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daj95376
Joined: 23 Aug 2008
Posts: 3854
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 Posted: Thu Apr 08, 2010 10:41 pm Post subject: Puzzle 10/04/08 ___ BBDB |
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So Ted can find big steps. 
| Code: | +-----------------------+
| 3 . . | 9 5 8 | . . . |
| . 5 . | . 2 7 | . 9 8 |
| . . 9 | 4 . . | . 2 . |
|-------+-------+-------|
| 9 . 5 | 1 . . | . . . |
| 2 7 . | . 4 5 | . 3 1 |
| 1 3 . | . 9 2 | . . . |
|-------+-------+-------|
| . . . | . . . | 2 . . |
| . 9 3 | . 1 . | . 8 5 |
| . 2 . | . 8 . | . 6 . |
+-----------------------+
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Play this puzzle online at the Daily Sudoku site |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 1:12 am Post subject: |
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| Quote: | | So Ted can find big steps. |
Or so Marty can find little steps.  This bent a little more than I was expecting.
| Quote: | Multi-coloring (6)
X-Wing (4)
XY-Wing (164) |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Apr 09, 2010 4:41 am Post subject: |
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| Hmmm. Well, your solution has me stumped. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 4:47 am Post subject: |
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| I'll try it again Friday. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 11:53 am Post subject: |
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Danny, here's my post-basics grid:
| Code: |
+-------------+-------------+--------------+
| 3 146 2 | 9 5 8 | 146 147 467 |
| 46 5 146 | 36 2 7 | 1346 9 8 |
| 7 8 9 | 4 36 1 | 5 2 36 |
+-------------+-------------+--------------+
| 9 46 5 | 1 367 36 | 8 47 2 |
| 2 7 68 | 68 4 5 | 9 3 1 |
| 1 3 48 | 78 9 2 | 46 5 467 |
+-------------+-------------+--------------+
| 8 146 1467 | 5 367 3469 | 2 14 349 |
| 46 9 3 | 2 1 46 | 7 8 5 |
| 5 2 147 | 37 8 349 | 134 6 349 |
+-------------+-------------+--------------+
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Play this puzzle online at the Daily Sudoku site
Note the Skyscraper on 6 in c14. Extend the 6 from r5c4 to r4c2. That multi-coloring chain eliminates the 6 from r7c2, exposing a 14 pair in r7. After that cleanup, there's an X-Wing on 4 in r47. The elimination therefrom of the 4 from r1c2 exposes a 164 XY-Wing pivoted in r1c2 with pincers in r2c1 and r7c2. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Apr 09, 2010 2:10 pm Post subject: |
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A one step solution IF IT IS VALID.
Using the code posted by Marty, notice the hidden pair 46 in r2c13. Either r2c13=46 or r2c3=1.
HP46[(46)r2c13 = (1)r2c3]r2c13 - r79c3 = r7c2 - (1=4)r7c8 - r4c8 = r4c2 - r1c2 = r2c13.
Thus if r2c3=1, then either r2c1=4 or r2c3=4 but r2c3<>4 since the condition was based on r2c3=1 so r2c1=4.
Ted |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Apr 09, 2010 3:14 pm Post subject: |
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Marty,
Very nice thinking on the skyscraper but consider perhaps:
Taking the pincers at r8c1 and r5c4 we have three possible outcomes:
(FF not possible which is why anything that sees both pincers is toast)
1.F T
2.T F
3.T T
However doesn't your extension require 1 and 2 to work ? What happens in the instance of 3 ? Certainly it makes an elimination in a regular skyscraper but can it continue your colouring pattern ? |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Apr 09, 2010 3:23 pm Post subject: |
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Marty: Nice multi-coloring step! It reduced the number of total steps nicely.
Ted: I just awoke and I'm still fuzzy-headed -- no wisecracks about that always being the case -- but it seems to me that your conclusion doesn't work. See explanation later. If you shorten your chain, then there is a valid conclusion.
