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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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 Posted: Thu Apr 02, 2009 9:57 pm Post subject: A VH+ (with grouped coloring?) |
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Try this one: | Code: | Puzzle: BB040209sh
+-------+-------+-------+
| . . 9 | . . . | 7 . . |
| . 7 . | 9 . 5 | . 8 . |
| 6 . . | 1 . 7 | . . 3 |
+-------+-------+-------+
| . 5 6 | . 2 . | 9 7 . |
| . . . | 6 . 9 | . . . |
| . 9 8 | . 5 . | 3 6 . |
+-------+-------+-------+
| 5 . . | 4 . 3 | . . 7 |
| . 2 . | 8 . 6 | . 3 . |
| . . 4 | . . . | 6 . . |
+-------+-------+-------+ |
If you are going to try the puzzle, read no further (for now)!
The following is not needed: There are more conventional ways. After basics:
| Code: | +-------------------+-------------------+-------------------+
| 1348 1348 9 | 2 36 48 | 7 45 1456 |
| 1234 7 23 | 9 36 5 | 14 8 146 |
| 6 48 5 | 1 48 7 | 2 9 3 |
+-------------------+-------------------+-------------------+
| 14 5 6 | 3 2 148 | 9 7 148 |
| 7 134 23 | 6 48 9 | 145 45 12458 |
| 124 9 8 | 7 5 14 | 3 6 124 |
+-------------------+-------------------+-------------------+
| 5 6 1 | 4 9 3 | 8 2 7 |
| 9 2 7 | 8 1 6 | 45 3 45 |
| 38 38 4 | 5 7 2 | 6 1 9 |
+-------------------+-------------------+-------------------+ |
Here is the pattern of <4>: | Code: | +---------+---------+---------+
| 4 4 . | . . 4 | . 4 4 |
| 4 . . | . . . | 4 . 4 |
| . 4 . | . 4 . | . . . |
+---------+---------+---------+
| 4 . . | . . 4 | . . 4 |
| . 4 . | . 4 . | 4 4 4 |
| 4 . . | . . 4 | . . 4 |
+---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | 4 . 4 |
| . . . | . . . | . . . |
+---------+---------+---------+ |
Ignoring the skyscraper, and the swordfish, is there anything wrong with this logic:
Step 1: Assume R1C6 is <4>, mark it with "T". Mark cells that can then not be <4> with "t". | Code: | +---------+---------+---------+
| t t . | . . T | . t t |
| 4 . . | . . . | 4 . 4 |
| . 4 . | . t . | . . . |
+---------+---------+---------+
| 4 . . | . . t | . . 4 |
| . 4 . | . 4 . | 4 4 4 |
| 4 . . | . . t | . . 4 |
+---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | 4 . 4 |
| . . . | . . . | . . . |
+---------+---------+---------+ |
Step 2: Now either by looking at R3, or noting that the <4> in B3 lies in R2, we get to: | Code: | +---------+---------+---------+
| t t . | . . T | . t t |
| t . . | . . . | 4 . 4 |
| . T . | . t . | . . . |
+---------+---------+---------+
| 4 . . | . . t | . . 4 |
| . 4 . | . 4 . | 4 4 4 |
| 4 . . | . . t | . . 4 |
+---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | 4 . 4 |
| . . . | . . . | . . . |
+---------+---------+---------+ |
Step 3: There is an X-wing in R28, resulting in: | Code: | +---------+---------+---------+
| t t . | . . T | . t t |
| t . . | . . . | 4 . 4 |
| . T . | . t . | . . . |
+---------+---------+---------+
| 4 . . | . . t | . . t |
| . 4 . | . 4 . | 4 4 t |
| 4 . . | . . t | . . t |
+---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | 4 . 4 |
| . . . | . . . | . . . |
+---------+---------+---------+ |
Step 4: The <4> in B6 must lie in R5, giving: | Code: | +---------+---------+---------+
| t t . | . . T | . t t |
| t . . | . . . | 4 . 4 |
| . T . | . t . | . . . |
+---------+---------+---------+
| 4 . . | . . t | . . t |
| . t . | . t . | 4 4 t |
| 4 . . | . . t | . . t |
+---------+---------+---------+
| . . . | . . . | . . . |
| . . . | . . . | 4 . 4 |
| . . . | . . . | . . . |
+---------+---------+---------+ |
Conclusion: There is no possible <4> in B5, so R1C6 is not <4>.
