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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Thu Oct 30, 2008 1:10 am Post subject: My kind of puzzle |
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Not yet finished ...
| Code: | Puzzle: M5668611sh(25)
+-------+-------+-------+
| . . 9 | . . 6 | 5 . . |
| 5 . . | 7 . . | . . 1 |
| 3 . 4 | . . 5 | 2 . 6 |
+-------+-------+-------+
| 7 . . | 6 5 . | . . 9 |
| . 4 . | . 9 . | . 6 . |
| . . . | . 8 7 | . . . |
+-------+-------+-------+
| 4 . 6 | . . 9 | 3 . 8 |
| 8 . . | 1 . . | . . 4 |
| . . 7 | . . 8 | 6 . . |
+-------+-------+-------+ |
Keith |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Oct 30, 2008 3:44 am Post subject: |
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Here's a path I found. Perhaps someone can find a more efficient solution.
[1] Finned X-Wing c49: r9c5<>2
[2] 78 W-Wing c78: r2c7|r4c8<>8
[3] Finned X-Wing c67: r4c8<>4
[4] 234 XY Wing: r2c8<>3
That gets us here:
| Code: | +-------------+-----------------+----------------+
| 1 2r7 9 | 8 2g4 6 | 5 347 37 |
| 5 6 2g8 | 7 2r3r4 3g4 | 49 489 1 |
| 3 78 4 | 9 1 5 | 2 78 6 |
+-------------+-----------------+----------------+
| 7 38 138 | 6 5 24 | 148 23 9 |
| 2 4 58 | 3 9 1 | 78 6 57 |
| 6 9 135 | 24 8 7 | 14 2345 235 |
+-------------+-----------------+----------------+
| 4 12 6 | 25 7 9 | 3 125 8 |
| 8 5 2r3 | 1 6 2g3r | 79 79 4 |
| 9 123 7 | 245 34 8 | 6 125 25 |
+-------------+-----------------+----------------+ |
[5] Medusa Wrap, as marked: r2c5=4. |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Thu Oct 30, 2008 4:15 am Post subject: |
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Basics, to here: | Code: | +----------------+----------------+----------------+
| 1 27 9 | 8 234 6 | 5 347 37 |
| 5 6 28 | 7 234 234 | 489 3489 1 |
| 3 78 4 | 9 1 5 | 2 78 6 |
+----------------+----------------+----------------+
| 7 38 138 | 6 5 24 | 148 2348 9 |
| 2 4 58 | 3 9 1 | 78 6 57 |
| 6 9 135 | 24 8 7 | 14 2345 235 |
+----------------+----------------+----------------+
| 4 12 6 | 25 7 9 | 3 125 8 |
| 8 5 23 | 1 6 23 | 79 79 4 |
| 9 123 7 | 245 234 8 | 6 125 25 |
+----------------+----------------+----------------+ |
Type 6 UR takes out <2> in R9C8. Probably irrelevant.
W-wing <78> takes out <8> in R4C8.
Extended half M-wing <38> in R4C2 and <78> in R5C7 takes out <8> in R4C7.
Leading to here:
| Code: | +-------------+-------------+-------------+
| 1 27 9 | 8 24 6 | 5 47 3 |
| 5 6 28 | 7 234 234 | 9 48 1 |
| 3 78 4 | 9 1 5 | 2 78 6 |
+-------------+-------------+-------------+
| 7 38 138 | 6 5 24 | 14 23 9 |
| 2 4 5 | 3 9 1 | 8 6 7 |
| 6 9 13 | 24 8 7 | 14 235 25 |
+-------------+-------------+-------------+
| 4 12 6 | 25 7 9 | 3 125 8 |
| 8 5 23 | 1 6 23 | 7 9 4 |
| 9 123 7 | 245 234 8 | 6 15 25 |
+-------------+-------------+-------------+ |
Which seems to be more resolved than Asellus' position. Do we need Medusa?
