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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Sat Jun 07, 2008 11:32 am Post subject: LA Times / Freep - June 6, 2008 |
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| Code: | Puzzle: FP060608
+-------+-------+-------+
| . 9 . | 8 . . | 2 1 . |
| 4 6 . | . . . | . . 5 |
| . . 5 | . . 1 | 9 . . |
+-------+-------+-------+
| . . 2 | . 8 . | . . . |
| . . . | 9 . 7 | . . . |
| . . . | . 2 . | 3 . . |
+-------+-------+-------+
| . . 3 | 1 . . | 8 . . |
| 9 . . | . . . | . 4 2 |
| . 5 4 | . . 8 | . 3 . |
+-------+-------+-------+ |
Still not done - I got stuck on a hidden pair for a while. Now I am looking at some interesting uniqueness possibilities.
Keith |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Jun 07, 2008 1:16 pm Post subject: |
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I only stumbled on the hidden pair while analyzing a possible UR, and it exposed the Type 2 UR but the resulting elimination does not appear helpful. Other standard techniques have not been fruitful so far.
Ted |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jun 07, 2008 1:30 pm Post subject: |
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basics go a long way. up to here:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 3 9 7 | 8 56 56 | 2 1 4 |
| 4 6 1 | 23 39 29 | 7 8 5 |
| 28 28 5 | 4 7 1 | 9 6 3 |
+--------------------------+--------------------------+--------------------------+
| 17 147 2 | 36 8 346 | 5 9 16 |
| 5 3 6 | 9 1 7 | 4 2 8 |
| 18 148 9 | 56 2 456 | 3 7 16 |
+--------------------------+--------------------------+--------------------------+
| 6 27 3 | 1 4 29 | 8 5 79 |
| 9 17 8 | 3567 356 356 | 16 4 2 |
| 127 5 4 | 267 69 8 | 16 3 79 |
+--------------------------+--------------------------+--------------------------+
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I believe there is an interesting chain -16-17-27-29-69-16- in boxes 7,8,9 (a loop but not a regular xy-loop)
from r8c2 to r9c7 it removes 1 from r8c7 and r9c1
from r8c7 to r9c5 it removes 6 from r8c456 and r9c7 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jun 07, 2008 2:01 pm Post subject: |
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In Nataraj' grid, there is a <56> UR that takes out <3> in R8C4. Then: | Code: | +--------------------------+--------------------------+--------------------------+
| 3 9 7 | 8 56@ 56@ | 2 1 4 |
| 4 6 1 | 23 39 29 | 7 8 5 |
| 28 28 5 | 4 7 1 | 9 6 3 |
+--------------------------+--------------------------+--------------------------+
| 17 147 2 | 36 8 346 | 5 9 16 |
| 5 3 6 | 9 1 7 | 4 2 8 |
| 18 148 9 | 56@ 2 456@ | 3 7 16 |
+--------------------------+--------------------------+--------------------------+
| 6 27 3 | 1 4 29 | 8 5 79 |
| 9 17 8 | 567@ 356@ 356 | 16 4 2 |
| 127 5 4 | 267 69 8 | 16 3 79 |
+--------------------------+--------------------------+--------------------------+ |
The cells marked @ are a potential deadly pattern (unique swordfish) on <56>.
R6C6 is <4>, and / or R8C4 is <7>, and / or R8C5 is <3>. Any of these leads to R6C4 is <5>.
Then, an XY-wing leads to a BUG+1 to solve it.
Not very elegant, but it works for me!
