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leocar
Joined: 04 Mar 2010
Posts: 12
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 Posted: Thu Jun 16, 2022 3:17 am Post subject: Learning W-Wings |
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Hi, I'm learning how to find and use W-Wings. Today's daily sudoku (16/06/2022) I think may have had one even though it has nothing to do with solving the puzzle. Can someone please let me know if I have found a W-Wing or if I am way off. From what I can see the 1,9's R2C7, R5C8 (*) are linked by 3,9 R7C7 and 2,9 R8C8(#) meaning 1 is removed from R5C7 is that correct?
| Code: |
+----------+------------+-------------+
| 2 5 1 | 4 9 3 | 7 6 8 |
| 4 7 8 | 6 5 2 | 19* 3 19 |
| 6 9 3 | 1 7 8 | 5 4 2 |
+----------+------------+-------------+
| 39 6 59 | 235 1238 4 | 28 7 139|
| 8 2 459 | 35 13 7 | 1349 19* 6 |
| 37 1 47 | 9 28 6 | 28 5 34 |
+----------+------------+-------------+
| 1 4 29 | 23 6 5 | 39# 8 7 |
| 79 3 279 | 8 4 1 | 6 29# 5 |
| 5 8 6 | 7 23 9 | 134 12 134|
+----------+------------+-------------+
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Thanks
Leo |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 16, 2022 3:08 pm Post subject: |
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Hi Leo and welcome
It’s all about strong links for these various wings to work.
Looking for wings is helpful but also consider things from a fundamental level.
You have described something that has two ends or pincers - the remote pairs of 19’s in box 3 and box 6. One of these must be 1. It doesn’t matter which.
If you set one of the pairs to 9 and follow the chain the other pair becomes 1 making your elimination. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 16, 2022 3:14 pm Post subject: |
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| Mogulmeister wrote: | Hi Leo and welcome
It’s all about strong links for these various wings to work.
Looking for wings is helpful but also consider things from a fundamental level.
You have described something that has two ends or pincers - the remote pairs of 19’s in box 3 and box 6. One of these must be 1. It doesn’t matter which.
If you set one of the pairs to 9 and follow the chain the other pair becomes 1 making your elimination. |
So the definition of W wings:
“They consist of two bivalue cells with the same candidates, that are connected by a strong link on one of the candidates.”
Which you have. |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Thu Jun 16, 2022 3:35 pm Post subject: |
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Very good explanation.
For years I have always thought W wings as contradictory (as well as other stuff)
In this puzzle, r5c7 <> 1 as by using the <19> pair this would lead to no <9> in box 9 or in column 9 |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Thu Jun 16, 2022 4:39 pm Post subject: |
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Excellent !
So this Leo is a really good way to get into the guts of a puzzle. Same solution but arrived at in a very different way. Instead of starting out looking for a wing of some sort, consider the effect of a placement.
Tom has shown what happens if you put a 1 in r5c7 ?
It is very elegant because we are looking to disrupt that pair of 19’s and how!
This causes contradictions on a massive scale - no 9’s in column 9 and no 9 in box 9. So r5c7 can never be 1.
This method may seem inside out but, if anything it is even more powerful than the w wing search. Definitely worth adding to your armoury. |
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TomC
Joined: 30 Oct 2020
Posts: 358
Location: Wales
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| Posted: Thu Jun 16, 2022 5:18 pm Post subject: |
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A pair of cells containing <19> can go four ways 1:1 1:9 9:1 9:9
W wings prove that if one cell is 1 the other is 9 and vice versa, but always consider what would if happen if both were 1 or both were 9
Here, I can see the effect if both were 9 and just look to cause maximum damage by sticking 1 in r5c7 |
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leocar
Joined: 04 Mar 2010
Posts: 12
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| Posted: Thu Jun 16, 2022 10:41 pm Post subject: |
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| Thank you both for the replies. It has helped me understand the method better as well as proving it and having another potential solving method. |
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leocar
Joined: 04 Mar 2010
Posts: 12
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| Posted: Thu Jun 30, 2022 3:01 am Post subject: |
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Hi, while I was waiting for another VH, I looked at one from a few years back (I think it was from Tue 3-Jun-2014). After completing a X-Y wing I was left with the puzzle below which is graded hard.
I think I have found a W-Wing on 19's R8C1 and R9C7 with a few links eg R89C4 with both 1 and 9.
