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April 11- hard

 
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SL
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PostPosted: Tue Apr 11, 2006 3:03 am    Post subject: April 11- hard Reply with quote

Appear not an unique answer.
(3,Cool can be appeared in (r8c5, r8c9,r9c5,r9c9).
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SL
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PostPosted: Tue Apr 11, 2006 3:05 am    Post subject: Re: April 11- hard Reply with quote

SL wrote:
Appear not an unique answer.
(3,Cool can be appeared in (r8c5, r8c9,r9c5,r9c9).


it should be ( 3,8 )
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 11, 2006 4:55 am    Post subject: Go fishing!! Reply with quote

The puzzle is unique, and quite interesting. After eliminating pinned values and using pairs, you get to:

Code:


+-------------------+-------------------+-------------------+
| 9     6     38    | 24    24    1     | 7     38    5     |
| 5     123   4     | 79    79    8     | 6     123   13    |
| 7     128   128   | 3     5     6     | 1248  12489 189   |
+-------------------+-------------------+-------------------+
| 4     7     6     | 8     1     3     | 9     5     2     |
| 3     29    25    | 579   6     79    | 18    18    4     |
| 1     89    58    | 459   49    2     | 3     7     6     |
+-------------------+-------------------+-------------------+
| 28    134   13    | 249   23489 5     | 1248  6     7     |
| 28    134   9     | 6     23478 47    | 5     12348 138   |
| 6     5     7     | 1     23489 49    | 248   23489 389   |
+-------------------+-------------------+-------------------+



Note that the <9> in B9 is in R9. So, R9C6 is not <9>, it must be <4>, which solves the puzzle.

But, there are many fish swimming here!

1. An X-wing on <4> in R1 R6.
2. An X-wing on <9> in C8 C9.
3. A Swordfish on <9> in C6 C8 C9 (destroyed by 2. above).
4. A Jellyfish on <9> in R2 R5 R6 R7.
5. A Jellyfish on <4> in C2 C6 C7 C8.
6. An X-wing on <9> in R2 R7.

I think any one of these is enough to solve the puzzle.

Keith
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Sarah



Joined: 04 Apr 2006
Posts: 6
Location: Brooklyn

PostPosted: Tue Apr 11, 2006 4:42 pm    Post subject: Reply with quote

Keith - I happened to solve it the first way you mentioned, eliminating the 9 from r9c6.
However, I'm curious about the rest of the terminology you're using ... x-wing, jellyfish, etc. Is there somewhere on this site to learn about that? Or a book?
Right now I simply follow the logic of the numbers, but it would be nice to understand what you're talking about. Laughing
Thanks!
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 11, 2006 9:02 pm    Post subject: Reply with quote

Sarah,

To solve the Daily Sudoku puzzles you need to know about forced squares, pinned squares, pairs and triples, and intersections.

This logic
Quote:

Note that the <9> in B9 is in R9. So, R9C6 is not <9>,

is an intersection of B9 with R9.

The Daily Sudoku do not require more "advanced" methods, but you can of course apply such methods if you wish.

Take a look at C8.
Code:

+-------------------+---------------------+---------------------+
| 9     6     38    | 24    24     1      | 7     38     5      |
| 5     123   4     | 79    79     8      | 6     123    13     |
| 7     128   128   | 3     5      6      | 1248  12489a 189c   |
+-------------------+---------------------+---------------------+
| 4     7     6     | 8     1      3      | 9     5      2      |
| 3     29    25    | 579   6      79     | 18    18     4      |
| 1     89    58    | 459   49     2      | 3     7      6      |
+-------------------+---------------------+---------------------+
| 28    134   13    | 249   23489  5      | 1248  6      7      |
| 28    134   9     | 6     23478  47     | 5     12348  138    |
| 6     5     7     | 1     23489e 49f    | 248   23489b 389d   |
+-------------------+---------------------+---------------------+

There are only two possibilities for <9>, the squares labeled a and b. One of them MUST be <9>. This is called a strong link.

Now, look at C9. There are only two possibilities for <9>, the squares labeled c and d. One of them MUST be <9>. This is another strong link.

Notice that the ends of these two strong links line up in R3 and R9. Think about it. It turns out that either a and d are <9>, or b and c are <9>.