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Thu Oct 30, 2008 4:53 am Post subject: |
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W-Wing 78
ER 4
Hidden UR 12
Finned X-Wing 2
XY-Wing 243
XY-Wing 342 with pincer coloring
My final step appears in Asellus' grid with pivot in r2c6, knocking out the 2 from r8c3. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Oct 30, 2008 7:22 am Post subject: |
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[Replaced]
| Code: | finned X-Wing c49\r69 => [r9c5]<>2
finned X-Wing c67\r24 => [r4c8]<>4
W-Wing [r3c8] sl(7:c9) [r5c7] => [r2c7],[r4c8]<>8
XY-Wing [r4c6]/[r2c6]+[r4c8] => [r2c8]<>3
Half M-Wing [r8c3] sl(2:r2) [r2c5] [r9c5] => [r8c6],[r9c2]<>3
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Last edited by daj95376 on Thu Oct 30, 2008 2:29 pm; edited 1 time in total |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Thu Oct 30, 2008 7:37 am Post subject: |
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Starting with coloring, I found (not too helpful)
Kite (4) row 1, col 6: r4c8<>4
multi-coloring (2): r9c2<>2 (this one goes all around the board)
w-wing (8)r3c8=r5c7
| Code: |
+--------------------------+--------------------------+--------------------------+
| 1 27 9 | 8 234 6 | 5 347 37 |
| 5 6 28+ | 7 234 234 | 4-89 3489 1 |
| 3 78+ 4 | 9 1 5 | 2 78* 6 |
+--------------------------+--------------------------+--------------------------+
| 7 38 138 | 6 5 24 | 148 23-8 9 |
| 2 4 5-8 | 3 9 1 | 78* 6 57 |
| 6 9 135 | 24 8 7 | 14 2345 235 |
+--------------------------+--------------------------+--------------------------+
| 4 12 6 | 25 7 9 | 3 125 8 |
| 8 5 23 | 1 6 23 | 79 79 4 |
| 9 13 7 | 245 234 8 | 6 125 25 |
+--------------------------+--------------------------+--------------------------+
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This w-wing is quite interesting, since it not only eliminates 8 from r2c7 and r4c8 (the two cells that directly see the ends of the w-wing)
but ALSO r5c3<>8 !!! (transport via sl in box 1)
The (25) UR inr69c89 /w sl (5) in row 6 makes r9c8<>2.
Now turning to candidate "2":
there is a "useless" w-wing here: (in fact, several w-wings)
| Code: |
+--------------------------+--------------------------+--------------------------+
| 1 27 9 | 8 24 6 | 5 47 3 |
| 5 6 28 | 7 234 234 | 9 48 1 |
| 3 78 4 | 9 1 5 | 2 78 6 |
+--------------------------+--------------------------+--------------------------+
| 7 38 138 | 6 5 24 | 14 23 9 |
| 2 4 5 | 3 9 1 | 8 6 7 |
| 6 9 13 | 24 8 7 | 14 235 25 |
+--------------------------+--------------------------+--------------------------+
| 4 12 6 | 25 7 9 | 3 125 8 |
| 8 5 23 | 1 6 23 | 7 9 4 |
| 9 13 7 | 245 234 8 | 6 15 25 |
+--------------------------+--------------------------+--------------------------+
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w-wing (2):r1c5,r6c4 (via sl (4) in row 9)
and (2):r4c8,r8c3 (via sl (3) col 2)
Add these 2 strong links to the existing web of strong links in (2) - or, in other words: "transport them" -and there are so many eliminations that the puzzle falls apart (I lost track which one actually solved the puzzle) |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu Oct 30, 2008 1:48 pm Post subject: |
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Can you have a double-edged ER?
In the grid below (for this puzzle) There are only two <2>s in R4
If I choose the left one, I can go UP to the hinge in Box2 and DOWN to eliminate R9C5.
If I choose the right one I can use the hinge in Box9 to make the same elimination.
This leads to the elimination of <2> in R2C6 which doesn't seem to help this puzzle. But that ain't the point!
I come across these from time to time. Asellus once told me
about ER’s with transported pincers but this looks different.
| Code: |
+-------+-------+-------+
| . . . | . 2 . | . . . |
| . . . | . 2 2 | . . . |
| . . . | . . . | . . . |
+-------+-------+-------+
| . . . | . . 2 | . 2 . |
| . . . | . . . | . . . |
| . . . | 2 . . | . 2 2 |
+-------+-------+-------+
| . . . | . . . | . 2 . |
| . . . | . . . | . 2 . |
| . . . | . 2 . | . 2 2 |
+-------+-------+-------+
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Oct 30, 2008 2:58 pm Post subject: |
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| cgordon wrote: | Can you have a double-edged ER?
