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Freep Dec 28, 2007

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keith

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

Posted: Fri Dec 28, 2007 6:24 pm Post subject: Freep Dec 28, 2007

In Daily Sudoku terms, this is a Very Hard:

Code:

Puzzle: FP122807
+-------+-------+-------+
| . . . | . 5 . | . . . |
| 9 . . | 6 . . | . . 3 |
| . 7 . | 8 . 2 | . 4 . |
+-------+-------+-------+
| 2 . 4 | . 8 . | . . 1 |
| . . 7 | 9 . 4 | 8 . . |
| 6 . . | . 7 . | 5 . . |
+-------+-------+-------+
| . 9 . | 3 . 8 | . 2 . |
| 8 . . | . . 5 | . . 6 |
| . . . | . 2 . | . . . |
+-------+-------+-------+

Keith

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Fri Dec 28, 2007 8:48 pm Post subject:

x-wing on 1's xy-wing {1,4,5} the pincers in r2c2 and r5c1 that did it for me. norm

keith

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

Posted: Fri Dec 28, 2007 10:02 pm Post subject:

storm_norm wrote:

x-wing on 1's
xy-wing {1,4,5} the pincers in r2c2 and r5c1
that did it for me.

norm

Exactly what I did. Note that there are two XY-wings that accomplish the same thing, solve R5. The pivots are in R1C1 or in R2C2.

Keith

Marty R.

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

Posted: Fri Dec 28, 2007 10:28 pm Post subject:

One W-Wing on 14 did it for me.

Johan

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

Posted: Sat Dec 29, 2007 12:49 am Post subject:

There is a useless [14-145-15] xyz-wing@, when the common digit <1> is placed in R1C1, R7C1 or R7C3, they all have the same end result : R7C7=4, solving the
puzzle.

Code:

+--------------------------+--------------------------+--------------------------+
|@14 26 268 | 14 5 3 | 267 78 9 |
| 9 1245 1258 | 6 14 7 | 12 18 3 |
| 3 7 16 | 8 9 2 | 16 4 5 |
+--------------------------+--------------------------+--------------------------+
| 2 3 4 | 5 8 6 | 79 79 1 |
| 15 15 7 | 9 3 4 | 8 6 2 |
| 6 8 9 | 2 7 1 | 5 3 4 |
+--------------------------+--------------------------+--------------------------+
|@145 9 @15 | 3 6 8 |-[1]4 2 7 |
| 8 124 123 | 7 14 5 | 1349 19 6 |
| 7 146 136 | 14 2 9 | 134 5 8 |
+--------------------------+--------------------------+--------------------------+

alanr555

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

Posted: Sat Dec 29, 2007 12:13 pm Post subject:

Johan wrote:

There is a useless [14-145-15] xyz-wing@,
When the common digit <1> is placed in R1C1, R7C1 or R7C3,
they all have the same end result : R7C7=4, solving the puzzle.

I do not understand this comment - but I am only just coming to
grips with the xyz-wing.

Given the trio of cells with 145 as stated, one can eliminate the
common digit (1) from any cells which can "see" all three in the trio.

The only cells that can do that are r8c1 and r9c1 but one is an initial
cell and the other was resolved much earlier. Hence, perhaps the
"uselessness" of the xyz-wing!

When the common digit "1" is placed in r7c1 or r7c3 it does indeed
imply that r7c7 is 4. However, when a "1" is put in r1c1 it does NOT
have the same implication - without considering the effect of the
15 that is, conveniently, situated in r5c1.

Thus this appears not to be an xyz-wing as I have just learned it.
Does this pattern have a separate name or is it just fortuitous in
the same way that any placing can assist with solution?

The puzzle has seven cells containing just "14". They are all
strongly linked in a chain and so "breaking in" to that chain is
likely to resolve a lot but the 145 triangle does not do it for me
as there is no compulsion for ANY cell in that triangle to have
the value "1". Having r5c1 and r7c7=1 would avoid any of the
trio being 1 - although no doubt would lead to a contradiction
from other aspects of the puzzle.

+++
Please let me know what I have missed or misunderstood.

alanr555

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

Posted: Sat Dec 29, 2007 12:28 pm Post subject:

Marty R. wrote:

One W-Wing on 14 did it for me.

I do not know what W-wing is referenced here.
However, having just learned about the W-wing I decided to look for
one and discovered that cells r5c2 and r7c3 each have value "15"
whilst a strong link exists on "5" between r5c1 and r7c1.

a) Is this indeed a W-wing pattern?
(or have I misled myself?)

If it is a W-wing, how should I document it?
Currently I am unable to interpret the shorthand references.
There seem to be three elements.
- the original two cells
- the digit used as the strong link
- the cells between which the strong link exists
How is this information condensed into a format that is
widely understood without ambiguity?

b) Does this then permit the removal of "1" from r8c2 and r9c2?

