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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Dec 04, 2010 1:53 am Post subject: Nataraj HS, Dec 3, 2010 Advanced

http://www.saueregger.at/sudoku/

Sudoku Susser insists this is more complicated than I found it ...

Code:

+-------+-------+-------+
| . 6 . | . . . | 4 . 3 |
| . . 2 | . 1 . | . 6 . |
| 8 . . | . 6 . | . . . |
+-------+-------+-------+
| 2 . . | 4 . 9 | . . 7 |
| . . . | . 8 . | . . . |
| 9 . . | 3 . 7 | . . 1 |
+-------+-------+-------+
| . . . | . 4 . | . . 9 |
| . 9 . | . 7 . | 3 . . |
| 5 . 1 | . . . | . 7 . |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Hint:

Quote:

The UR's are the way to go.

Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Dec 04, 2010 5:59 am Post subject:

I think I'm up with the Susser in the complexity. I used eight steps, a little of everything, or so it seemed. But my 5th move was an ER which opened things up for three easy finishing moves. You didn't refer to me as "Multi-step Marty" for nothing. This was my toughest challenge yet on Nataraj's puzzles.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sat Dec 04, 2010 6:06 am Post subject:

Code:

+------------------+-----------------+--------------------+
| 1 6 57 | 2578 9 258 | 4 258 3 |
| 347 3457 2 | 578 1 34 | 9 6 58 |
| 8 34 9 | 25 6 34 | 7 1 25 |
+------------------+-----------------+--------------------+
| 2 1 6(8) | 4 5 9 | 6(8) 3 7 |
| 347 3457 3457 | 16 8 16 | 5(2) 9 (24) |
| 9 458 568-4 | 3 2 7 | 568 8(4) 1 |
+------------------+-----------------+--------------------+
| 367 2378 378 | 2568 4 2568 | 1 258 9 |
| 46 9 (48) | 12568 7 12568 | 3 258-4 24568 |
| 5 248 1 | 9 3 268 | (28) 7 2468 |
+------------------+-----------------+--------------------+

(4=8)r8c3 - (8)r4c3 = (8)r4c7 - (8=2)r9c7 - (2)r5c7 = (2-4)r5c9 = (4)r6c8;
r8c8 <> 4
r6c3 <> 4

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Dec 04, 2010 7:30 am Post subject:

After basics (and before any UR's):

Code:

+-------------------+-------------------+-------------------+
| 1 6 57 | 2578 9 258 | 4 258 3 |
| 347 3457 2 | 578 1 34 | 9 6 58 |
| 8 34 9 | 25 6 34 | 7 1 25 |
+-------------------+-------------------+-------------------+
| 2 1 68 | 4 5 9 | 68 3 7 |
| 347 3457 3457 | 16 8 16 | 25 9 24 |
| 9 458 4568 | 3 2 7 | 568 48 1 |
+-------------------+-------------------+-------------------+
| 367 2378 378 | 2568 4 2568 | 1 258 9 |
| 46 9 48 | 12568 7 12568 | 3 2458 24568 |
| 5 248 1 | 9 3 268 | 28 7 2468 |
+-------------------+-------------------+-------------------+

A grouped skyscraper in R59: R6C2 <>4.
A 68 UR in R46C37 takes out 8 in R6C37.

Leaving an XY-wing 5-68 that solves it.

I hope that Nataraj might occasionally comment on puzzles like these: What solution path did he contemplate?

Keith

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Sat Dec 04, 2010 9:31 am Post subject:

Hmm... a w-wing did it for me, admittedly with a simple transport...

Code:

*--------------------------------------------------------------------*
| 1 6 57 | 2578 9 258 | 4 258 3 |
| 347 3457 2 | 578 1 34 | 9 6 58 |
| 8 34 9 | 25 6 34 | 7 1 25 |
|----------------------+----------------------+----------------------|
| 2 1 6(8) | 4 5 9 | 6(8) 3 7 |
| 347 3457 3457 | 16 8 16 | 25 9 2-4 |
| 9 458 568-4 | 3 2 7 | 568 (48) 1 |
|----------------------+----------------------+----------------------|
| 367 2378 378 | 2568 4 2568 | 1 258 9 |
| 46 9 (48) | 12568 7 12568 | 3 258-4 24568 |
| 5 2(4)8 1 | 9 3 268 | 28 7 2(4)68 |
*--------------------------------------------------------------------*
w-wing(48) ; (4=8)r6c8 - r4c7=r4c3 - (8=4)r8c3 ; r6c3<>4, r8c8<>4
with transport (4)r8c3 - r9c2=r9c9 ; r5c9<>4

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Dec 04, 2010 4:23 pm Post subject:

Quote:

A grouped skyscraper in R59: R6C2 <>4.

