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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Tue Apr 01, 2008 1:12 pm Post subject: Another L-O-N-G puzzle |
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M6743041 (23)
| Code: |
+---------------+-------------+-----------+
| 137 4 2 | 18 1378 9 | 67 68 5 |
| 137 6 178 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+---------------+-------------+-----------+
| 147 27 9 | 6 17 5 | 8 124 3 |
| 14567 578 147 | 3 2 178 | 67 146 9 |
| 167 278 3 | 9 178 4 | 5 126 17 |
+---------------+-------------+-----------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
+---------------+-------------+-----------+
|
Play this puzzle online
Looks easy, and indeed it can be done with fairly straightforward moves - colouring / X(Y)-things / etc. It's just that I needed a LOT of moves: despite the plethora of flightless things etc., I couldn't see any really smart stuff. Ravel managed to cleverly shortcut a similar problem recently (where some people hadn't a chance because I'd made a posting mistake, which I haven't done here). Can anybody spot a quick way here? |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Apr 01, 2008 3:47 pm Post subject: |
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The XY-Wing 14-17-47 pivoted in r9c9, with pincer coloring, takes out two 7s from column 3, leaving us here:
| Code: | +---------------+-------------+-----------+
| 137 4 2 | 18 1378 9 | 67 68 5 |
| 137 6 18 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+---------------+-------------+-----------+
| 147 27 9 | 6 17 5 | 8 124 3 |
| 14567 578 14 | 3 2 178 | 67 146 9 |
| 167 278 3 | 9 178 4 | 5 126 17 |
+---------------+-------------+-----------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
+---------------+-------------+-----------+ |
Now a W-Wing on 14 takes out the 4 in r9c3, but I didn't carry it through to see how far it takes you. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Apr 01, 2008 9:10 pm Post subject: |
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Try as I will, I can't see that {14} W-Wing. The external strong link on <1> eludes me.
However, the two {14}s together with {17} at r6c9 form an M-Wing that removes <1>s from r5c8 and r6c1. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Tue Apr 01, 2008 9:26 pm Post subject: |
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| Quote: | | Try as I will, I can't see that {14} W-Wing. |
I can't either. Brain dead.  |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Apr 01, 2008 10:43 pm Post subject: |
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This puzzle responds nicely to basic Medusa (no "extensions"). First, however, I used the Skyscraper on <7> in c67, followed by Coloring of <7> (which removes more <7>s in r5c23 and r6c1).
Then, leaving the <7> coloring in place, expand into Medusa:
| Code: | +---------------------+-------------------+---------------------+
| 137A 4 2 | 18 138 9 | 6A7a 6a8A 5 |
| 13 6 1A8a | 5 #137-8 178 | 4 9 2 |
| 5a9A 5A9a 7a8A | 4 6 2 | 1 3 7A8a |
+---------------------+-------------------+---------------------+
| 147 27 9 | 6 17 5 | 8 124 3 |
| 145A67 5a8A 1a4A | 3 2 178a | 6a7A #-146 9 |
|#-16 278a 3 | 9 178A 4 | 5 126 1A7a |
+---------------------+-------------------+---------------------+
| 4A9a 1 6 | 7 5a9A 3 | 2 5A8a 4a8A |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 7a9A 4a7A | 2 5A9a 6 | 3 1A5a 1a4A |
+---------------------+-------------------+---------------------+ |
Eliminations are located in the cells marked #. Not surprisingly, those M-Wing <1>s go quickly. Continuing...
| Code: | +--------------------+------------------+--------------------+
| 137A 4 2 | 18 138 9 | 6A7a 6a8A 5 |
| 13 6 1A8a | 5 137 178A | 4 9 2 |
| 5a9A 5A9a 7a8A | 4 6 2 | 1 3 7A8a |
+--------------------+------------------+--------------------+
|#14a-7 27 9 | 6 17 5 | 8 124A 3 |
|#1-45A7 5a8A 1a4A | 3 2 178a | 6a7A 4a6A 9 |
| 6 278a 3 | 9 178A 4 | 5 12 1A7a |
+--------------------+------------------+--------------------+
| 4A9a 1 6 | 7 5a9A 3 | 2 5A8a 4a8A |
| 2 3 5 | 18 4 #1-8 | 9 7 6 |
| 8 7a9A 4a7A | 2 5A9a 6 | 3 1A5a 1a4A |
+--------------------+------------------+--------------------+ |
After these eliminations, we find a Medusa Wrap:
| Code: | +-------------------+----------------+------------------+
| 3a7A 4 2 | 1 3A8a 9 | 6A7a 6a8A 5 |
| 1a3A 6 1A8a | 5 3a7A 7a8A | 4 9 2 |
| 5a9A 5A9a 7a8A | 4 6 2 | 1 3 7A8a |
+-------------------+----------------+------------------+
| 14a 27 9 | 6 17 5 | 8 124A 3 |
| 15A7a 5a8A 1a4A | 3 2 @7A8a |@6a7A 4a6A 9 |
| 6 278a 3 | 9 178A 4 | 5 12 1A7a |
+-------------------+----------------+------------------+
| 4A9a 1 6 | 7 5a9A 3 | 2 5A8a 4a8A |
| 2 3 5 | 8 4 1 | 9 7 6 |
| 8 7a9A 4a7A | 2 5A9a 6 | 3 1A5a 1a4A |
+-------------------+----------------+------------------+ |
Row 5 contains two "A" <7>s, marked @. So, all "A" values are false and all "a" values are true. |
