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Dec 13th VH
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 1:13 am    Post subject: Dec 13th VH Reply with quote

This is a place holder to establish the topic and to avoid the
sort of duplication that occurred on 11th when the same puzzle
had two thread due to contemporaneous composing of posts.
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 1:33 am    Post subject: Reply with quote

This is an example of a puzzle where Mandatory Pairs can solve a LOT
of the preliminary work.

Before deriving any pencil mark profiles and using purely the M/Pairs
techniques the number of unresolved cells has been reduced to 28
by solving 27 in addition to the 26 original values set. That reduces
the pencil marks by around 50%

Of the 28 unresolved cells ten are in mutual reception pairs (ie two
cells within the same region which can be occupied only by one of
two identified digits). Of the 18 remaining six are in what one might
term "Mandatory Triples" (the first use of this term!) in that they are
in a set of three cells within a region with only three possible values
between them and each digit constrained to just two of the three cells.
This leaves only twelve cells which at this stage are not in a strong
relationship with another cell.

The next stage is to derive the profiles and then to discern the
patterns which will enable the full solution.

As it is now the early hours of the morning in UK, I may need to sleep
on this one before posting further. The protocol on this site is one
benefit of being on the American continent!
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 2:28 am    Post subject: Reply with quote

There is A resolution using implication chains. The challenge is then
to refine these into a more elegant solution.

Cell r4c9 can take values 1 and 5.
Positing value 1 for this cell leads to the following

a) r6c9 must be 6 and so r6c6 must be 2.
b) r4c1 must be 5 and so either r4c4 or r4c5 must be 2
This would result in two cells in region five having value 2.

Using this "reductio ad absurdem" approach means that the
value in r4c9 must be 5. Given this the rest of the puzzle
resolves easily.


+++

This puzzle appears to have only ONE "crunch point" and so
the VH grading must rely upon the quality of the techniques
required rather than the old method of crunch-point quantity.

The technique of reductio ad absurdem (or contradictory
implications) was argued by David Bryant (who seems not
to have posted since October 2006) as very much NOT being
"trial and error".

This leaves two possibilities.

a) Either the solver uses this method and ipso facto demonstrates
that the method is not trial and error
or
b) There is a more elegant technique included in the program of
the solver and I have not found it!

Other contributors to this forum may be able to advise whether
Reductio ad absurdem is a valid method within the protocols
of this site.

Now, having solved this one I can retire to bed!

+++
Postscript:

It is pertinent to note that a reductio ad absurdem will almost
certainly involve an odd number of "in-region" relationships
as the rectilinear relationships (using just rows and columns)
will generally be congruent in binary link terms. This is more
a comment on solution methods than this puzzle.

Here having the double cell r4c4/r4c5 adds complexity to the
implication chain but assuming just one of these cells (and
they are functionally equivalent in this case) would lead to
a closed chain from r4c9 back to itself using links as
HHVHV where HV are horizontal/vertical and D is diagonal.
If this is a rule (and I have not the skills to prove it) then it may
prove an aid to "spotting" possible implication chains. For this
puzzle, the efficacy of the M/Pairs preliminary work resulted in
a lot of two-element cell profiles and so it was relatively easy to
spot the potential for an implication chain.
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Dec 13, 2007 3:49 am    Post subject: Reply with quote

Code:
7      5      4      | 1      68     68     | 3      9      2
9      6      2      | 3      7      5      | 8      1      4
1      8      3      | 24     9      24     | 5      6      7
---------------------+----------------------+-------------------
25     4      6      | 28     128    7      | 9      3      15
35     1      7      | 46     346    9      | 2      8      56
23     9      8      | 5      1236   26     | 47     47     16
---------------------+----------------------+-------------------
6      27     9      | 2478   5      248    | 1      47     3
4      27     1      | 9      26     3      | 67     5      8
8      3      5      | 467    46     1      | 467    2      9


after basics
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storm_norm



Joined: 18 Oct 2007
Posts: 1741

PostPosted: Thu Dec 13, 2007 4:00 am    Post subject: Reply with quote

put me down for a xy-wing, {2,4,6}
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Marty R.



Joined: 12 Feb 2006
Posts: 5731
Location: Rochester, NY, USA

PostPosted: Thu Dec 13, 2007 6:06 am    Post subject: Reply with quote

storm_norm wrote:
put me down for a xy-wing, {2,4,6}

That finished it off, although I earlier played a Type 1 UR and a W-Wing, and I'm not sure if either was necessary to the solution.
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Marty R.



Joined: 12 Feb 2006
Posts: 5731
Location: Rochester, NY, USA

PostPosted: Thu Dec 13, 2007 6:17 am    Post subject: Reply with quote

Quote:
Other contributors to this forum may be able to advise whether
Reductio ad absurdem is a valid method within the protocols
of this site.

I don't know about validity, but it's not necessary, since as far as I know, all VHs can be solved with X-, XY- and XYZ-Wings. But almost everyone uses other techniques as well, as evidenced by the discussions that occur after every VH is published.

