: 31

PostPosted: Wed Jun 06, 2007 2:38 am    Post subject: Reply with quote

I resorted to trial and error on this one, and never spotted Dulaby's very nice xy-wing.

But the w-wing!!! Very exciting new technique! Let's see if I understand it....

Code:

.    .    .  |  NotG NotG NotG | .   .  . 
GW   .    .  |   .    .      . | .   .  .
.    .    .  |    .   .      . | .   . GW


If you have an GW pair in boxes either in the same column or the same row of boxes, and the row/column which is not part of the GW pair cannot contain G, then you can eliminate W from the cells that the GW pair have in common.

And so you end up with
Code:

.     .    .  |  NotG NotG NotG | .    .    . 
GW    .    .  |   .    .      . |NotW NotW NotW 
NotW NotW NotW|   .    .      . | .    .    GW
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Asellus



Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA

PostPosted: Wed Jun 06, 2007 8:44 am    Post subject: Ah... I see! Reply with quote

I missed the "Not G" in the third row/column part. It's very valid indeed! A W-Wing it is!
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dulaby



Joined: 02 May 2007
Posts: 13

PostPosted: Wed Jun 06, 2007 1:54 pm    Post subject: Reply with quote

TexCat , the xy-wing is formed by r2c3(3Cool,r2c9(36) and r9c9(6Cool so that <8> is out of r9c3,therefore r9c3 is <7>.
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cgordon



Joined: 04 May 2007
Posts: 769
Location: ontario, canada

PostPosted: Wed Jun 06, 2007 9:37 pm    Post subject: Reply with quote

No need for "new discoveries" !!
Looking for skyscrapers on 1's eliminates the 1 in R2C5 - which leaves a pair of 46's in col 5. Plain sailing from there.
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Mogulmeister



Joined: 03 May 2007
Posts: 695

PostPosted: Wed Jun 06, 2007 9:40 pm    Post subject: Reply with quote

Yes - but nice to see that unusual cast of mind in action.
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TexCat



Joined: 07 Jul 2006
Posts: 31

PostPosted: Thu Jun 07, 2007 12:05 am    Post subject: Reply with quote

cgordon wrote:

No need for "new discoveries" !!
Looking for skyscrapers on 1's eliminates the 1 in R2C5 - which leaves a pair of 46's in col 5. Plain sailing from there.

I certainly agree that there is no need for w-wings on this puzzle. Dulaby's xy-wing solves it nicely. I cannot see any skyscraper on 1's though.
sdq_pete wrote:

Code:

+------------+-------------+-------------+
| 17  6  378 | 148  5   48 | 49   2  39  |
| 5   18 38  | 9    14  2  | 7    46 36  |
| 9   4  2   | 3    7   6  | 8    1  5   |
+------------+-------------+-------------+
| 6   5  1   | 2    8   7  | 3    9  4   |
| 8   2  9   | 46   46  3  | 1    5  7   |
| 3   7  4   | 5    9   1  | 26   68 268 |
+------------+-------------+-------------+
| 24  38 5   | 468  346 9  | 246  7  1   |
| 247 13 6   | 78   13  5  | 249  48 289 |
| 147 9  78  | 1678 2   48 | 2456 3  68  |
+------------+-------------+-------------+

Play this puzzle online at the Daily Sudoku site

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Lynnda



Joined: 07 Jun 2007
Posts: 3
Location: Sydney, Australia

PostPosted: Thu Jun 07, 2007 1:29 am    Post subject: June 5 Reply with quote

"Looking for skyscrapers on 1's eliminates the 1 in R2C5 - which leaves a pair of 46's in col 5.

I know everyone else can follow this but I haven't yet been able to work out exactly what a skyscraper should look like (yes, i am new, sorry Confused )

Can someone draw the skyscraper on the 1s for me please?

I have read the solving guide and tried to apply it but it is taking me a while to get the hang of it!
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Earl



Joined: 30 May 2007
Posts: 546
Location: St Louis MO

PostPosted: Thu Jun 07, 2007 2:24 am    Post subject: June 5 Reply with quote

Gordon,

I do not see the skyscraper that elinates the 1 in r2c5.
Can you help me?

Earl
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Marty R.



Joined: 12 Feb 2006
Posts: 5166
Location: Rochester, NY, USA

PostPosted: Thu Jun 07, 2007 3:52 am    Post subject: Reply with quote

I don't see a skyscraper on 1 either.

Lynnda,

This is an explanation of a skyscraper I recently made 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.

Hope that's clear.
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