So, the <9> in R9 is either b or d, and e and f cannot be <9>.

This is an "X-wing", where two strong links line up to form a rectangle. The possible values occur on one diagonal or the other, hence the term "X". If the links are in columns, you can eliminate values in rows, and vice-versa.

Swordfish is the extension of X-wings to three rows and columns, jellyfish is the extension to four rows and columns.

You can learn more at the SadMan site:

http://www.sadmansoftware.com/sudoku/techniques.htm

The explanantions are very good. When you need to know more, look at the solvers' discussion, especially the list of links:

http://www.sudoku.com/forums/viewtopic.php?t=3315

Finally, at this site, Daily Sudoku, just go to the "Other Puzzles" forum, where you will find many helpful people.

Best wishes,

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Tue Apr 11, 2006 9:28 pm    Post subject: Reply with quote

Quote:
This is an "X-wing", where two strong links line up to form a rectangle. The possible values occur on one diagonal or the other, hence the term "X". If the links are in columns, you can eliminate values in rows, and vice-versa.

Keith,

The logic in your example is, of course, unassailable. However, the definition of an X-Wing that I learned was that there could only be two occurrences of the number in both the rows and columns. So it seems to me that three possibilities are in play here:

1) My definition is not correct

2) My definition is correct, except that the number can appear in other columns when the X-Wing rectangle is wholly within one chute

3) The example here is technically not an X-Wing, even though it strongly resembles one.
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TKiel



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

PostPosted: Tue Apr 11, 2006 10:25 pm    Post subject: Reply with quote

Marty,

To form an x-wing, either both rows have only two cells with the candidate (the columns can have more) and those 4 cells line up in two columns or both columns have only two cells with the candidate (then the rows can have more) and those 4 cells must line up in two rows. After all, if there were only two occurrences of the number in both the rows and the columns (all of which would form the x-wing), where would one make exclusions?
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Tue Apr 11, 2006 10:35 pm    Post subject: Reply with quote

Marty,

The X-wing starts with two possibilities in each of two rows (or columns). That line up. The result is eliminations in columns (or rows), so you end up with an X-wing rectangle that has possibilities at its corners, with solutions only on one diagonal, and no other possibilities in the rectangle's rows and columns.

Take at look at SadMan's explanation. And, there are SadMan puzzles that use the technique.

http://www.sadmansoftware.com/sudoku/technique6.htm

It took me a long time to understand this stuff: It was the definition of strong (and weak) links that was most helpful for me.

Keith
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alanr555



Joined: 01 Aug 2005
Posts: 193
Location: Bideford Devon EX39

PostPosted: Wed Apr 12, 2006 1:15 am    Post subject: Reply with quote

Code:

> To solve the Daily Sudoku puzzles you need to know about
> forced squares, pinned squares, pairs and triples, and
> intersections.

This assertion is taking things a bit far!!

I am able to solve almost all Daily Sudoku puzzles (well Hard,
Very Hard and Medium, I ignore the Easy ones) but I do NOT
know out forced squares or pinned squares. Are these squares
special versions of the rectangles like "Unique Rectangle" which
debars a pattern with the same pair in each corner of a
rectangular pattern?

Pairs, Triples and Intersects are all components of any approach
(a rose being as sweet by any other name). As well as them, I
am finding "Sole Position" very useful - not in its usual form of
scanning the candidate profiles but by looking at every unresolved
cell in a line (row or column) and attempting to spot cases where
a digit in the "cross"-line precludes the target digit in all except
one of the cells. This is more onerous (complex?) than use of the
"Sole candidate" technique with which we are mostly familiar.
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TKiel



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

PostPosted: Wed Apr 12, 2006 1:24 am    Post subject: Reply with quote

I think forced squares and pinned squares are other names for naked and hidden singles, although I'm not sure which is which.
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SL
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PostPosted: Wed Apr 12, 2006 3:21 am    Post subject: Reply with quote

Keith,

You're right.
I'ven't carefully checked my answer. Sorry.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Wed Apr 12, 2006 3:57 pm    Post subject: Reply with quote

TKiel wrote:
Marty,

To form an x-wing, either both rows have only two cells with the candidate (the columns can have more) and those 4 cells line up in two columns or both columns have only two cells with the candidate (then the rows can have more) and those 4 cells must line up in two rows. After all, if there were only two occurrences of the number in both the rows and the columns (all of which would form the x-wing), where would one make exclusions?