Keith,

I'm probably missing something, but do we need this terminology? This looks like a Finned X-Wing that happens to have two fins, but still a Finned X-Wing. Question

nataraj

Joined: 03 Aug 2007
Posts: 1048
Location: near Vienna, Austria

Posted: Sat Dec 04, 2010 6:45 pm Post subject:

keith wrote:

I hope that Nataraj might occasionally comment on puzzles like these: What solution path did he contemplate?

Keith

Ah, now that you mention it, Keith, I was in fact almost ready to comment on some of the puzzles (e.g. which of the November puzzles I thought would be the most interesting) when I was completely blown away by the ingenious ways people here (including yourself, Marty, Danny and other regulars) were solving the puzzles in completely different ways from what I expected.

So I kinda thought let the puzzles stand on their own, beauty (or ugliness) lies in the eye of the beholder.

Helmut's Sudoku Helper suggests a kite (4), then an xyz-wing. Doing the puzzle on paper, and looking at the nataraj diagram for (4), I'd use both the kite AND the m-wing (6) based on the same strong link (cand 4) in row 9 that forms the kite, and never need the xyz-wing.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Dec 04, 2010 8:09 pm Post subject:

Marty R. wrote:

Quote:

A grouped skyscraper in R59: R6C2 <>4.

Keith,

I'm probably missing something, but do we need this terminology? This looks like a Finned X-Wing that happens to have two fins, but still a Finned X-Wing. Question

Marty,

I use that name because that is how I see it. Once I figured out grouped coloring, I stopped looking for finned fish. (Full disclosure: I stopped looking for fish other than X-wings a long time ago.)

The logic is quite simple:

Code:

+-------+-------+-------+
| . # . | . . . | ^ . ^ |
| . / . | . . . | . # . |
| . / . | . . . | . # . |
+-------+-------+-------+
| . / . | . . . | . / . |
| . / . | . . . | . / . |
| . / . | . . . | . / . |
+-------+-------+-------+
| . / . | . . . | . / . |
| . @ . | . . . | . @ . |
| . / . | . . . | . / . |
+-------+-------+-------+

. Any candidates
@, # Contain candidate X
/ Do not contain candidate X
^ Cells where candidate X can be eliminated

One (or both) of the cells @ is not X. At least one of the cells # is X. X can be eliminated in the cells marked ^, in any cell that sees all the # cells.

The pattern above is not a finned X-wing. Maybe it is a finned skyscraper Razz

(Yes, I know, someone will point out it is a finned sashimi kraken franken something.)

As I said, I used the name because it is descriptive of how I found it. In the same vein, if I had been looking for an ER (and if it applied in the pattern above) I'd call it that.

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Dec 04, 2010 8:20 pm Post subject:

Quote:

(Yes, I know, someone will point out it is a finned sashimi kraken franken something.)

I'll point that out. It's a Sashimi X-Wing with double fin per Sudopedia.

http://www.sudopedia.org/wiki/Sashimi_X-Wing

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Dec 04, 2010 9:07 pm Post subject:

Marty R. wrote:

Quote:

(Yes, I know, someone will point out it is a finned sashimi kraken franken something.)

I'll point that out. It's a Sashimi X-Wing with double fin per Sudopedia.

http://www.sudopedia.org/wiki/Sashimi_X-Wing

Do I have to know that for the final exam? Razz

And, let me add, I am sort of with you on this "almost" or "finned" thing. To a pattern guy like me, a little suspect.

However, I do like the "grouped" thing. All it says is that "in this pattern, these cells act together". Like a pseudocell.

Keith

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Sat Dec 04, 2010 9:47 pm Post subject:

Marty R wrote:

I'll point that out. It's a Sashimi X-Wing with double fin per Sudopedia.

Yep

Personally I'm happy for anyone to use any name that is understandable - but for me a skyscraper is distinguished from its x-wing/sashimi/finned cousins by making an at least potential elimination on both "sides" of the strong links. As far as I can see "grouped" skyscrapers never do that. Now grouped kites I do think are a bona fide distinguishable move...

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Dec 04, 2010 9:53 pm Post subject:

Quote:

And, let me add, I am sort of with you on this "almost" or "finned" thing. To a pattern guy like me, a little suspect.

Let me admit to the world that I am a hypocrite on this issue. Embarassed

Consider the following UR:

Code:

+-------+-----------+-------+
| . . . | . . . | . . . |
| . . . | 12 . 12 | . . . |
| . . . | . . . | . . . |
+-------+-----------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 125 . 126 | . . . |
+-------+-----------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-----------+-------+

Play this puzzle online at the Daily Sudoku site

Obviously a 5 or 6 is needed so I go on a fishing expedition to see what each one reels in. Just a Forcing Chain that I used based on an "almost" pattern. Basically the same thing as the other "almosts", yet I can't accept the almost NPs. NTs, XYs and the like. Go figure.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Dec 04, 2010 10:21 pm Post subject:

Marty R. wrote:

Quote:

And, let me add, I am sort of with you on this "almost" or "finned" thing. To a pattern guy like me, a little suspect.

