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Dec 21 VH
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TerenceF



Joined: 21 Dec 2007
Posts: 24
Location: Takapuna, NZ

PostPosted: Fri Dec 21, 2007 2:29 am    Post subject: Dec 21 VH Reply with quote

Finally! A VH that has not already been posted....

Once the naked pairs and triples are eliminated, I found it quite straightforward.

From here:
Code:

+-----------+----------------+--------------+
| 3 28  1   | 45    28   6   | 45   9    7  |
| 6 24  7   | 13459 2359 124 | 345  345  8  |
| 5 48  9   | 34    7    48  | 346  2    1  |
+-----------+----------------+--------------+
| 9 135 35  | 7     26   24  | 8    1456 56 |
| 4 6   2   | 8     1    5   | 9    7    3  |
| 7 15  8   | 469   269  3   | 2456 1456 56 |
+-----------+----------------+--------------+
| 1 9   356 | 356   4    78  | 3567 3568 2  |
| 2 35  4   | 1356  3568 178 | 3567 3568 9  |
| 8 7   356 | 2     356  9   | 1    356  4  |
+-----------+----------------+--------------+

the XY-wing on 28-48-24 eliminates the [2] from R2C6, which makes the [2] in R4C6 the only possibility for a [2] in C6

I'm posting this so that other users can correct my use of technical terms if necessary ...
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Marty R.



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

PostPosted: Fri Dec 21, 2007 4:45 am    Post subject: Reply with quote

Welcome to the forum. I saw no problem with your terminology.

Quote:
Finally! A VH that has not already been posted....


That shouldn't be difficult for you. These puzzles are made available to members by time zones (I can't see it yet) so you probably see it a zillion hours earlier than most. Laughing
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keith



Joined: 19 Sep 2005
Posts: 3329
Location: near Detroit, Michigan, USA

PostPosted: Fri Dec 21, 2007 7:45 am    Post subject: Reply with quote

Quote:
the XY-wing on 28-48-24 eliminates the [2] from R2C6,

I think you neglected to say that it also takes out <2> in R46C5.

For me, the hardest part of this puzzle was getting to R9C1 is <8>.

Keith
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andras



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

PostPosted: Fri Dec 21, 2007 10:28 am    Post subject: Reply with quote

Yes, that xy seems to be the simple solution, though I suspect that there are, as usual, others.

The big problem was finding it among all the various pairs still visible at that stage. All in all a very good puzzle!

John
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Earl



Joined: 30 May 2007
Posts: 590
Location: Victoria, KS

PostPosted: Fri Dec 21, 2007 2:26 pm    Post subject: Dec 21 VH Reply with quote

Two x-wings did it for me.

Earl
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cgordon



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

PostPosted: Fri Dec 21, 2007 3:24 pm    Post subject: Reply with quote

It took a long time to get rid of the initial clutter before spotting the
<356> triple in C3.
But anyway - forget that - I wanna go back to the hard time I was given on the last VH over - what was it called - "pincer colouring" ?? So let me see if I have understood it or just got lucky. I'm looking at the triple in C2 - Can I let the <42> be the pivot and extend <28> to the <28> in C5 and take out the <8> in R3C6. Or alternately let the <28> in C5 be the pivot and extend things in reverse to take out the <4> in R3C2.
Am I about to take flight !!??

Code:
            
+-------+-------+-------+   
| . 28. | . 28. | . . . |   
| . 42. | . . . | . . . |   
| . 48. | . .48 | . . . |   
+------+------- +-------+   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
+-------+-------+-------+   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |   
| . . . | . . . | . . . |
+-------+-------+-------+
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alanr555



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

PostPosted: Fri Dec 21, 2007 3:36 pm    Post subject: Reply with quote

Marty R. wrote:

Quote:
Finally! A VH that has not already been posted....


These puzzles are made available to members by time zones (I can't see it yet) so you probably see it a zillion hours earlier than most.


How does that work??
I understood that the puzzles were automatically posted onto a
single website at midnight UK time. This would mean US residents
getting it in the evening and NZ people at noon the next day.

How would the system know when to release the puzzle to each user?
On what feature of the user would her/his time zone be based?
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Johan



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

PostPosted: Fri Dec 21, 2007 3:37 pm    Post subject: Reply with quote

Quote:
Yes, that xy seems to be the simple solution, though I suspect that there are, as usual, others


This is also a one step move.

