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DB Saturday Puzzle - September 30, 2006

 
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 30, 2006 9:22 am    Post subject: DB Saturday Puzzle - September 30, 2006 Reply with quote
Code:
Puzzle: DB093006  ******
+-------+-------+-------+
| . . . | . 9 1 | . . 3 |
| . . . | . . . | . 7 . |
| 9 . . | 2 . 6 | . 8 1 |
+-------+-------+-------+
| . 4 . | . 3 . | . . 2 |
| 3 2 . | . . . | . 9 8 |
| 8 . . | . 6 . | . 5 . |
+-------+-------+-------+
| 1 7 . | 9 . 3 | . . 5 |
| . 8 . | . . . | . . . |
| 4 . . | 7 2 . | . . . |
+-------+-------+-------+

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
PostPosted: Sat Sep 30, 2006 12:49 pm    Post subject: Reply with quote
This one could be subtitled "Fun with strong links, colouring, multi-colouring (both 2 & 3 chains), fork, turbot fish, skyscraper, etc..."

Thanks again, Keith, for posting these.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 30, 2006 2:08 pm    Post subject: Reply with quote
Tracy,

You must be having more fun than I am. All I found was an XY-wing.

Keith
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
PostPosted: Sat Sep 30, 2006 3:54 pm    Post subject: Reply with quote
Well, when you miss seeing the XY-wing, there are other ways to solve, including a 3 chain multi-colouring. Here's the grid:

Code:
 
 *--------------------------------------------------------------------*
 | 7      56     8      | 45     9      1      | 2456   246    3      |
 | 256A   156    12456  | 3      458    48     | 4569   7      469C   |
 | 9      35     345    | 2      7      6      | 45     8      1      |
 |----------------------+----------------------+----------------------|
 | 56a    4      1567   | 8      3      9      | 167    16     2      |
 | 3      2      16b    | 145    45     7      | 146B   9      8      |
 | 8      19     179    | 14     6      2      | 3      5      47     |
 |----------------------+----------------------+----------------------|
 | 1      7      26     | 9      48     3      | 2468-  246    5      |
 | 25     8      2359   | 6      1      45     | 2479   234    479    |
 | 4      3569   3569   | 7      2      58     | 1689-  136    69c    |
 *--------------------------------------------------------------------*


The XY-wing is there is box 4 & 7. (Now I see it.)

Another way is notice the strong links on 6, in column 1, row 5 and column 9. And the fun part is they connect together in a way that can be used. Each of the strong links form a two cell chain. The chain in column 1 is the key. The chain in column 9 links with one end of the chain in column 1. The chain in row 5 links to the other end of the chain in column 1. If the cell in column 9 and row 5 that link to the chain in column 1 are both true, then column 1 has no 6. That can't happen. So we know that at least one of the cells on the other end of those chains must be true. That means that any cell that 'sees' both of those cells can have 6 excluded (the cells marked with -).

Once those are made, we have this grid:

Code:
 
 *--------------------------------------------------------------------*
 | 7      56     8      | 45     9      1      | 2456   246    3      |
 | 256    156    12456  | 3      458    48     | 4569   7      469    |
 | 9      35     345    | 2      7      6      | 45     8      1      |
 |----------------------+----------------------+----------------------|
 | 56     4      1567   | 8      3      9      | 167    16     2      |
 | 3      2      16b    | 145    45     7      | 146B   9      8      |
 | 8      19     179    | 14     6      2      | 3      5      47     |
 |----------------------+----------------------+----------------------|
 | 1      7      26d    | 9      48     3      | 248    246D   5      |
 | 25     8      2359   | 6      1      45     | 2479   234    479    |
 | 4      3569   3569   | 7      2      58     | 189    136    69     |
 *--------------------------------------------------------------------*


Now we have another set of strong links on 6 in row 7, which we can combine with our strong links from row 5. Some would call this a fork, some would call it multi-colouring, some would call it a sideways skyscraper, some would call it a turbot fish. No matter what it's called, it excludes the 6 from r4c8 and solves the puzzle.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sat Sep 30, 2006 5:08 pm    Post subject: Very nice! Reply with quote
Tracy,

Very nice!

Of course, I have to point out another couple of things:



This is the situation after your first elimination of <6> in R7C7.

There are two strong links emanating from Box 4. They make a fork and eliminate <6> in R2C7. (This was there before.)

[You can take the "new" strong link in R7 and add it to the previous chain. Then, R4C1 and R7C3 make a fork to eliminate <6> in R4C3.] Edit: I am not sure this is precisely correct.

[Also, there is a contradiction in C3. The plain (not the ball) ended cells in the strong links must be <6>] Edit: An incorrect statement. See below.

Keith

(The picture is from Sudoku Susser. I added the links. The cells with a blue background have <6> as a candidate..)

Last edited by keith on Sun Oct 01, 2006 2:44 pm; edited 1 time in total
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Marty R.



Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
PostPosted: Sat Sep 30, 2006 5:09 pm    Post subject: Reply with quote
I found an XY-Wing which didn't appear very helpful, then a Finned X-Wing on "6" which also didn't appear very helpful. But a few minutes later, a second Finned X-Wing on "6" broke open the puzzle.

I have written a number of times about how I am fascinated at all the different techniques people use on a given puzzle. Presumably, part of the explanation is that we use different sequences of steps as we go about solving them.
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TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI
PostPosted: Sun Oct 01, 2006 1:45 pm    Post subject: Reply with quote
keith wrote:
You can take the "new" strong link in R7 and add it to the previous chain. Then, R4C1 and R7C3 make a fork to eliminate <6> in R4C3.


Very good. Nice graphics, too. Much easier to follow the links when it's presented this way.

I would say combine it with the previous chain, rather that add it to, since it is a totally seperate chain.

keith wrote:
Also, there is a contradiction in C3. The plain (not the ball) ended cells in the strong links must be <6>.


I don't think this is the case. The plain and the ball end in the chain in row 7 could have just as easily been reversed. This kind of contradiction only happens when two of the same coloured cells from a single chain share a group or when both of the colours of one chain share a group with the same colour from another chain.
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keith



Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
PostPosted: Sun Oct 01, 2006 2:40 pm    Post subject: Missing link? Reply with quote
Tracy,

I see I made an incorrect statement. In the final solution R7C3 is <6>. I will edit my post. I will study the figure to understand where I went wrong.

Keith
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