Tracy, I probably didn't make myself clear. I realize there is nothing to be eliminated if there are no other occurrences in BOTH rows and columns. See my response to Keith below.

Quote:
The X-wing starts with two possibilities in each of two rows (or columns). That line up. The result is eliminations in columns (or rows), so you end up with an X-wing rectangle that has possibilities at its corners, with solutions only on one diagonal, and no other possibilities in the rectangle's rows and columns.

Yes, I messed up again, a not infrequent happening. It's a classic X-Wing. One of my problems is that I think vertically, not horizontally, and when this grid gets rotated 90, it's an X-Wing as I'm used to seeing them. I think of only two occurrences in rows, with the eliminations being in columns.

By the way, and I don't know why it took until today to see this, these "9s" are also a case of locked candidates. Since all the possibilities in box 9 are in r9, the other "9s" in r9 can be eliminated based on that.
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Wed Apr 12, 2006 8:58 pm    Post subject: Terminology Reply with quote

Alan,

I am afraid I am using some unfamiliar terminology (or terminology unfamiliar to some).

By "square" I mean "cell". We can use SadMan as a decoder ring:

http://www.sadmansoftware.com/sudoku/techniques.htm

Go there to see what is meant by his term, you can translate my terms to yours.

(Keith = SadMan)

Forced square = Naked single

Pinned square = Hidden single

Intersections = Block and column / row interactions (= locked candidates, a term used by Marty)

Pair, triple = Naked and hidden subsets

I believe that all Daily Sudoku can be solved with only these techniques. (I would be delighted if the Daily Sudoku became more difficult.)

The terminology I use is from Robert Woodhead's Sudoku Susser Manual, I did not make it up.

Keith
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keith



Joined: 19 Sep 2005
Posts: 3165
Location: near Detroit, Michigan, USA

PostPosted: Wed Apr 12, 2006 9:36 pm    Post subject: Another two-link Reply with quote

I am afraid I have to make another observation about this puzzle.

I a previous message, I pointed out an X-wing, which occurs when two strong links line up to form a rectangle. There is degraded form, where two strong links line up only at one end.

Here is our puzzle:

Code:

+--------------------+-------------------+-------------------+
| 9     6      38    | 24    24     1    | 7     38    5     |
| 5     123    4     | 79    79     8    | 6     123   13    |
| 7     128    128   | 3     5      6    | 1248  12489 189   |
+--------------------+-------------------+-------------------+
| 4     7      6     | 8     1      3    | 9     5     2     |
| 3     29     25    | 579   6      79   | 18    18    4     |
| 1     89     58    | 459   49     2    | 3     7     6     |
+--------------------+-------------------+-------------------+
| 28    134a   13    | 249e  23489f 5    | 1248  6     7     |
| 28    134b   9     | 6     23478  47c  | 5     12348 138   |
| 6     5     7      | 1     23489  49d  | 248   23489 389   |
+--------------------+-------------------+-------------------+


The squares marked a and b are a strong link on <4> in their column, C2. The squares marked c and d are a strong link on <4> in C6. These strong links line up at one end only (a and c.)

It turns out that one of the ends which do not line up (a or d) must be <4>. Think about it.

a or b is <4>.
c or d is <4>.
If b is <4>, c cannot be <4>, and vice-versa.

In other words, the possible solutions containing <4> are:

a and c
a and d
b and d.

One of b or d is always <4>.

So, neither of the squares e and f can be <4>.

The point: If you are looking for X-wings by finding strong links that line up at both ends, you should be also looking for links that line up at one end. They may be useful!

(And, yes, I know there are simpler ways to solve this. For example, the pair cd in C6 excludes all other possible values of <4> in B8.)

Best wishes,

Keith
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TKiel



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

PostPosted: Wed Apr 12, 2006 11:20 pm    Post subject: Reply with quote

This is known as 'multiple colouring', which is merely two (or more) different conjugate (what you refer to as a strong link) chains linked on one end. They then function just like a single conjugate chain, in that any cell or cells that see both ends of the chains can be excluded.
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