+++
If the above eliminations are correct, column two resolves to a
triple (246) and a pair (15) leaving r1c1 as the sole position for
a "4" in region one. The full resolution follows directly from this.

keith

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

Posted: Sat Dec 29, 2007 1:38 pm Post subject:

After the X-Wing on <1> in C58 that makes six eliminations in R28:

The XYZ-wing:

Code:

+----------------+----------------+----------------+
| 14@ 26 268 | 14$ 5 3 | 267 78 9 |
| 9 1245 1258 | 6 14% 7 | 12$ 18 3 |
| 3 7 16 | 8 9 2 | 16% 4 5 |
+----------------+----------------+----------------+
| 2 3 4 | 5 8 6 | 79 79 1 |
| 15 15 7 | 9 3 4 | 8 6 2 |
| 6 8 9 | 2 7 1 | 5 3 4 |
+----------------+----------------+----------------+
| 145@ 9 15@ | 3 6 8 |-14 2 7 |
| 8# 124 123 | 7 14 5 | 1349 19 6 |
| 7# 146 136 | 14 2 9 | 134 5 8 |
+----------------+----------------+----------------+

Look at the cells marked @. One of them must be <1>. This excludes <1> from their common peers #, which is not much use.

However, go coloring on <1>, starting in R1C1. If R1C1 is <1>, so are the cells %, and in particular, R3C7. You can exclude <1> in R7C7.

Now, the W-wing:

Code:

+----------------+----------------+----------------+
| 14@ 26 268 | 14 5 3 | 267 78 9 |
| 9 1245 1258 | 6 14 7 | 12 18 3 |
| 3 7 16# | 8 9 2 | 16# 4 5 |
+----------------+----------------+----------------+
| 2 3 4 | 5 8 6 | 79 79 1 |
| 15 15 7 | 9 3 4 | 8 6 2 |
| 6 8 9 | 2 7 1 | 5 3 4 |
+----------------+----------------+----------------+
| 1-45 9 15 | 3 6 8 | 14@ 2 7 |
| 8 124 123 | 7 14 5 | 1349 19 6 |
| 7 146 136 | 14 2 9 | 134 5 8 |
+----------------+----------------+----------------+

The cells @ have the same candidates <14>. They are linked by the strong link on <1>, # in R3. You can eliminate <4> in R7C1.

And, the puzzle is solved.

Keith

TKiel

Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

Posted: Sat Dec 29, 2007 3:13 pm Post subject:

Alan,

Quote:

Thus this appears not to be an xyz-wing as I have just learned it.

It's not. It's the combination of two techniques (XYZ-wing & coloring) and has been explained by Keith in his post above. Coloring can also be used with W-wings and XY-wings.

Quote:

However, having just learned about the W-wing I decided to look for one and discovered that cells r5c2 and r7c3 each have value "15" whilst a strong link exists on "5" between r5c1 and r7c1.

a) Is this indeed a W-wing pattern?

b) Does this then permit the removal of "1" from r8c2 and r9c2?

Yes, to both.

Quote:

If it is a W-wing, how should I document it?

Document it in what way?

alanr555

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

Posted: Sun Dec 30, 2007 12:02 am Post subject:

TKiel wrote:

Quote:

If it is a W-wing, how should I document it?

Document it in what way?

When reference is made in this forum to the technique that has
been used it is usually stated in a concise form.

Comments such as "The PQR-wing (or whatever) on 0 (digit
specified) solved it for me" seem deficient to me.

What I am seeking is a form in which a particular occurrence of a W-wing can be precisely specified. In this puzzle, there are at least two
W-wings that have been identified.

Isa comment like:
"A W-wing on 15 in regions four and seven" sufficient - or should
the strong link in column one be mentioned or the fact of
digit 5 being the link?

alanr555

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

Posted: Sun Dec 30, 2007 12:16 am Post subject:

keith wrote:

After the X-Wing on <1> in C58 that makes six eliminations in R28:

Using Mandatory Pairs techniques, there is no need to resort to
the X-wing in order to reach the position quoted.

keith wrote:

The XYZ-wing is not much use.

However, go coloring on <1>, starting in R1C1. If R1C1 is <1>, so are the cells %, and in particular, R3C7. You can exclude <1> in R7C7.

Colouring seems to me to be akin to implication chains. Is not one
of the objectives to avoid "chain" techniques wherever possible?
That has been my motivation for exploring wing formations - as I
was previously finding solutions by implication chains and was
seeking a more "elegant" approach to the solutions.

In this case the W-wing on 15 in in r5c2/r7c3 linked by 5 in column
one enables column two to be reduced leading to a sole position
for the "4" in region one - without using chains or their variants.

keith

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

Posted: Sun Dec 30, 2007 3:37 am Post subject:

alanr555 wrote:

Alan,

"Elegance" is in the eye of the beholder. So far as I am concerned, "chains" and "wings" are two sides of the same coin. I tend to prefer methods that are based on recognizing a pattern (X-wings, for example), but I am also disposed towards methods that exploit, well, a "method". That would include coloring and W-wings, in my book.

The point of my message was to clarify methods that others had mentioned. When you are faced with a truly hard puzzle, it seems to me that there are no techniques to avoid "wherever possible".

Keith

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