I know the elimination is correct, but does anyone think there is a problem with this logic?
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Apr 02, 2009 11:48 pm Post subject: |
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[Amended:] You need to set R5C7 to "t" in Step 3.
Last edited by daj95376 on Fri Apr 03, 2009 9:28 am; edited 2 times in total |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Apr 03, 2009 3:04 am Post subject: |
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I see it this way.
(4)r2c1 = (4)r2c79 - (4)r1c8 = (4)r5c8 - (4)r5c5 = (4)r3c5; r3c2 <> 4 |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Apr 03, 2009 3:53 am Post subject: |
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| daj95376 wrote: | | Your logic seems excessive but accurate -- except for not marking [r5c7]=t in Step 3. |
Danny,
My explanation may be excessive, but I wanted to avoid a back and forth discussion.
I might have noted in Step 3 that you can label R5C5 as "T", which (with the X-wing) leads to a contradiction in B6, and the same conclusion.
Keith |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Apr 03, 2009 4:02 am Post subject: |
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| storm_norm wrote: | I see it this way.
(4)r2c1 = (4)r2c79 - (4)r1c8 = (4)r5c8 - (4)r5c5 = (4)r3c5; r3c2 <> 4 |
Norm,
I don't understand. Can you please explain (your notation) further?
Thank you,
Keith |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Apr 03, 2009 6:03 am Post subject: |
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Keith,
forget I put the chain up.
that was just my way of showing another elimination on 4 that can be made using the grouped link in box 3 (which happens to be the upper part of the x-wing you pointed out).
your use of the x-wing in r28c79 A.K.A. box/line interactions in those columns and rows is exploiting a nice weak inference.
the weak inference is on the 4's in r456c79 in box 5 and the x-wing on 4's in r2879.
(4)r456cc79 - (x-wing{4})r28c79
because neither can both be true
but your initial assertion of placing 4 in r1c6 is like Danny said, the long way about getting to that point.
the easy way is to notice the strong inference between the 4 in r2c1 and the x-wing... both can't be false
so this strong inference is made
(4)r2c1 = (x-wing{4})r28c79...
now combine the two inferences
(4)r2c1 = (x-wing{4})r28c79 - (4)r456c79...
neither the 4 in r5c8 nor the other 4's in box 6 can both be false...
(4)r2c1 = (x-wing{4})r28c79 - (4)r456cc79 = (4)r5c8...
then extend it via the 4's in column 5.. (4)r3c5 = (4)r5c5...
and you get this chain.
(4)r2c1 = (x-wing{4})r28c79 - (4)r456cc79 = (4)r5c8 - (4)r5c5 = (4)r3c5; r3c2 <> 4
once that 4 is eliminated then its obvious that the 4 in r1c6 can't exist either.
I hope I got this right. if not I am sure Asellus will come to the rescue.
:edited for corrections:
Last edited by storm_norm on Fri Apr 03, 2009 5:11 pm; edited 2 times in total |
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ttt
Joined: 06 Dec 2008
Posts: 42
Location: vietnam
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| Posted: Fri Apr 03, 2009 5:03 pm Post subject: |
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| storm_norm wrote: | | (4)r2c1 = (x-wing{4})r28c79 - (4)r456cc79 = (4)r5c8 - (4)r5c5 = (4)r3c5; r3c2 <> 4 (correct typo) |
| Code: | +-------------------+-------------------+-------------------+
| 1348 1348 9 | 2 36 48 | 7 45 1456 |
| 123(4)7 23 | 9 36 5 | 1(4) 8 1(4)6 |
| 6 48 5 | 1 4*8 7 | 2 9 3 |
+-------------------+-------------------+-------------------+
| 14 5 6 | 3 2 148 | 9 7 1[4]8 |
| 7 134 23 | 6 [4]8 9 | 1[4]5 4*5 12[4]58 |
| 124 9 8 | 7 5 14 | 3 6 12[4] |
+-------------------+-------------------+-------------------+
| 5 6 1 | 4 9 3 | 8 2 7 |
| 9 2 7 | 8 1 6 |(4)5 3 (4)5 |
| 38 38 4 | 5 7 2 | 6 1 9 |
+-------------------+-------------------+-------------------+ |
Yes, I like that and always try to use it on my solutions.