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Johan
Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium
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| Posted: Wed Apr 02, 2008 1:49 am Post subject: |
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Needed five steps for this one
First an ER <7> in Box 5 takes out <7> in R1C5 and opens up a Finned x-wing
| Code: | +-------------------------+-------------------------+------------------------+
| 137 4 2 | 18 13-[7]8 9 | 67 68 5 |
| 137 6 178 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+-------------------------+-------------------------+------------------------+
| 147 27 9 | 6 er 17 5 er | 8 124 3 |
| 14567 578 147 | 3 2 178 | 67 146 9 |
| 167 278 3 | 9 er 178 4 er | 5 126 17 |
+-------------------------+-------------------------+------------------------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
+-------------------------+-------------------------+------------------------+ |
The *Finned x-wing eliminates both <7>'s in R5C23
| Code: | +-------------------------+-------------------------+------------------------+
|*137 4 2 | 18 138 9 |*67 68 5 |
| 13 6 18 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+-------------------------+-------------------------+------------------------+
|F147 27 9 | 6 17 5 | 8 124 3 |
|*14567 5-78 14-7 | 3 2 178 |*67 146 9 |
|F167 278 3 | 9 178 4 | 5 126 17 |
+-------------------------+-------------------------+------------------------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
+-------------------------+-------------------------+------------------------+
|
Then M-wing {14} pair(a,c) connected with the strong link(b) on <4> extended with <1> to R6C9(d) eliminating <1> in R5C8 and R6C1
| Code: | +-------------------------+-------------------------+------------------------+
| 137 4 2 | 18 138 9 | 67 68 5 |
| 13 6 18 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+-------------------------+-------------------------+------------------------+
| 147 27 9 | 6 17 5 | 8 124 3 |
| 14567 58 a 14 | 3 2 178 | 67 -[1]46 9 |
|-[1]67 278 3 | 9 178 4 | 5 126 d 17 |
+-------------------------+-------------------------+------------------------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 b 47 | 2 59 6 | 3 15 c 14 |
+-------------------------+-------------------------+------------------------+
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The fourth step a 6-cell xy-chain with pincer ends at R8C6(A) and R5C3(F), that takes out <1> in R5C6
| Code: | +-------------------------+-------------------------+------------------------+
| 137 4 2 | 18 C 138 9 | 67 D 68 5 |
| 13 6 18 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+-------------------------+-------------------------+------------------------+
| 147 27 9 | 6 17 5 | 8 124 3 |
| 14567 58 F 14 | 3 2 -[1]78 | 67 E 46 9 |
| 67 278 3 | 9 178 4 | 5 126 17 |
+-------------------------+-------------------------+------------------------+
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 B 4 A 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
+-------------------------+-------------------------+------------------------+ |
Finally @xy-wing with pivot in R7C1 solves the puzzle
| Code: | +-------------------------+-------------------------+------------------------+
| 137 4 2 | 18 138 9 | 67 68 5 |
| 13 6 18 | 5 1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
+-------------------------+-------------------------+------------------------+
|@47 27 9 | 6 17 5 | 8 124 3 |
| 14567 58 14 | 3 2 78 | 67 46 9 |
| 67 278 3 | 9 178 4 | 5 126 17 |
+-------------------------+-------------------------+------------------------+
|@49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 @79 47 | 2 59 6 | 3 15 14 |
+-------------------------+-------------------------+------------------------+ |
Thx Victor nice puzzle |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Wed Apr 02, 2008 8:46 am Post subject: |
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As an alternative to Johan's xy-chain you can use the UR 13:
| Code: | *------------------------------------------------*
|#137 4 2 | 18 #138 9 | 67 68 5 |
|#13 6 18 | 5 #1378 178 | 4 9 2 |
| 59 59 78 | 4 6 2 | 1 3 78 |
|----------------+----------------+--------------|
| 147 27 9 | 6 17 5 | 8 124 3 |
| 1457 578 14 | 3 2 178 | 67 146 9 |
| 6 278 3 | 9 178 4 | 5 12 17 |
|----------------+----------------+--------------|
| 49 1 6 | 7 59 3 | 2 58 48 |
| 2 3 5 | 18 4 18 | 9 7 6 |
| 8 79 47 | 2 59 6 | 3 15 14 |
*------------------------------------------------* |
There is a x-wing for 3, so the 1 in r1c5 goes directly, and the 1 in r2c5 with the link r2c5=1 => r1c45<>1 => r1c1=1. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Wed Apr 02, 2008 5:10 pm Post subject: |
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I'm impressed, folks! I like to think that I'm quite good at this kind of puzzle, but in fact I got kind of bogged down & took too long to finish - couldn't see the trees for the wood.
