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May 12 Very Easy, Very Hard

 
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cgordon



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

PostPosted: Sat May 12, 2007 4:33 pm    Post subject: May 12 Very Easy, Very Hard Reply with quote

That has to be the easiest "very hard" puzzle ever. The XYZ wing step is reached in no time at all - and at this stage, there are few unsolved cells left.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat May 12, 2007 5:38 pm    Post subject: Reply with quote

There is an unneeded Unique Swordfish, an X-wing, and a BUG. If you do not use the BUG, there is a choice of a couple of XY-wings or an XYZ-wing that will solve it.

Keith


Last edited by keith on Sat May 12, 2007 5:49 pm; edited 1 time in total
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sdq_pete



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

PostPosted: Sat May 12, 2007 5:40 pm    Post subject: Reply with quote

Certainly easy up to the sticking point, which, as you say, was at an advanced stage. That point for me was the following and I found this a bit tricky:
Code:

+------------+-------------+--------+
| 3   8   6  | 57  57   4  | 9 2  1 |
| 2   45  45 | 8   1    9  | 7 6  3 |
| 9   7   1  | 2   3    6  | 5 8  4 |
+------------+-------------+--------+
| 4   259 27 | 3   257  8  | 1 79 6 |
| 567 1   3  | 567 9    57 | 2 4  8 |
| 67  269 8  | 4   267  1  | 3 79 5 |
+------------+-------------+--------+
| 1   26  27 | 67  8    3  | 4 5  9 |
| 8   3   45 | 9   45   2  | 6 1  7 |
| 567 456 9  | 1   4567 57 | 8 3  2 |
+------------+-------------+--------+

Play this puzzle online at the Daily Sudoku site

Before a fairly easily spotted XY-wing I needed here to use what I think is described as a finned X-wing to eliminate the 6 in R6C2. Column 5 has two 6's; column 1 almost completes an X-wing on 6's except there is an extra 6 in block 4. Nevetheless, it is enough to eliminate the 6 in R6C2.

Did you not need this?

Peter
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat May 12, 2007 5:55 pm    Post subject: Reply with quote

In the position posted above, there is an X-wing on <5> in C16.

Note the "Unique Swordfish" on <45> in R289. Then neither of R9C25 can be <45>. They must be <4> because of the strong link on <4> in R9 - then neither of them is <5>. These eliminations are made also by the X-wing.

Keith
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cgordon



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

PostPosted: Sat May 12, 2007 7:36 pm    Post subject: Reply with quote

For all my bragging about how easy this was - I seem to have screwed up here. My correct solution has a 7 in R9C1. But surely the 567 in R5CI form an XYZ with the 67 in R6C1 and 57 in R9C6. I'm new to these XYZ wings but shouldn't the above XYZ eliminate the 7 in R9C1. I am so confused.
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sdq_pete



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

PostPosted: Sat May 12, 2007 7:57 pm    Post subject: Reply with quote

I suppose the simple way forward is the X-wing mentioned by Keith which somehow fell on my blind spot. Your potential XYZ-wing doesn't work, I fear. Like a number of potential XYZ-wings, the triplet is there but all three cells - the pivot and both pincers - must be able to see a victim and this we don't have. In the case of your proposed XYZ-wing, I actually don't see this at all since the pivot (R1C5) can't even see R9C6. I thought at first you meant the 57 in R5C6. But here too there is in fact no victim that all three cells can see.

So I think it's either one of Keith's routes or my elimination of the 6 in R6C2.

Peter
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George Woods



Joined: 28 Mar 2006
Posts: 304
Location: Dorset UK

PostPosted: Sat May 12, 2007 9:11 pm    Post subject: Many ways to skin a cat Reply with quote

Don't know if it counts as an XY wing , but I used the 67 at r7c4 if 7 then r7c3 is 2, and if 6 then r4c5 is 2 so we have an XY wing (in my book) eliminating the 2 at r4c3 and giving a solution.