Keith
Last edited by keith on Sat Jun 07, 2008 2:09 pm; edited 1 time in total |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Sat Jun 07, 2008 2:06 pm Post subject: |
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| nataraj wrote: | basics go a long way. up to here:
| Code: |
+--------------------------+--------------------------+--------------------------+
| 3 9 7 | 8 56 56 | 2 1 4 |
| 4 6 1 | 23 39 29 | 7 8 5 |
| 28 28 5 | 4 7 1 | 9 6 3 |
+--------------------------+--------------------------+--------------------------+
| 17 147 2 | 36 8 346 | 5 9 16 |
| 5 3 6 | 9 1 7 | 4 2 8 |
| 18 148 9 | 56 2 456 | 3 7 16 |
+--------------------------+--------------------------+--------------------------+
| 6 27 3 | 1 4 29 | 8 5 79 |
| 9 17 8 | 3567 356 356 | 16 4 2 |
| 127 5 4 | 267 69 8 | 16 3 79 |
+--------------------------+--------------------------+--------------------------+
|
I believe there is an interesting chain -16-17-27-29-69-16- in boxes 7,8,9 (a loop but not a regular xy-loop)
from r8c2 to r9c7 it removes 1 from r8c7 and r9c1
from r8c7 to r9c5 it removes 6 from r8c456 and r9c7 |
Very nice solution Nataraj. I believe that Susser calls this a "Simple Forcing Chain". I was struggling to find a chain, but I just am not very good at that process. It also showed that the Type 2 UR in r18c56 that eliminated a <3> in r8c4 was indeed useless as I assumed. 
Ted |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Jun 07, 2008 2:50 pm Post subject: |
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| nataraj wrote: | | I believe there is an interesting chain -16-17-27-29-69-16- in boxes 7,8,9 (a loop but not a regular xy-loop) |
I needed some time to understand, what you mean. Its no loop (where you end with the same number in the cell you started), but 2 overlapping xy-chains.
Both result in the placements r8c7=6 and r9c7=1 (leaving a BUG).
[Added:]Of course i like Keiths solution, especiallly because i did see the DP, but not how to use it (only had a useless elimination r4c2<>1). |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jun 07, 2008 3:18 pm Post subject: |
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| Quote: | | i like Keiths solution |
ravel, thank you. I might note that you do not need the first UR. Because of the strong link in C4, any value other than <5> in R8C4 forces <5> in R6C4.
Keith |
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Earl
Joined: 30 May 2007
Posts: 677
Location: Victoria, KS
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| Posted: Sat Jun 07, 2008 4:49 pm Post subject: DFP |
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There is an xy-chain in boxes 7-8-9 with a <1> pincer which leads to a BUG+1 in box 4 to solve the puzzle.
Earl |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Sat Jun 07, 2008 5:04 pm Post subject: |
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nataraj's chain is an xy-chain, all cells contain exactly 2 candidates. this property allows you to connect them... easy way to connect them is using "if/then" statements as you go around.
visually...
its an AIC which means you can work the chain in both directions. the 1's in r8c2 and r9c7 are left on the ends and therefore become pinces.
and Ravel is right, its like a 6 cell xy-wing because that is exactly what it is. a XY-wing is a 3 cell XY-chain 
or you can view it this way...
| Code: |
--------------------------------------
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1(6 - 6)(9 - 9)(2 - 2)(7 - 7)1 |
the ending 1's become pinces becasue either way through the chain you go, the 1's on the ends have to be true.
this is the same with an xy-wing...
| Code: |
---------------------
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A(B - B)(C - C)A |
candidate A has to be true as in every xy-wing which eliminates any other a's they see.
here is a better than average description of xy-chains...
http://www.scanraid.com/XY_Chains |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jun 07, 2008 5:37 pm Post subject: |
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| Code: | +--------------------------+--------------------------+--------------------------+
| 3 9 7 | 8 56 56 | 2 1 4 |
| 4 6 1 | 23 39 29 | 7 8 5 |
| 28 28 5 | 4 7 1 | 9 6 3 |
+--------------------------+--------------------------+--------------------------+
| 17 147 2 | 36 8 346 | 5 9 16 |
| 5 3 6 | 9 1 7 | 4 2 8 |
| 18 148 9 | 56 2 456 | 3 7 16 |
+--------------------------+--------------------------+--------------------------+
| 6 27 3 | 1 4 29 | 8 5 79 |
| 9 1-7@ 8 | 3567@ 356 356 | 16 4 2 |
| 127@ 5 4 | 267@ 69 8 | 16 3 79 |
+--------------------------+--------------------------+--------------------------+ |
If you stare long enough at the four cells @, you will solve R8C2, leading to a BUG+1.