HP46[(46)r2c13 = (1)r2c3]r2c13 - r79c3 = r7c2 - (1=4)r7c8 - r4c8 = r4c2; => r1c2<>4
This forces one of r2c13 to be <4> and advances the solution a bit.
Mogulmeister: Marty's logic as an X-Chain.
(6)r8c1 = r2c1 - r2c4 = r5c4 - r5c3 = (6)r4c2; => r7c2<>6
[Edit: replaced illogical statement with a reference to a later post with an explanation.]
Last edited by daj95376 on Sat Apr 10, 2010 5:01 am; edited 4 times in total |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 3:59 pm Post subject: |
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| MM, I'm sorry, I just don't understand your comments. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Apr 09, 2010 4:40 pm Post subject: |
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| Marty R. wrote: | | MM, I'm sorry, I just don't understand your comments. |
I once got into a "warm" discussion with Keith over the X pattern not being a true Skyscraper.
| Code: | +-----------------------+
| . . . | . . . | . . . |
| X . . | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . Y . | . . . | . . . |
| . . Y | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| X . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------+
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I suspect the use of Skyscraper is what Mogulmeister is stumbling over.
Mogulmeister: Many in this forum call this pattern a Skyscraper. They then extend it to a strong link -- as Marty did in [b4] for Y. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 4:50 pm Post subject: |
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| Quote: | | I once got into a "warm" discussion with Keith over this pattern not being a true Skyscraper. |
Glad it was just "warm", not "hot." That "X" pattern is the very definition of a Skyscraper as I learned it. What else might qualify as a "true" skyscraper? |
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peterj
Joined: 26 Mar 2010
Posts: 974
Location: London, UK
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| Posted: Fri Apr 09, 2010 5:14 pm Post subject: |
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Similar to marty... though looks like the first 2 x-wings aren't needed...
| Quote: | x-wing(1)
x-wing(3)
multi-colour trap on 6 ("extended skyscraper" in previous posts)
x-wing(4)
xy-wing(164) |
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arkietech
Joined: 31 Jul 2008
Posts: 1834
Location: Northwest Arkansas USA
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| Posted: Fri Apr 09, 2010 5:58 pm Post subject: |
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| daj95376 wrote: | | Many in this forum call this pattern a Skyscraper. They then extend it to a strong link -- as Marty did in [b4] for Y. |
| Code: | +-----------------------+
| . . . | . . . | . . . |
| X . . | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . Y . | . . . | . . . |
| . . Y | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . * . | . . . | . . . |
| X * . | . . . | . . . |
| . * . | . . . | . . . |
+-----------------------+
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Can candidates in r789c2 be eliminated? |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 7:29 pm Post subject: |
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| arkietech wrote: | | daj95376 wrote: | | Many in this forum call this pattern a Skyscraper. They then extend it to a strong link -- as Marty did in [b4] for Y. |
| Code: | +-----------------------+
| . . . | . . . | . . . |
| X . . | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . Y . | . . . | . . . |
| . . Y | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . * . | . . . | . . . |
| X * . | . . . | . . . |
| . * . | . . . | . . . |
+-----------------------+
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Can candidates in r789c2 be eliminated? |
Yes, either r4c2 or r8c1 must be true. |
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Mogulmeister
Joined: 03 May 2007
Posts: 1151
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| Posted: Fri Apr 09, 2010 8:33 pm Post subject: |
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No problems and thanks Danny, I was looking at a skyscraper in isolation and as far as I am concerned this is all fine either as an x chain or extended skyscraper.
A skyscraper after all was a convenient name to describe two parallel strong links of different height with a common base/row.
When I was starting out I found Havard's explanation quite lucid.
http://www.sudoku.frihost.net/forum/viewtopic.php?t=323
Nice one Marty and great catch. FYI The F/Ts are True/False. |
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Marty R.
Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA
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| Posted: Fri Apr 09, 2010 8:50 pm Post subject: |
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| Quote: | 1.F T
2.T F
3.T T
However doesn't your extension require 1 and 2 to work ? What happens in the instance of 3 ? Certainly it makes an elimination in a regular skyscraper but can it continue your colouring pattern ? |
| Quote: | | FYI The F/Ts are True/False. |
I knew that, I wasn't relating it to the pincers for some reason. As to your question, I don't know why any of 1, 2 and 3 can't be valid. |
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tlanglet
Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills
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| Posted: Fri Apr 09, 2010 9:08 pm Post subject: |
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| daj95376 wrote: | Ted: I just awoke and I'm still fuzzy-headed -- no wisecracks about that always being the case -- but it seems to me that your conclusion doesn't work. The easiest explanation is that r2c1=4 is true in the solution. If you shorten your chain, then there is a valid conclusion.
HP46[(46)r2c13 = (1)r2c3]r2c13 - r79c3 = r7c2 - (1=4)r7c8 - r4c8 = r4c2; => r1c2<>4
This forces one of r2c13 to be <4> and advances the solution a bit.
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Danny, I agree that the solution is that r2c1=4, but that does not help me prove or dis-prove my original step. Again, assuming r2c3=1 then r2c13=4 so the only I see way to meet this condition is for r2c1=4. In my simple view of an AIC, the initial premise is retain in order to deduce any eliminations.
Do you have any suggestions where I could go to get further help on this questions?
Thanks,
Ted |
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keith
Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA
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| Posted: Fri Apr 09, 2010 10:11 pm Post subject: |
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| daj95376 wrote: | | Marty R. wrote: | | MM, I'm sorry, I just don't understand your comments. |
I once got into a "warm" discussion with Keith over the X pattern not being a true Skyscraper.
| Code: | +-----------------------+
| . . . | . . . | . . . |
| X . . | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . Y . | . . . | . . . |
| . . Y | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . . . | . . . | . . . |
| X . . | . . . | . . . |
| . . . | . . . | . . . |
+-----------------------+
|
I suspect the use of Skyscraper is what Mogulmeister is stumbling over.
Mogulmeister: Many in this forum call this pattern a Skyscraper. They then extend it to a strong link -- as Marty did in [b4] for Y. |
I see that I am quoted, but I do not understand the discussion.
Can you please post the diagram, using:
X for cells that contain a candidate
/ for cells that do not contain X
* for cells where X can be eliminated
. for cells where the candidates do not matter
Since a skyscraper is a single-digit pattern, do we need more?
Keith |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Apr 09, 2010 11:48 pm Post subject: |
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| arkietech wrote: | | Code: | +-----------------------+
| . . . | . . . | . . . |
| X . . | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . Y . | . . . | . . . |
| . . Y | X . . | . . . |
| . . . | . . . | . . . |
|-------+-------+-------|
| . * . | . . . | . . . |
| X * . | . . . | . . . |
| . * . | . . . | . . . |
+-----------------------+
|
Can candidates in r789c2 be eliminated? |
Yes ... as the X-Chain I listed for Mogulmeister. However, a finned Franken Swordfish c14b4\r258 w/fin cell r4c2 will also work for Marty's elimination in r8c2. |
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daj95376
Joined: 23 Aug 2008
Posts: 3854
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| Posted: Fri Apr 09, 2010 11:56 pm Post subject: |
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| Marty wrote: | Glad it was just "warm", not "hot." That "X" pattern is the very definition of a Skyscraper as I learned it. What else might qualify as a "true" skyscraper?
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You answer lies here.
| Mogulmeister wrote: | A skyscraper after all was a convenient name to describe two parallel strong links of different height with a common base/row.
|
I would add that the non-aligned endpoints must be in the same band/stack for it to be a proper Skyscraper as defined by Havard. In the diagram I presented, this last condition is not met by the X pattern.
Last edited by daj95376 on Sat Apr 10, 2010 12:25 am; edited 1 time in total |
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