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this seems unsolvable -am i right??

 
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vicnikster



Joined: 29 Jun 2006
Posts: 1

PostPosted: Thu Jun 29, 2006 2:16 am    Post subject: this seems unsolvable -am i right?? Reply with quote

85x|47x|2x9
972|8x3|x4x
x64|295|7x8
x2x|9xx|487
x8x|742|x9x
749|xx8|xx2
495|187|623
617|329|854
238|xx4|971

I can't solve this?? Help!!! Shocked
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 29, 2006 3:24 am    Post subject: A UR is part of the way Reply with quote

If you get to here:

Code:

+----------------+----------------+----------------+
| 8    5    13   | 4    7    16   | 2    136  9    |
| 9    7    2    | 8    16   3    | 15   4    56   |
| 13   6    4    | 2    9    5    | 7    13   8    |
+----------------+----------------+----------------+
| 135  2    136  | 9    1356 16   | 4    8    7    |
| 135  8    136  | 7    4    2    | 135  9    56   |
| 7    4    9    | 56   1356 8    | 135  16   2    |
+----------------+----------------+----------------+
| 4    9    5    | 1    8    7    | 6    2    3    |
| 6    1    7    | 3    2    9    | 8    5    4    |
| 2    3    8    | 56   56   4    | 9    7    1    |
+----------------+----------------+----------------+

a Type 1 UR on <56> will take out <56> from R6C5. Next step?

Keith
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Thu Jun 29, 2006 11:36 am    Post subject: Reply with quote

Alternatively there is a finned X-wing for 6 based on columns 6 and 8. This eliminates 6 from r6c45 and solves the puzzle.

Steve
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Thu Jun 29, 2006 2:57 pm    Post subject: Isn't this a "fork"? Reply with quote

Steve R wrote:
... there is a finned X-wing for 6 based on columns 6 and 8.

I'm confused. I thought this sort of deal was called a fork.

For the benefit of vicnikster, here's an amplfication of Steve's excellent insight.

-- There are only two ways to fit a "6" in column 6, either at r1c6 or at r4c6.

-- There are only two ways to fit a "6" in column 8, either at r1c8 or at r6c8.

-- If r1c6 = 6 then r6c8 = 6. And if r1c6 <> 6, then r4c6 = 6. Either way there cannot possibly be a "6" in either of the cells r6c4 and r6c5. dcb
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Myth Jellies



Joined: 27 Jun 2006
Posts: 64

PostPosted: Thu Jun 29, 2006 3:44 pm    Post subject: Re: A UR is part of the way Reply with quote

Code:

+----------------+-----------------+----------------+
| 8    5    13   | 4    7    *16   | 2   *136  9    |
| 9    7    2    | 8    16    3    | 15   4    56   |
| 13   6    4    | 2    9     5    | 7    13   8    |
+----------------+-----------------+----------------+
| 135  2    136  | 9    1356 #16   | 4    8    7    |
| 135  8    136  | 7    4     2    | 135  9    56   |
| 7    4    9    |-56  -1356 *8    | 135 *16   2    |
+----------------+-----------------+----------------+
| 4    9    5    | 1    8     7    | 6    2    3    |
| 6    1    7    | 3    2     9    | 8    5    4    |
| 2    3    8    | 56   56    4    | 9    7    1    |
+----------------+-----------------+----------------+


Another way of looking at it.

This is a sashimi variation of a finned x-wing. Either the fin in r4c6 is true, or the x-wing in r16c68 is true (note that a finned x-wing, like most other swordfish, does not require a candidate at every vertex, hence the sashimi variation). In either case you can eliminate the 6's in r6c45. On other sites, this pattern has also been called a sky-scraper, as well as, apparently, a fork.

Note that like other fish, there is a complementary finned fish (in this case a finned jellyfish) in the rows, as shown below...
Code:

+----------------+-----------------+----------------+
| 8    5    13   | 4    7     16   | 2    136  9    |
| 9    7   *2    |*8   *16    3    | 15   4   *56   |
| 13   6    4    | 2    9     5    | 7    13   8    |
+----------------+-----------------+----------------+
| 135  2   *136  |*9   *1356 #16   | 4    8   *7    |
| 135  8   *136  |*7   *4     2    | 135  9   *56   |
| 7    4    9    |-56  -1356  8    | 135  16   2    |
+----------------+-----------------+----------------+
| 4    9    5    | 1    8     7    | 6    2    3    |
| 6    1    7    | 3    2     9    | 8    5    4    |
| 2    3   *8    |*56  *56    4    | 9    7   *1    |
+----------------+-----------------+----------------+
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Thu Jun 29, 2006 7:40 pm    Post subject: Reply with quote

David

Thanks for making clear the logic underlying the fork, which indeed it is.