Quote:
The technique of reductio ad absurdem (or contradictory
implications) was argued by David Bryant (who seems not
to have posted since October 2006) as very much NOT being
"trial and error".

David was a heavy user of implication chains. I suppose T&E is like beauty, in the eye of the beholder, and I'll leave it to others to decide whether it is or not. But I no longer feel good about solving a puzzle when I have to resort to it.
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nataraj



Joined: 03 Aug 2007
Posts: 1047
Location: near Vienna, Austria

PostPosted: Thu Dec 13, 2007 6:57 am    Post subject: Reply with quote

Came to that same 2,4,6 and it solved the puzzle.

____

quo usque tandem abutere, Catalana, patientia nostra?
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andras



Joined: 31 Oct 2007
Posts: 56
Location: Mid Wales

PostPosted: Thu Dec 13, 2007 9:27 am    Post subject: Reply with quote

I found the 146, but my wife found a simple x-wing on 1, and that broke the puzzle as well. No doubt other solutions are also possible.

John
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 9:41 am    Post subject: Reply with quote

Marty R. wrote:

Quote:

Other contributors to this forum may be able to advise whether Reductio
ad absurdem is a valid method within the protocols of this site.

I don't know about validity, but it's not necessary, since as far as I know, all VHs can be solved with X-, XY- and XYZ-Wings. But almost everyone uses other techniques as well, as evidenced by the discussions that occur after every VH is published.


This reference to X-, XY-, XYZ- wings emphasises the need for a good
knowledge source on these techniques.

Almost certainly the information has been posted previously, What is
needed is a collation of the material. Is anyone able to compile a
set of URLs to the salient posts?

Possibly one way would be to prepare a summary post with some
URLs contained within it and then for a "sticky" to be posted in the
Techniques part of this forum - containing just an introduction and
a list of techniques plus a URL for each technique leading to the
compile description/explanation for each.

I would be quite willing to develop a comprehensive post on the
Mandatory Pairs approach but I will be reliant on others to impart
to me an understanding of the "wing" techniques - beloved (?) as
I recall by someone somewhere from Munich.
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 9:53 am    Post subject: Reply with quote

andras wrote:
I found the 146, but my wife found a simple x-wing on 1, and that broke the puzzle as well. No doubt other solutions are also possible.
John


There are "1" digits in r4c5, r4c9, r6c5, r6c9 which form a rectangle
but no other occurrences of "1" exist apart from resolved cells.

How does this help?
Does it have any connection with the "simple x-wing on 1"?

Others have referred to 246, the quote above is to 146.
What patterns are being identified and how do they assist
with the solution?

Given the large number of fairly strong relationships (enumerated
in an earlier post) it is not surprising that there should be quite a
few entry points to the solution.
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nataraj



Joined: 03 Aug 2007
Posts: 1047
Location: near Vienna, Austria

PostPosted: Thu Dec 13, 2007 10:09 am    Post subject: Reply with quote

andras wrote:
... a simple x-wing on 1, and that broke the puzzle as well.John


John,

I think you are mistaken. There is no need for x-wing up to the position posted by storm_norm and in that position the "1"s are already reduced to the x-wing shape.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Thu Dec 13, 2007 1:14 pm    Post subject: Reply with quote

The [246] xy-wing did it for me, but looking for some other steps to solve the grid I came across this one. There

is a potential [46] DP* in R59C45, only three ways for avoiding that DP :

1. R9C4=7
2. R5C5=3
3. R9C4=7 and R5C5=3

Suppose R9C4=7 => R5C4=6 => R5C9=5 => R5C1=3 => R6C1=2 => R6C6=6 => contradiction in Box 5 (R5C4 and R6C6 are both <6>)

This means that R5C5 must be <3>, solving the puzzle.

Code:

+--------------------------+--------------------------+--------------------------+
| 7           5        4   | 1        68        68    | 3         9          2   |
| 9           6        2   | 3        7         5     | 8         1          4   |
| 1           8        3   | 24       9         24    | 5         6          7   |
+--------------------------+--------------------------+--------------------------+
| 25          4        6   | 28       128       7     | 9         3          15  |
| 35          1        7   |*46      *346       9     | 2         8          56  |
| 23          9        8   | 5        1236      26    | 47        47         16  |
+--------------------------+--------------------------+--------------------------+
| 6           27       9   | 2478     5         248   | 1         47         3   |
| 4           27       1   | 9        26        3     | 67        5          8   |
| 8           3        5   |*467     *46        1     | 467       2          9   |
+--------------------------+--------------------------+--------------------------+ 
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cgordon



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

PostPosted: Thu Dec 13, 2007 2:18 pm    Post subject: Reply with quote

Quote:
put me down for a xy-wing, {2,4,6}


Yep: Put me down for the same wing. Easier to understand than some of the posts!
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 3:25 pm    Post subject: Reply with quote

cgordon wrote:
Quote:
put me down for a xy-wing, {2,4,6}


Yep: Put me down for the same wing. Easier to understand than some of the posts!