Does this mean R9C1 and R8C7 cannot be 1 or 9 i.e. R9C1=5 and R8C7=8?
| Code: |
+------------+--------------+-----------+
| 2 8 4 | 6 13 13 | 79 79 5 |
| 7 6 9 | 5 4 2 | 3 1 8 |
| 3 5 1 | 8 9 7 | 6 4 2 |
+------------+--------------+-----------+
| 159 2 8 | 7 15 19 | 4 6 3 |
| 4 13 35 | 2 1358 6 | 78 578 9 |
| 6 39 7 | 39 58 4 | 2 58 1 |
+------------+--------------+-----------+
| 8 139 2 | 4 7 139 | 5 39 6 |
| 19 4 6 | 139 2 5 | 189 389 7 |
| 159 7 35 | 139 6 8 | 19 2 4 |
+------------+--------------+-----------+
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Play this puzzle online at the Daily Sudoku site |
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glesco
Joined: 12 May 2022
Posts: 36
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| Posted: Thu Jun 30, 2022 3:03 pm Post subject: |
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| A 9 in column 4 is also possible in R6. 1s in column 4 are restricted to R89, so the 19 W-Wing in R8C1 & R9C7 removes 9s in R9C1 & R8C7 |
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Pat
Joined: 23 Feb 2010
Posts: 207
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| Posted: Thu Jul 07, 2022 2:12 am Post subject: |
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| glesco wrote: |
1s in column 4 are restricted
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— to box 8,
this solves the 1 for row 7. |
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leocar
Joined: 04 Mar 2010
Posts: 12
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| Posted: Mon Aug 08, 2022 10:33 pm Post subject: |
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| Code: |
+------------+----------+----------+
| 28 1 3 | 28 7 5 | 9 4 6 |
| 49 7 2489 | 3 89 6 | 1 28 5 |
| 6 5 289 | 289 1 4 | 3 7 28 |
+------------+----------+----------+
| 49 3 49 | 7 2 8 | 6 5 1 |
| 7 6 28 | 1 5 9 | 4 28 3 |
| 1 28 5 | 6 4 3 | 7 9 28 |
+------------+----------+----------+
| 28 4 7 | 58 6 1 | 25 3 9 |
| 3 28 1 | 589 89 7 | 25 6 4 |
| 5 9 6 | 4 3 2 | 8 1 7 |
+------------+----------+----------+
|
Play this puzzle online at the Daily Sudoku site
Hi, I was looking at this puzzle from yesterday and noticed a W-Wing with 28 in R5C3 and R3C9 with links to 2 and 8 in R6C29, from what I can see that means R3C3 cannot be either 2 or 8 therefore it has to be 9, is that correct? In this situation both numbers 2 and 8 are removed and not just one of them?
Cheers
Leo |
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storm_norm22
Joined: 24 Oct 2020
Posts: 15
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| Posted: Wed Dec 21, 2022 4:09 pm Post subject: |
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| leocar wrote: | | Code: |
+------------+----------+----------+
| 28 1 3 | 28 7 5 | 9 4 6 |
| 49 7 2489 | 3 89 6 | 1 28 5 |
| 6 5 289 | 289 1 4 | 3 7 28 |
+------------+----------+----------+
| 49 3 49 | 7 2 8 | 6 5 1 |
| 7 6 28 | 1 5 9 | 4 28 3 |
| 1 28 5 | 6 4 3 | 7 9 28 |
+------------+----------+----------+
| 28 4 7 | 58 6 1 | 25 3 9 |
| 3 28 1 | 589 89 7 | 25 6 4 |
| 5 9 6 | 4 3 2 | 8 1 7 |
+------------+----------+----------+
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Play this puzzle online at the Daily Sudoku site
Hi, I was looking at this puzzle from yesterday and noticed a W-Wing with 28 in R5C3 and R3C9 with links to 2 and 8 in R6C29, from what I can see that means R3C3 cannot be either 2 or 8 therefore it has to be 9, is that correct? In this situation both numbers 2 and 8 are removed and not just one of them?
Cheers
Leo |
sometimes its better to see a picture of it.
obviously, the W-wing is one of the more sought after patterns because its fairly easy to spot the bi-value cells. in this case, form your grid, we have a multitude.
in the picture, we have (2=8) in r5c3 and (2=8) in r3c9.
easy to spot, easy to see.
what gives these two cells its power to eliminate the 2 in r3c3 takes a bit more logic.
what connects these cells are the 8's in r5c8 and r6c9.
these 8's being the only 8's in BOX 6 are strongly inferenced.
we denote this strong inference like so (8)r5c8 = (8)r6c9
in the image above, you can put the chain together
(2=8)r3c9 - (8)r6c9 = (8)r5c8 - (8=2)r5c3
notice how the 2's are now strongly inferenced and are at the ends of the chain. if r5c3 is NOT a 2, then r3c9 is a 2
if r3c9 is NOT a 2 then r5c3 is a 2.
just like the 8's in BOX 6. |
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