PS glad to see, Marty, that I'm not the only person capable of making silly mistakes. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Mon Apr 07, 2008 11:01 pm Post subject: |
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victor,
I have another LONG one for your collection. there is also a 12 cell xy-chain present at some point along the way.
| Code: | ...|7..|5..
3.5|.8.|.1.
2..|3..|8..
---+---+---
..9|.48|..1
.6.|...|.9.
4..|92.|7..
---+---+---
..6|..1|..9
.2.|.6.|1.8
..4|..7|... |
good luck |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Mon Apr 07, 2008 11:17 pm Post subject: |
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| Thanks Norm, I'll have a go tomorrow. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Tue Apr 08, 2008 10:16 am Post subject: |
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Storm_norm's puzzle:
UR 79 in r13c26 pinned 9 to r1c2 and r3c6
| Code: | *------------------------------------------------*
| 6 9 8 | 7 1 #24 | 5 234 234 |
| 3 47 5 | 46 8 246 | 9 1 247 |
| 2 147 17 | 3 5 9 | 8 46 467 |
|---------------+-------------+------------------|
| 57 357 9 | 56 4 8 | 236 2356 1 |
| 8 6 2 | 1 7 35 | 34 9 345 |
| 4 135 13 | 9 2 356 | 7 8 356 |
|---------------+-------------+------------------|
| 57 578 6 | 28 3 1 |#24 2457 9 |
| 9 2 37 | 45 6 45 | 1 37 8 |
| 1 358 4 | 28 9 7 | 236 2356 2356 |
*------------------------------------------------*
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The pair 24:
r1c6=4 => r8c6=5 => r5c6=3 => r5c7=4 => r7c7=2
r1c6=2 => r2c46=46 => r2c2=7 => r8c3=7 => r8c8=3 => r9c789=256 => r7c7=4.
So one of them is 2 and one is 4.
r7c7=4 => r6c9=4 ==> r1c9<>4
r1c6=2 => r2c9=2 ==> r9c9<>2
r7c7=2 => r3c8=2 ==> r1c8<>2
| Code: | *----------------------------------------------*
| 6 9 8 | 7 1 24 | 5 #34 23 |
| 3 47 5 | 46 8 246 | 9 1 247 |
| 2 147 17 | 3 5 9 | 8 46 467 |
|--------------+-------------+-----------------|
| 57 357 9 | 56 4 8 | 236 2356 1 |
| 8 6 2 | 1 7 35 |#34 9 345 |
| 4 135 13 | 9 2 356 | 7 8 356 |
|--------------+-------------+-----------------|
| 57 578 6 | 28 3 1 | 24 2457 9 |
| 9 2 37 | 45 6 45 | 1 37 8 |
| 1 358 4 | 28 9 7 | 236 2356 356 |
*----------------------------------------------*
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The pair 34:
r1c8=4 => r7c7=4 => r5c7=3
r1c8=3 => r1c6=4 => r8c6=5 => r5c6=3 => r5c7=4
So this is a remote pair also where one must be 3 and one 4
r5c7=3 => r6c6=3 => r4c2=3 => r8c3=3 ==> r48c8<>3
r5c7=4 => r7c8=4 ==> r3c8<>4
Remark: Thanks for that, storm_norm. Of course these chains are rather long. But when you know where you want to get to and it is there, it does not take much time. Because i like to use the pairs, this was not a very long puzzle for me. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Tue Apr 08, 2008 5:41 pm Post subject: |
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First...
| ravel wrote: | | r7c7=2 => r3c8=2 ==> r1c8<>2 |
For those trying to follow, that should be:
r7c7=2 => r4c8=2 ==> r1c8<>2
Here is a shorter solution from ravel's first grid:
(3-6)r6c6=(6)r2c6-(6=4)r2c4-(4)r2c2=(4-1)r3c2=(1)r6c2-(1=3)r6c3-(3)r6c6; r6c6<>3
This solves the puzzle.
In ravel's way of writing it:
r6c6=3 => r2c6=6 => r2c4=4 => r3c2=4 => r6c2=1 => r6c3=3 ==> r6c6<>3 |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Tue Apr 08, 2008 8:30 pm Post subject: |
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First time round, I did indeed need long chains, including a 12-step one. But I tried again & found a single chain that does it. Guess it shows (yet again) that there's some luck involved. There's an XY-chain from the 3 of r5c6 to the 3 of r6c1: 35-56-64-47-71-13, & that's enough to solve the puzzle, whether or not you've done the UR eliminations in r13: gives r6c6 <> 3, as in the chain given by Asellus.
PS: Ravel, glad to see that I'm not alone in writing carelessly: you wrote "79" instead of "49". I do of course like using the conjugate 24s. |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Apr 08, 2008 8:35 pm Post subject: |
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| I like to look for ways around the xy-chain without having to look at every cell around the board and you guys gave me a way to do that, thanx. |
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