I came across this contradiction in Box 2 when R8C5=8, it results in a naked [56] pair in C4 of Box 8, and places digit <4> in R2C6, so putting <8> in R8C5

takes out <4> and <5> in R1C4 at the same time, which means that R8C5=8, causes a contradiction in Box 2, so <8> can't reside in R8C5, that pins <8> in R1C5,

solving the puzzle, nevertheless I found the xy-wing a neater path to finish this one.

Code:

+--------------------------+--------------------------+--------------------------+
| 3          28       1    | 45       [2]8       6    | 45        9          7   |
| 6          24       7    | 1459      259       12[4]| 345       35         8   |
| 5          48       9    | 3         7         48   | 6         2          1   |
+--------------------------+--------------------------+--------------------------+
| 9          135      35   | 7         26        24   | 8         14         56  |
| 4          6        2    | 8         1         5    | 9         7          3   |
| 7          15       8    | 469       69        3    | 2         14         56  |
+--------------------------+--------------------------+--------------------------+
| 1          9        356  | [56]      4        [7]8  | 357       3568       2   |
| 2          35       4    | 1[56]     356[8]   |1]78 | 357       3568       9   |
| 8          7        356  | 2         356       9    | 1         356        4   |
+--------------------------+--------------------------+--------------------------+
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eddieg



Joined: 12 Jan 2006
Posts: 47
Location: San Diego, CA USA

PostPosted: Fri Dec 21, 2007 4:11 pm    Post subject: terence Reply with quote

"the XY-wing on 28-48-24 eliminates the [2] from R2C6, which makes the [2] in R4C6 the only possibility for a [2] in C6"

You did mean to elininate the '2' in R4C5? That was how I solved the puzzle.
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alanr555



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

PostPosted: Fri Dec 21, 2007 4:17 pm    Post subject: Reply with quote

andras wrote:

That xy seems to be the simple solution, though I suspect that there are, as usual, others.
The big problem was finding it among all the various pairs still visible at that stage. All in all a very good puzzle!


Most puzzles reduce to a number of binary chains.
The objective is to identify them - especially the "closed"
chains and then to "break into them".
The simplest example of such a "closed" chain is the triple
which contains a "circular" relationship as in Jean Paul Satre's
play Huis Clos (Of three people each loves one and loathes one
with no mutual loving or loathing).

Column 2 rows 1-3 is an example.
The pairs are (28)(26)(48).
Solve one and the whole chain is solved.
Indeed, that is what occurs when the puzzle is "broken".

I found value 6 in r4c5 and the grade on the draw/play changed
from Very Hard to Easy. I use that facility to confirm that I have
actually found a solution to the puzzle - having done the work
on paper first, of course!

As ever the challenge is identification.
In this puzzle column two seems to be key as it contains two triples.
Triples are useful as they act as "polarity reversers" in implication
chains - akin to diagonals within regions.

Not being a theoretical mathematician, I offer no formal proof but
it seems to be that where two cells are connected by two chains and
one of them contains a "polarity reverser" there is likely to be
some useful information resulting.

This gives a clue as to the starting point. Then the more cells with
pairs the better as the chains formed are by their nature bound
to be binary chains.

In this case I started with the 28 in r1c2 and "followed my nose"
until I got to r4c5 as there were two routes to reach it. The trick
is perhaps to try and keep the two routes within striking distance
of each other and the two cells r4c5,r4c6 seemed suitable. This
realisation was assisted by noting the 135 triple and concentrating
on (coincidentally) the even digits rather than the odds (which would
probably have another set of implication chains).

The solution came from

r1c2 to r1c5 to r4c5 - direct route
r1c2 via the triple to r3c2 then r3c6,r4c6 to r4c5

I prefer to have one "short chain" and one longer one but the
routes could have been targetted on r4c6 just as well.

The implication chains demonstrate that r4c5 must be 6 (and r5c6=2).

My suspicion is that I am dealing with the same data as the data
involved in some of the advanced techniques used by others.

If so, it may be that the concept of "polarity reversing" could be
useful to those searching for patterns to use in such techniques.