Let me admit to the world that I am a hypocrite on this issue. Embarassed

Consider the following UR:

Code:

What is "almost" about this pattern? Isn't it just a Type 3 with a 56 pseudocell that you can exploit? Like this:

Code:

+-------+-----------+-------+
| . . . | . . . | . . . |
| . . . | 12 . 12 | . . . |
| . . . | . . . | . . . |
+-------+-----------+-------+
| . . . | 68 . . | * * * |
| . . . | . . . | . . . |
| . . . | 125 * 126 | . . 58|
+-------+-----------+-------+
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | . . . | . . . |
+-------+-----------+-------+

8 can be eliminated from any cell *. The pseudocell is part of an XY-wing 56-8.

Where is the fin or the "almost"?

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Dec 04, 2010 11:22 pm Post subject:

keith wrote:

What is "almost" about this pattern? Isn't it just a Type 3 with a 56 pseudocell that you can exploit?

I don't know about calling the pattern "almost", but I've seen previous examples of Marty's "fishing expeditions", and the following is a Marty-esque UR catch that's not a UR Type 3.

Code:

+------------------------------------+
| . . . | . . . | . . . |
| . . . | 12 . 12 | . . . |
| . . . | . . . | . . . |
|-----------+------------+-----------|
| . . . | . -6 . | . . . |
| . . . | . -6 . | . . . |
| . . . | 125 -6 126 | . . . |
|-----------+------------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 35 36 . | . . . |
+------------------------------------+

Marty would probably see it as a forcing chain based on the UR:

Code:

r6c6=6 => r456c5<>6
r6c4=5 r9c4=3 r9c5=6 => r456c5<>6

It also works as a chain based on a UR:

Code:

<12>UR[(6)r6c6 = (5)r6c4)]r26c46 - (5=3)r9c4 - (3=6)r9c5 => r456c5<>6

As for Keith's example being a UR Type 3, I'd file it under the title: Unique Rectangle meets XY-Wing

Code:

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Dec 05, 2010 12:05 am Post subject:

Quote:

What is "almost" about this pattern? Isn't it just a Type 3 with a 56 pseudocell that you can exploit?

It's "almost" a Type 1. Laughing

I couldn't do what you've done there. Sure, I could use a pseudo cell if it were part of a subset, but not as a part of an XY-Wing. With the 5 and 6 I'd first try to see if there's a pincer potential, otherwise I'd test each one which is basically a Forcing Chain.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Dec 05, 2010 1:51 am Post subject:

Quote:

Code:

This is not a UR meets an XY-wing 35-6 Question

(Not that I disagree an XY-wing is a chain.)

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Dec 05, 2010 4:11 am Post subject:

keith wrote:

Quote:

Code:

This is not a UR meets an XY-wing 35-6 Question

(Not that I disagree an XY-wing is a chain.)

This is my example grid. I was describing your example grid as UR meets an XY-wing.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Dec 05, 2010 4:49 am Post subject:

daj95376 wrote:

keith wrote:

Quote:

Code:

This is not a UR meets an XY-wing 35-6 Question

(Not that I disagree an XY-wing is a chain.)

This is my example grid. I was describing your example grid as UR meets an XY-wing.

So, let me describe your example as UR meets XY-wing.

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sun Dec 05, 2010 6:02 am Post subject:

keith wrote:

So, let me describe your example as UR meets XY-wing.

Maybe. I can see how you might consider it an XY-Wing using the <56> strong link provided by the UR as a substitute for a bivalue cell.

I have a problem accepting it because I consider the <56> pseudo-cell to only have peers in [r6] and [b5]. With this constraint, the pseudo-cell doesn't see the vertex cell, r9c4, in my example grid. So, I don't consider the pseudo-cell to be a pincer cell.

In your example grid, the pseudo-cell would be considered the vertex cell and the <58> & <68> pincer cells are present in either [b5] or [r6]; i.e., peers of the vertex cell.

Regards, Danny

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Dec 05, 2010 6:45 am Post subject:

Danny,

You are correct, given the parameters you describe.

I have, however, become used to the idea that the components of a pseudocell may have different peers

In fact, the components of the pseudocell themselves do not have to be peers!

Code:

+------------------------------------+
| . . . | . . . | . . . |
| . . . | 12 . 126 | . . 36 |
| . . . | . . . | . . . |
|-----------+------------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 125 . 12 | . . . |
|-----------+------------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 35 . . | . . -3 |
+------------------------------------+

+------------------------------------+
| . . . | . . . | . . . |
| . . . | 12 . 126 | . . -6 |
| . . . | . . . | . . . |
|-----------+------------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 125 . 12 | . . . |
|-----------+------------+-----------|
| . . . | . . . | . . . |
| . . . | . . . | . . . |
| . . . | 35 . -6 | . . 36 |
+------------------------------------+

I should be lucky enough to find these in the wild!

(I think the last one is particularly elegant. I may have to make a bumper sticker ...)

Keith

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