Johan's solution uses implication logic - just as did mine.
I share the unease at this as it is akin to trial and error.

Whilst Johan and I used very different starting points for our
implication chains, we both arrived at a contradiction being
in region five. This suggests that it may be possible to discern
a clue from some pattern relating to that region - but how?

The language of the quote above is much simpler than some of
the other posts, agreed, but it is easier to understand fully ONLY
if one knows what an xy-wing is and the significance of the {246}
in the context of the current puzzle.

Where is the explanation for the xy-wing?
With that cross-reference the simple language posts might THEN
be easier to understand fully. Without that understanding some
of us are scrabbling about in the dark seeking clues that might
just enable us to prise open the door. Finding the key might be
preferable but that demands light. Can anyone shed some?

Certainly I understand that there is a solution using xy-wing but
that is akin to my understanding that it is possible to send a
landing craft to Mars. Without an explanation as to how to do it
I would have no idea even where to begin (not that I would wish
even to attempt sending an object to Mars - although I am very
pleased that it is possible).
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alanr555



Joined: 01 Aug 2005
Posts: 198
Location: Bideford Devon EX39

PostPosted: Thu Dec 13, 2007 3:42 pm    Post subject: Reply with quote

Johan wrote:

There is a potential [46] DP* in R59C45.


What is a DP*?

I understand the technique but not the terminology.

row 5: 46/346
row 9: 467/46

This has the potential for being a unique rectangle if one is
able to exclude either the 3 or the 7.

A Unique rectangle is where three corners of a rectilinear
set of four cells within two regions (adjacent or not) have
the same pair of digits as their only candidates (ie two sides
of the rectangle consist of pairs - remote or otherwise).

The rule is that the fourth corner cannot be either of the two
digits as that would contradict the basic assumption that
there is a unique solution to the puzzle.

Thus if the pattern above were to be:
row 5: 46/46
row 9: 467/46

then the first cell on row nine would HAVE to be 7 to avoid
the puzzle having a non-unique solution.

This technique does not resolve the 46 pairs but hopefully
resolution of the 7 would assist progress.

However in the current puzzle there were TWO "interlopers"
and so the technique does not apply. I noticed the pattern
but did not see it as being useful - probably because I not
yet learned HOW to make use of such a pattern!
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Asellus



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

PostPosted: Thu Dec 13, 2007 4:08 pm    Post subject: Reply with quote

Alan,

DP is Deadly Pattern, the general term for any arrangement of digit placements that result in a non-unique solution. A UR is just the simplest form of DP.

Elsewhere (I don't currently have the link) there is a description of 6 Types of UR solutions. Usually, one of these established Type patterns is used when exploiting a UR. But, not always. Sometimes it is possible to note a particular pattern in a UR instance that allows it to be exploited. That was the case here. By noting that the <7> placement results in a contradiction it could be discarded, leaving a Type 1 UR: three matching bivalue corners where the UR digits can be removed from the 4th corner. Here, that left only the <3>, which was determined.
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tjones99999



Joined: 13 Dec 2007
Posts: 1

PostPosted: Thu Dec 13, 2007 5:53 pm    Post subject: xy-wing 246... Reply with quote

Can someone post which cells are involved in this xy wing?
Thanks
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cgordon



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

PostPosted: Thu Dec 13, 2007 6:09 pm    Post subject: Reply with quote

Quote:
Elsewhere (I don't currently have the link) there is a description of 6 Types of UR solutions


I think you are alluding to this UR reference posted by Keith. I like it cos it's got pictures.
http://www.sudoku.com/boards/viewtopic.php?p=29105


Quote:
Where is the explanation for the xy-wing?

I think it's tacitly assumed that VH doers understand xy-wings. But anyway - the pivot is in R5C4 - can't remember where the wing cells and target cell are but they should be self evident.
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Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Thu Dec 13, 2007 7:19 pm    Post subject: Reply with quote

Quote:
Can someone post which cells are involved in this xy wing?


tjones99999,

welcome to the forum
The [46-26-24] xy-wing with pivot(xy) in R6C6, eliminating <4> in R3C4

Code:

+--------------------------+--------------------------+--------------------------+
| 7           5        4   | 1        68        68    | 3         9          2   |
| 9           6        2   | 3        7         5     | 8         1          4   |
| 1           8        3   | 2-[4]    9      xz 24    | 5         6          7   |
+--------------------------+--------------------------+--------------------------+
| 25          4        6   | 28       128       7     | 9         3          15  |
| 35          1        7   | 46 zy    346       9     | 2         8          56  |
| 23          9        8   | 5        1236   xy 26    | 47        47         16  |
+--------------------------+--------------------------+--------------------------+
| 6           27       9   | 2478     5         248   | 1         47         3   |
| 4           27       1   | 9        26        3     | 67        5          8   |
| 8           3        5   | 467      46        1     | 467       2          9   |
+--------------------------+--------------------------+--------------------------+ 
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