I apologise for attempting VH puzzles when I have no understanding
of the various advanced techniques. My contribution is in aiding the
solution process by highlighting the merits of Mandatory Pairs in the
initial simplification (eg finding the 8 in r9c1 which arises from the
reduction of row nine to a triple 356 plus r9c1) and then looking at
ways to identify the "breaking" pattern in the cell profiles using
relatively simple processes (akin to using Newtonian rather than
Quantum physics!). I admit readily that my approaches are NOT
easily susceptible to computer programming but my purpose is
to look for HUMAN solutions rather than mechanistic ones. I see no
real value in solving Sudoku mechanistically - other than in the
challenge of developing the programs to achieve such task. The
real LOVE of Sudoku must come from the human satisfaction of
meeting the challenge at the relevant level. For some the easy or
medium will give satisfaction in merely the solution - whilst others
will need to add factors like target time or absence of pencil marks.
This all makes a contribution to human diversity. Let us celebrate it.
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Marty R.



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

PostPosted: Fri Dec 21, 2007 4:57 pm    Post subject: Reply with quote

Code:
+-----------+----------------+--------------+
| 3 28  1   | 45    28   6   | 45   9    7  |
| 6 24  7   | 13459 2359 124 | 345  345  8  |
| 5 48  9   | 34    7    48  | 346  2    1  |
+-----------+----------------+--------------+
| 9 135 35  | 7     26   24  | 8    1456 56 |
| 4 6   2   | 8     1    5   | 9    7    3  |
| 7 15  8   | 469   269  3   | 2456 1456 56 |
+-----------+----------------+--------------+
| 1 9   356 | 356   4    78  | 3567 3568 2  |
| 2 35  4   | 1356  3568 178 | 3567 3568 9  |
| 8 7   356 | 2     356  9   | 1    356  4  |
+-----------+----------------+--------------+


Quote:
But anyway - forget that - I wanna go back to the hard time I was given on the last VH over - what was it called - "pincer colouring" ?? So let me see if I have understood it or just got lucky. I'm looking at the triple in C2 - Can I let the <42> be the pivot and extend <28> to the <28> in C5 and take out the <8> in R3C6. Or alternately let the <28> in C5 be the pivot and extend things in reverse to take out the <4> in R3C2.
Am I about to take flight !!??


Craig,

Before you have pincer coloring, you need pincers, as from an XY-Wing or W-Wing. In the XY-Wing here, the pincers are the 2s in r4c6 and r1c5. We don't need coloring here, but use the 2 in r1c5 as an example. Due to strong links, if r1c5 is 2, then r1c2 is not 2 and r2c2 must be = 2. Thus, if r1c5 is 2, then r2c2 also must be = 2 and can be used as a substitute pincer for r1c5. The new combination would zap the 2 from r2c6.

Hope that's clear.
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tlanglet



Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

PostPosted: Fri Dec 21, 2007 8:06 pm    Post subject: Reply with quote

After completing the basics, I immediately started looking for w-wings since I am still trying to fully understand them and this puzzle seemed to offer some possibilities.

In fact, I soon found a w-wing on <24> at r2c2 & r4c6 with a strong link on <4> at r3c2 & r3c6 that resulted in the elimination of a <2> at r2c6. This is the same <2> that is eliminated by the xy-wing previously discussed.

Ted
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cgordon



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

PostPosted: Fri Dec 21, 2007 10:21 pm    Post subject: Reply with quote

Quote:
Hope that's clear.


Marty: No it ain't!!! I don't see what's wrong with my grid - it's a simple xy wing - pivot R2C2 and wings R1C2/R3C2 - which I have extended by using the xz-xy-yz=yz alluded to by Keith-et-al in the last VH puzzle posts.

I was expecting accolades - and recommendations that my grid become required reading for all Sudoku undergrads.

So where did I go wrong. IF INDEED I DID EH!!
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Marty R.



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

PostPosted: Fri Dec 21, 2007 10:45 pm    Post subject: Reply with quote

cgordon wrote:
Quote:
Hope that's clear.


Marty: No it ain't!!! I don't see what's wrong with my grid - it's a simple xy wing - pivot R2C2 and wings R1C2/R3C2 - which I have extended by using the xz-xy-yz=yz alluded to by Keith-et-al in the last VH puzzle posts.

I was expecting accolades - and recommendations that my grid become required reading for all Sudoku undergrads.

So where did I go wrong. IF INDEED I DID EH!!

Craig,

First of all, in your "XY-Wing", since the three cells are in one house, we think of that as a naked triple, not a Wing. However, if we use that as a Wing, the pincers are 8. You can extend each of the pincers to a three-cell chain, but it eliminates nothing.