Keith |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jun 07, 2008 6:54 pm Post subject: |
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| Quote: | | If you stare long enough at the four cells @, you will solve R8C2, leading to a BUG+1. |
I stared and I stared and I stared some more and guess what cell I couldn't solve?  |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Sat Jun 07, 2008 7:52 pm Post subject: |
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| Marty R. wrote: | | Quote: | | If you stare long enough at the four cells @, you will solve R8C2, leading to a BUG+1. |
I stared and I stared and I stared some more and guess what cell I couldn't solve? |
Marty,
If R8C2 is <7>, R9C1 must be <1> (in B7), R9C4 must be <2> (in R9), R8C4 must be <7> (in C4). R8C2 cannot be <7>.
You can similarly show that R9C4 is not <7>.
Keith |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sat Jun 07, 2008 8:00 pm Post subject: |
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Strong links are harder to spot, thats why i missed the DP elimination.
Two more ways:
r8c2=7 => r9c4=7 => r9c1=2 => r8c2=1 ==> r8c2<>7
or
r9c1=2 or r9c4=2:
r9c1=2 => r8c2=1
r9c4=2 => r8c4=7
either way R8c2 <>7 |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Sat Jun 07, 2008 8:24 pm Post subject: |
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Before I started with the basics I saw an easy to spot ER and knocked off the <1> in R4C1. Didn't seem to do anything cos I'm still stuck - but I'm a bit further on than the grids above - eg. I have a solved <7> and a <12> in C1.
Also there was an x wing on <4> in C26 somewhere along the way. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jun 07, 2008 9:04 pm Post subject: |
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Thank you guys for all your comments on the "not quite loop". It is just what it is: two xy-chains sharing a few links. I was hoping there'd be more but I guess not ...
Nice UR solutions, keith and ravel (I liked the potentially deadly swordfish!) |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sat Jun 07, 2008 9:29 pm Post subject: |
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I'm not much of an XY-Chain user, and couldn't do anything with my usual arsenal, so I Medusa'ed it (is Medusa a verb?).
| Quote: | | If R8C2 is <7>, R9C1 must be <1> (in B7), R9C4 must be <2> (in R9), R8C4 must be <7> (in C4). R8C2 cannot be <7>. |
That's certainly easy enough to follow, and I know you have an explanation, but how does that differ from a T&E forcing chain? |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Sat Jun 07, 2008 9:52 pm Post subject: |
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Keith's <7> elimination follows a fairly straightforward AIC:
(7-1)r8c2=(1)r9c1-(1=6)r9c7-(6=9)r9c5-(9=7)r9c9-(7)r9c4=(7)r8c4-(7)r8c2; r8c2<>7
The easiest way to find this would be with basic Medusa.
[Edit to add:]
By the way, this elimination makes the prior UR <3> elimination unnecessary. |
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nataraj
Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria
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| Posted: Sat Jun 07, 2008 10:36 pm Post subject: |
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| Marty R. wrote: | I'm not much of an XY-Chain user, and couldn't do anything with my usual arsenal, so I Medusa'ed it (is Medusa a verb?).
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As all devoted Calvin and Hobbes fans know, verbing weirds language, so "Medusa'd it" is another step in the right direction  |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Sun Jun 08, 2008 12:56 am Post subject: |
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| Quote: | | fairly straightforward AIC |
Sorry to say that this poster views that as an egregious oxymoron.  
| Quote: | | verbing weirds language |
My only familiarity with C&H is that I've heard of it, but I love that phrase!! |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Sun Jun 08, 2008 10:41 am Post subject: |
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| Marty R. wrote: | | ... egregious oxymoron |
My arsenal of English words is pretty enriched by this forum  |
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