- If r2c1=4 => r3c2<>4
- If r2c1<>4 => X-wing 4’s at r28c79 => r456c9 & r5c7<>4 => r5c8=4 => r5c5<>4 => r3c5=4 => r3c2<>4
Conclusion: r3c2<>4
ttt |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Fri Apr 03, 2009 5:08 pm Post subject: |
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[quote="ttt"] | storm_norm wrote: | (4)r2c1 = (x-wing{4})r28c79 - (4)r456cc79 = (4)r5c8 - (4)r5c5 = (4)r3c5; r3c2 <4> r3c2<>4
- If r2c1<4> X-wing 4’s at r28c79 => r456c9 & r5c7<4> r5c8=4 => r5c5<4> r3c5=4 => r3c2<>4
Conclusion: r3c2<>4
ttt |
ttt,
thanks for the corrections, I had the cells backwards. |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu Apr 09, 2009 7:54 am Post subject: |
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I haven't checked the board in quite a long while...
This discussion seems to be an overly complicated way to achieve a simple ER elimination. The ER is in b5 and the strong link in c8. While it is correct, I am personally not comfortable with the forcing approach of Keith that's starts with a truth assumption. Norm uses a complex series of implications that avoid a truth assumption (and appear to me to be legit). But, such complexity isn't needed here. There may be cases where such an approach is the only way forward, but I haven't yet encoutered one that I can recall. |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu Apr 09, 2009 6:28 pm Post subject: |
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I enjoyed the more conventional approach using most of the armoury.
ER(s) on 4
x wing on 4
Skyscraper on 1
Type 1 UR
Colouring on 4
xy wing
I noticed there was just one triple at the end but I couldn't find a Bug+1. I guess there has to be an xyz, xy, xz format available for those. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Thu Apr 09, 2009 7:29 pm Post subject: |
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| cgordon wrote: | I enjoyed the more conventional approach using most of the armoury.
ER(s) on 4
x wing on 4
Skyscraper on 1
Type 1 UR
Colouring on 4
xy wing
I noticed there was just one triple at the end but I couldn't find a Bug+1. I guess there has to be an xyz, xy, xz format available for those. |
Quite often, when there's a BUG+1 at the end, there is one or more XY-Wings present as well. I noticed that your last move was an XY-Wing. Coincidence? |
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cgordon
Joined: 04 May 2007
Posts: 769
Location: ontario, canada
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| Posted: Thu Apr 09, 2009 9:04 pm Post subject: |
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| Quote: | | Quite often, when there's a BUG+1 at the end, there is one or more XY-Wings present as well. |
Yabut - my point was that I thought if there was just one 3-digit number left, there had to be a BUG+1. But here there wasn't. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri May 01, 2009 6:27 am Post subject: |
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From the original markup I see this "sort of" swordfish.
Is this a franken fish?
| Code: | .---------------------.---------------------.---------------------.
| 138-4 @1348 9 | 2 36 #48 | 7 @45 156-4 |
| 1234 7 23 | 9 36 5 | 14 8 146 |
| 6 @48 5 | 1 #48 7 | 2 9 3 |
:---------------------+---------------------+---------------------:
| 14 5 6 | 3 2 148 | 9 7 148 |
| 7 @134 23 | 6 8-4 9 | 15-4 @45 1258-4|
| 124 9 8 | 7 5 14 | 3 6 124 |
:---------------------+---------------------+---------------------:
| 5 6 1 | 4 9 3 | 8 2 7 |
| 9 2 7 | 8 1 6 | 45 3 45 |
| 38 38 4 | 5 7 2 | 6 1 9 |
'---------------------'---------------------'---------------------' |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri May 01, 2009 2:07 pm Post subject: |
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| wapati wrote: | From the original markup I see this "sort of" swordfish.