Unless I'm missing something. ???
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Asellus



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

PostPosted: Fri Dec 21, 2007 11:15 pm    Post subject: Reply with quote

Craig,

Perhaps it would help if you would apply colors to this "pincer" coloring:
Code:

+--------+---------+-------+   
| . 28r. | . 28g.  | . . . |   
| . 42 . | . .  .  | . . . |   
| . 48G. | . .  48r| # # # |   
+--------+---------+-------+   
| . .  . | . .  .  | . . . |   
| . .  . | . .  .  | . . . |   
| . .  . | . .  .  | . . . |   
+--------+---------+-------+   
| . .  . | . .  .  | . . . |   
| . .  . | . .  .  | . . . |   
| . .  . | . .  .  | . . . |
+--------+---------+-------+

First, assuming the <8>s in r1 are strongly linked, we can color the <8> at r1c5 green. To eliminate the <8> at r3c6, it must see both red and green. But, it only sees two greens so there's no elimination.

However, if we assume that the <8>s in Box 2 are strongly linked, then the coloring extends to make the <8> at r3c6 red. Now, the cells marked # in Box 3 can see both a red and green <8>; so any <8>s in those cells would be eliminated due to this "pincer" coloring.

As it happens, this example is just your normal everyday coloring of <8>s because you are using a locked triple rather than an XY Wing, as Marty pointed out. So, this isn't really pincer coloring.

If I modify your example, I can show it as an actual pincer coloring:
Code:

+----------+---------+-------+   
| 28r .  . | . 28g.  | . . . |   
| .   42 . | . .  .  | . . . |   
| .   .  . | . .  48r| . . . |   
+----------+---------+-------+   
| .   48G. | . .  #  | . . . |   
| .   .  . | . .  .  | . . . |   
| .   .  . | . .  .  | . . . |   
+----------+---------+-------+   
| .   .  . | . .  .  | . . . |   
| .   .  . | . .  .  | . . . |   
| .   .  . | . .  .  | . . . |
+----------+---------+-------+

Now we have an XY Wing and the red pincer <8> at r1c1 is transported via coloring to r3c6. This allows elimination of <8> from the cell marked #.
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cgordon



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

PostPosted: Fri Dec 21, 2007 11:24 pm    Post subject: Reply with quote

Marty: Been thinking about this. Don't think there's anything wrong with my concept of a triple as an xy-wing. But maybe the "pincer colouring" extension needs TWO additions not one
i.e. not xz-xy-yz=yz but xz-xy-yz=yz=yz.
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cgordon



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

PostPosted: Fri Dec 21, 2007 11:28 pm    Post subject: Reply with quote

Asellus: Sorry - posted my post before looking at yours - which I will now digest.
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Marty R.



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

PostPosted: Sat Dec 22, 2007 1:27 am    Post subject: Reply with quote

cgordon wrote:
Marty: Been thinking about this. Don't think there's anything wrong with my concept of a triple as an xy-wing. But maybe the "pincer colouring" extension needs TWO additions not one
i.e. not xz-xy-yz=yz but xz-xy-yz=yz=yz.

Yes, two (or four) additions because for the pincer coloring to work, the new pincer must be of the same polarity. Plus-minus-plus or plus-minus-plus-minus-plus.
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keith



Joined: 19 Sep 2005
Posts: 3329
Location: near Detroit, Michigan, USA

PostPosted: Sat Dec 22, 2007 5:42 am    Post subject: Reply with quote

cgordon,

Yes, an XY-wing is a triple, but in two elements (line or box). Let's say it is XZ-XY-YZ.

If it is an XY-wing, the links are weak (or strong), and XZ and YZ do not "see" each other. Note that Z is true in one OR BOTH of them.

If it is a triple, all three cells in the same line or box, then XZ and YZ are a strong link (in Z). They can form a link in a coloring chain for Z, XY is more or less irrelevant. Z is true only in one of XZ and YZ, so the chain logic is subtly different.

Keith
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cgordon



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

PostPosted: Sat Dec 22, 2007 1:38 pm    Post subject: Reply with quote

Just one last comment on the chain thing. Asellus, in your grid, R3C6 is a <48> whereas the notation for a pincer chain discussed for the last VH was xz-xy-yz=yz=yz. So I assumed I had to "end" on a <28>. I see it now. Never got into chains - don't think I ever will.

To quote from the early Beatle's song "Chains"
"... and they ain't the kind - that you can see."
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