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Hello Craig. Your double-edged ER works for [r9c5]<>2. (Every elimination is important in this puzzle -- even [r2c6]<>2.)
Here's an alternate way, using sl(2:c9), to get your first elimination.
| Code: | [r9c9]=2 => [r9c5]<>2
[r6c9]=2 => [r6c4]<>2 => [r79c4]=2 => [r9c5]<>2
+-----------------------------------+
| . 2 . | . 2 . | . . . |
| . . 2 | . 2 2 | . . . |
| . . . | . . . | 2 . . |
|-----------+-----------+-----------|
| . . . | . . 2 | . 2 . |
| 2 . . | . . . | . . . |
| . . . | *2 . . | . 2 *2 |
|-----------+-----------+-----------|
| . 2 . | #2 . . | . 2 . |
| . . 2 | . . 2 | . . . |
| . 2 . | *2 -2 . | . 2 *2 |
+-----------------------------------+
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These cells also represent a finned X-Wing. If the fin cell (#) is true, then [r9c5]<>2; otherwise, the X-Wing (*) is true and [r9c5]<>2 as well.
There's an important finned X-Wing for (4) as well.
| Code: | +-----------------------------------+
| . . . | . 4 . | . 4 . |
| . . . | . 4 4 | 4 4 . |
| . . 4 | . . . | . . . |
|-----------+-----------+-----------|
| . . . | . . 4 | 4 4 . |
| . 4 . | . . . | . . . |
| . . . | 4 . . | 4 4 . |
|-----------+-----------+-----------|
| 4 . . | . . . | . . . |
| . . . | . . . | . . 4 |
| . . . | 4 4 . | . . . |
+-----------------------------------+
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu Oct 30, 2008 7:54 pm Post subject: |
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I like Marty's solution.
I found the same accidentally, when looking for UR's. Pure t&e of course, but i dont care  | Code: |
*-----------------------------------------------------------*
| 1 >27 9 | 8 *24 6 | 5 347 37 |
| 5 6 >28 | 7 234 *34 | 49 489 1 |
| 3 78 4 | 9 1 5 | 2 78 6 |
|-------------------+-------------------+-------------------|
| 7 38 138 | 6 5 24 | 148 23 9 |
| 2 4 58 | 3 9 1 | 78 6 57 |
| 6 9 135 | 24 8 7 | 14 2345 235 |
|-------------------+-------------------+-------------------|
| 4 #12 6 | 25 7 9 | 3 #125 8 |
| 8 5 @23 | 1 6 *23 | 79 79 4 |
| 9 #123 7 | 245 34 8 | 6 #125 @25 |
*-----------------------------------------------------------* |
From the UR 12 (r79c28) with the 1-x-wing you get directly r9c8<>2.
Looking at the boxes r8c3=2 or r9c9=2, r9c2<>2.
No help so far, also transporting r8c3 to r1c2, r2c5 or r4c6 did not lead to further eliminations.
But using the bivalue cells i got r8c3=2 => r8c6=3 => r2c6=4 => r1c5=2
Oops, not both r1c2 and r1c5 can be 2, so r8c3<>2.
So the UR was not needed at all, but was my way to find it. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Thu Oct 30, 2008 8:37 pm Post subject: |
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the 7 in r1c8 is all that stands in the way of a one stepper that joins two useless skyscrapers.  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Oct 30, 2008 10:37 pm Post subject: |
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ravel,
I believe your r8c3<>2 elimination is just another way of seeing the Medusa Wrap.
I, too, saw the UR based r9c2 elimination, but didn't include it because didn't help much. I found it based on the UR-induced strong link, however, which is just an alternate way to see the same thing:
(2=3)r8c3 - UR[(3)r9c2=(5)r79c8] - (5=2)r9c9
Craig,
While you used the ER in b9 as an ER (a grouped strong link between a box-row segment and a box-column segment), you are using the <2>s in b2 as a grouped strong link between two box-column segments, not as an ER. Works the same way, but isn't the same thing. |
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