Is this a franken fish?
| Code: | .---------------------.---------------------.---------------------.
| 138-4 @1348 9 | 2 36 #48 | 7 @45 156-4 |
| 1234 7 23 | 9 36 5 | 14 8 146 |
| 6 @48 5 | 1 #48 7 | 2 9 3 |
:---------------------+---------------------+---------------------:
| 14 5 6 | 3 2 148 | 9 7 148 |
| 7 @134 23 | 6 8-4 9 | 15-4 @45 1258-4|
| 124 9 8 | 7 5 14 | 3 6 124 |
:---------------------+---------------------+---------------------:
| 5 6 1 | 4 9 3 | 8 2 7 |
| 9 2 7 | 8 1 6 | 45 3 45 |
| 38 38 4 | 5 7 2 | 6 1 9 |
'---------------------'---------------------'---------------------' |
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Yes. Your pattern matches the second one below.
| Code: | Swordfish c258\r135 <> 4 [r1c169],[r5c79]
+-----------------------------------+
| -4 *4 . | . . -4 | . *4 -4 |
| 4 . . | . . . | 4 . 4 |
| . *4 . | . *4 . | . . . |
|-----------+-----------+-----------|
| 4 . . | . . 4 | . . 4 |
| . *4 . | . *4 . | -4 *4 -4 |
| 4 . . | . . 4 | . . 4 |
|-----------+-----------+-----------|
| . . . | 4 . . | . . . |
| . . . | . . . | 4 . 4 |
| . . 4 | . . . | . . . |
+-----------------------------------+
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| Code: | Franken Swordfish c28b2\r135 <> 4 [r1c19],[r5c579]
+-----------------------------------+
| -4 *4 . | . . *4 | . *4 -4 |
| 4 . . | . . . | 4 . 4 |
| . *4 . | . *4 . | . . . |
|-----------+-----------+-----------|
| 4 . . | . . 4 | . . 4 |
| . *4 . | . -4 . | -4 *4 -4 |
| 4 . . | . . 4 | . . 4 |
|-----------+-----------+-----------|
| . . . | 4 . . | . . . |
| . . . | . . . | 4 . 4 |
| . . 4 | . . . | . . . |
+-----------------------------------+
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You could have also used the Kraken X-Wing c28\r15 w/fin [r3c2]. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri May 01, 2009 2:55 pm Post subject: |
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| daj95376 wrote: |
Yes. Your pattern matches the second one below. |
Thanks!
| daj95376 wrote: |
You could have also used the Kraken X-Wing c28\r15 w/fin [r3c2]. |
That looks like a finned x-wing to me. What is the difference? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri May 01, 2009 3:08 pm Post subject: |
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| wapati wrote: | That looks like a finned x-wing to me.
Are "broken x-wings" kraken x-wings? |
You're right, it's also a finned X-Wing for [r1c1]<>4. There are many fish patterns, and I didn't check for all of them.
What I did see was that the Swordfish and Franken Swordfish produced eliminations in only two rows. Whenever this happens, I often investigate for smaller fish. What caught my attention was
| Code: | Skyscraper/Sashimi X-Wing c58\r15 for [r1c6]<>4
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that then exposed an X-Wing c28\r15. This caused me to examine the X-Wing columns in the original grid. Out popped the Kraken X-Wing!
A "broken" X-Wing is different than a Kraken X-Wing ... as I understand them. |
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wapati
Joined: 10 Jun 2008
Posts: 472
Location: Brampton, Ontario, Canada.
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| Posted: Fri May 01, 2009 3:34 pm Post subject: |
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| daj95376 wrote: |
A "broken" X-Wing is different than a Kraken X-Wing ... as I understand them. |
Yep, I looked it up after I posted. The similarity is that "fins" disturb a pattern in both cases.
Thanks again. |
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