I was wrong to call it a finned X-wing. It is more like two finned X-wings in one pattern. This is what Myth Jellies means by a sashimi variation of a finned x-wing, though perhaps it awards a rather grandiose title to such a humble, if useful, tool.

Regards

Steve
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keith



Joined: 19 Sep 2005
Posts: 3182
Location: near Detroit, Michigan, USA

PostPosted: Thu Jun 29, 2006 9:29 pm    Post subject: by any other name ... Reply with quote

Code:
+----------------+----------------+----------------+
| 8    5    13   | 4    7    16c  | 2    136b 9    |
| 9    7    2    | 8    16   3    | 15   4    56   |
| 13   6    4    | 2    9    5    | 7    13   8    |
+----------------+----------------+----------------+
| 135  2    136  | 9    1356 16d  | 4    8    7    |
| 135  8    136  | 7    4    2    | 135  9    56   |
| 7    4    9    | 56   1356 8    | 135  16a  2    |
+----------------+----------------+----------------+
| 4    9    5    | 1    8    7    | 6    2    3    |
| 6    1    7    | 3    2    9    | 8    5    4    |
| 2    3    8    | 56   56   4    | 9    7    1    |
+----------------+----------------+----------------+


Another name for this is "simple coloring" because there is a strong link (only two <6> candidates) in R1. Just follow the chain a b c d, and you conclude a or d must be <6>.

The "fork", which is a form of multi-coloring, does not require this strong link. Suppose there are other candidates <6> in R1. Then, we can still say: at least one of a and d is <6>.

If a is <6>, the assertion is true.
If a is not <6>, b is <6>, c is not <6>, and <d> is <6>.

(Actually, without the strong link in R1, it is possible that both a and d are <6>.)

This belongs in your bag of tools because you can easily look for the pattern while looking for X-wings. The fork is two strong links that line up at one end. The X-wing is two strong links that line up at both ends.

Keith
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Steve R



Joined: 24 Oct 2005
Posts: 289
Location: Birmingham, England

PostPosted: Fri Jun 30, 2006 1:46 am    Post subject: Reply with quote

Sorry, Keith. It is not.

Take this configuration:


Code:
-------------------------
| X . . | . . . | . . . |
| . X . | . . X | . . . |
| X . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| X . . | . . - | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------

There are only two places for X in the second row, cells r2c2 and r2c6. There are only two places for X in the second column, box 1 and cell r6c1. As box 1 contains a single X, one or other of r2c6 and r6c1 must contain it. Accordingly X may be eliminated from r6c6.

That it is all a fork is: two places for a candidate,

By all mean think of this as a trivial example of colouring, a turbot, an empty rectangle or a nice loop, if you find it more straightforward. However, the fork is an elementary concept at about the level of the X-wing. It can itself be useful on occasion.

It forms a building block in these more widely applicable techniques but using "fork" as a drscription of them adds several layers of confusion to an already confusing litany of terms.

Steve
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TKiel



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

PostPosted: Fri Jun 30, 2006 1:56 am    Post subject: Reply with quote

From the grid as posted, colouring on 6's shows that cells marked with (A) cannot be 6 and (a) must be.

Code:
 
 *-----------------------------------------------------------*
 | 8     5     13    | 4     7     16a   | 2     136   9     |
 | 9     7     2     | 8     16A   3     | 15    4     56a   |
 | 13    6     4     | 2     9     5     | 7     13    8     |
 |-------------------+-------------------+-------------------|
 | 135   2     136A  | 9     1356  16A   | 4     8     7     |
 | 135   8     136a  | 7     4     2     | 135   9     56A   |
 | 7     4     9     | 56    1356  8     | 135   136   2     |
 |-------------------+-------------------+-------------------|
 | 4     9     5     | 1     8     7     | 6     2     3     |
 | 6     1     7     | 3     2     9     | 8     5     4     |
 | 2     3     8     | 56    56    4     | 9     7     1     |
 *-----------------------------------------------------------*
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Myth Jellies



Joined: 27 Jun 2006
Posts: 64

PostPosted: Fri Jun 30, 2006 9:23 pm    Post subject: Reply with quote

Steve R wrote:
Sorry, Keith. It is not.

Take this configuration:


Code:
-------------------------
| X . . | . . . | . . . |
| . X . | . . X | . . . |
| X . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| X . . | . . - | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------


the above is not simple coloring, but it can be handled by grouped multi-coloring as shown below
Code:
-------------------------
|bX . . | . . . | . . . |
| .aX . | . .AX | . . . |
|bX . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|BX . . | . . - | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------

Since colors a and b exclude each other in box 1, one or both of their conjugate colors, A and B, must be true. Any cell seeing both an A and B cannot be X
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