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vicnikster
Joined: 29 Jun 2006
Posts: 1
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 Posted: Thu Jun 29, 2006 2:16 am Post subject: this seems unsolvable -am i right?? |
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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!!!  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jun 29, 2006 3:24 am Post subject: A UR is part of the way |
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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 |
+----------------+----------------+----------------+
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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
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| Posted: Thu Jun 29, 2006 11:36 am Post subject: |
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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
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| Posted: Thu Jun 29, 2006 2:57 pm Post subject: Isn't this a "fork"? |
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| 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
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| Posted: Thu Jun 29, 2006 3:44 pm Post subject: Re: A UR is part of the way |
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| 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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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
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| Posted: Thu Jun 29, 2006 7:40 pm Post subject: |
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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: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Jun 29, 2006 9:29 pm Post subject: by any other name ... |
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| 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
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| Posted: Fri Jun 30, 2006 1:46 am Post subject: |
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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
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| Posted: Fri Jun 30, 2006 1:56 am Post subject: |
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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
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| Posted: Fri Jun 30, 2006 9:23 pm Post subject: |
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| Steve R wrote: | Sorry, Keith. It is not.
Take this configuration:
| Code: | -------------------------
| X . . | . . . | . . . |
| . X . | . . X | . . . |
| X . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| X . . | . . - | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------
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the above is not simple coloring, but it can be handled by grouped multi-coloring as shown below
| Code: | -------------------------
|bX . . | . . . | . . . |
| .aX . | . .AX | . . . |
|bX . . | . . . | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
|BX . . | . . - | . . . |
-------------------------
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
-------------------------
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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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