Incidentally Draw/play gives solution of 5 in Box2 and shortly after a 5 in box5 - seems to me more difficult than my way!....
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat May 12, 2007 9:20 pm    Post subject: Reply with quote

Quote:
Don't know if it counts as an XY wing , but I used the 67 at r7c4 if 7 then r7c3 is 2, and if 6 then r4c5 is 2 so we have an XY wing (in my book) eliminating the 2 at r4c3 and giving a solution.


It isn't an XY-Wing based on my understanding of same. It looks to me like a forcing chain which reveals a pincerlike attack on the 2 in r4c3, as opposed to the basic forcing chain which forces a cell to be a certain value.
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cgordon



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

PostPosted: Sat May 12, 2007 9:32 pm    Post subject: Reply with quote

But surely that's guessing? I still don't see why the 7 isn't eliminated from R9C1 - since this cell "sees" the 7s in R5C1, R6C1 and R9C6. That's my understanding of how XYZ wings work.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

PostPosted: Sat May 12, 2007 9:55 pm    Post subject: Reply with quote

cg,

No. Here is how XYX-wings work:

There is a root cell, XYZ. It sees two other cells, XZ and YZ. The root cell has three possibilities:

It is Z.
It is X, in which case XZ is Z.
It is Y, in which case YZ is Z.

So, any other cell which sees all three cells in the XYZ-wing cannot be Z.

In this example, R9C1 is the root cell <567>, R9C6 is <57>, R6C1 is <67>. An XYZ-wing, yes. But, it makes no eliminations.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sat May 12, 2007 10:15 pm    Post subject: Reply with quote

I solved it as follows, maybe differently only because of differences in the sequences we use to look for things.

Code:

+------------+-------------+--------+
| 3   8   6  | 57  57   4  | 9 2  1 |
| 2   45  45 | 8   1    9  | 7 6  3 |
| 9   7   1  | 2   3    6  | 5 8  4 |
+------------+-------------+--------+
| 4   259 27 | 3   257  8  | 1 79 6 |
| 567 1   3  | 567 9    57 | 2 4  8 |
| 67  269 8  | 4   267  1  | 3 79 5 |
+------------+-------------+--------+
| 1   26  27 | 67  8    3  | 4 5  9 |
| 8   3   45 | 9   45   2  | 6 1  7 |
| 567 456 9  | 1   4567 57 | 8 3  2 |
+------------+-------------+--------+


There was the skyscraper on 5 in rows 4 and 8. Another skyscraper on 6 in rows 5 and 7. Basic eliminations then allow simple coloring on 5 to eliminate the 5 from r5c4. After further eliminations, an XYZ-Wing on 259 based in r4c2 finishes it off.
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cgordon



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

PostPosted: Sun May 13, 2007 5:28 pm    Post subject: Reply with quote

I can see that either R4C5 or R8C5 has to be a 5 - which eliminates the 5 from R1C5. But I can't see how the rest proceeds without a guess or assumption - whether on 5s or 6s. I thought these things could be solved without guessing.
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

PostPosted: Sun May 13, 2007 9:38 pm    Post subject: Reply with quote

cgordon wrote:
I can see that either R4C5 or R8C5 has to be a 5 - which eliminates the 5 from R1C5. But I can't see how the rest proceeds without a guess or assumption - whether on 5s or 6s. I thought these things could be solved without guessing.


I don't think your initial statement is correct. There's nothing that says r1c5 can't be a 5. The skyscraper involves the 5s in rows 4 and 8. In each row there are only two possibilities for a 5. They both can't be in column 5, thus at least one of the other possibilities in those rows, r4c2 and r8c3, must be a 5. Any cell that sees both of those cells (in this case that cell is r9c2) cannot be a 5. Hope that's clear enough.
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Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Sun May 13, 2007 11:09 pm    Post subject: Reply with quote

cg - if you want to see a graphic example of a skyscraper look at the one that is illustrated in Mesmin's puzzle in this thread

http://www.dailysudoku.com/sudoku/forums/viewtopic.php?t=1860&sid=9cb62644c9357068f48772c4a472f413

The skyscraper is in pink, the eliminated 5's in orange.

Hope that helps.
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