dailysudoku.com Forum Index dailysudoku.com
Discussion of Daily Sudoku puzzles
 
 FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

Please bail me out
Goto page 1, 2  Next
 
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles
View previous topic :: View next topic  
Author Message
Marty R.



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

PostPosted: Fri Aug 17, 2007 3:53 pm    Post subject: Please bail me out Reply with quote

This is the puzzle that would have been Mepham July 20.

Code:

+------------+-----------+------------+
| 4   6  58  | 3   89 7  | 59  2  1   |
| 3   29 59  | 25  1  4  | 7   6  8   |
| 27  1  578 | 258 6  29 | 345 49 349 |
+------------+-----------+------------+
| 269 29 3   | 7   5  8  | 1   49 469 |
| 67  5  679 | 4   2  1  | 36  8  369 |
| 1   8  4   | 9   3  6  | 2   5  7   |
+------------+-----------+------------+
| 5   3  1   | 28  48 29 | 46  7  469 |
| 8   7  2   | 6   49 3  | 49  1  5   |
| 69  4  69  | 1   7  5  | 8   3  2   |
+------------+-----------+------------+

Play this puzzle online at the Daily Sudoku site
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Fri Aug 17, 2007 4:52 pm    Post subject: Reply with quote

An elimination can be made at r1c3 if you pay attention to pincers at r2c3 and r1c7.
Back to top
View user's profile Send private message
klimke



Joined: 17 Aug 2007
Posts: 5

PostPosted: Fri Aug 17, 2007 7:56 pm    Post subject: Reply with quote

New to the site. Do not see how you conclude the pincers you reference are of opposite polarity. I do see a "play ahead" that determines r2c4 but I don't like that method. Help is welcomed.
Back to top
View user's profile Send private message
keith



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

PostPosted: Fri Aug 17, 2007 9:03 pm    Post subject: Reply with quote

How about this:

Look at the <49> UR in R34C89. Either R3C9 is <3> and/or R4C9 is <6>. Either way, R5C7 is <3>.

Takes you to here:
Code:
+-------------+-------------+-------------+
| 4   6   58  | 3   89  7   | 59  2   1   |
| 3   29  59  | 25  1   4   | 7   6   8   |
| 27  1   578 | 258 6   29  | 45  49  3   |
+-------------+-------------+-------------+
| 269 29  3   | 7   5   8   | 1   49  469 |
| 67  5   679 | 4   2   1   | 3   8   69  |
| 1   8   4   | 9   3   6   | 2   5   7   |
+-------------+-------------+-------------+
| 5   3   1   | 28  48  29  | 6   7   49  |
| 8   7   2   | 6   49  3   | 49  1   5   |
| 69  4   69  | 1   7   5   | 8   3   2   |
+-------------+-------------+-------------+

Little by little ...

Keith

(PS: There are any number of chains and loops that can be applied.)
Back to top
View user's profile Send private message
Marty R.



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

PostPosted: Fri Aug 17, 2007 9:24 pm    Post subject: Reply with quote

Thanks MM, but I don't see it. I can't get a W-Wing or XY-Chain out of that, so you might as well tell me directly.

Klimke, welcome to the forum. I don't know what your disliked method is to solve r2c4, but if it's a forcing chain or other trial-and-error, I've already solved it easily with one chain that leads to a contradiction.

Keith, I looked at that rectangle and realized that one had to be 3 or the other one 6, but I didn't go forward with it. I haven't settled on an opinion as to whether that's rectangle theory or a forcing chain. Actually, it's using rectangle theory to steer one towards a forcing chain. How do you view it re: its degree of trial-and-error?

Update, 15 minutes later. MM, I see it now but don't know what to call it, as it doesn't strictly meet the definition of an XY-Chain.


Last edited by Marty R. on Fri Aug 17, 2007 9:39 pm; edited 1 time in total
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Fri Aug 17, 2007 9:38 pm    Post subject: Reply with quote

They are the pincers of an xy chain.
Back to top
View user's profile Send private message
klimke



Joined: 17 Aug 2007
Posts: 5

PostPosted: Fri Aug 17, 2007 10:05 pm    Post subject: Reply with quote

Thanks for all the info.

Keith, I did get the 3's using the UR. Thanks for explaining.

I'm still stuck on the pincer argument. I see the convergence of the two pincer cells at r1c3 but do not understand how a conclusion that they are opposites is arrived at.
Back to top
View user's profile Send private message
Johan



Joined: 25 Jun 2007
Posts: 206
Location: Bornem Belgium

PostPosted: Fri Aug 17, 2007 10:10 pm    Post subject: Reply with quote

There is an 7-cell xy-chain which eliminates <2> in R2C4
Starting with <8> in R7C4.
[28][84][49][98][85][59][92]

Code:

+------------+-----------+------------+
| 4   6 E58  | 3  D89 7  | 59  2  1   |
| 3 G29 F59  |-25  1  4  | 7   6  8   |
| 27  1  578 | 258 6  29 | 345 49 349 |
+------------+-----------+------------+
| 269 29 3   | 7   5  8  | 1   49 469 |
| 67  5  679 | 4   2  1  | 36  8  369 |
| 1   8  4   | 9   3  6  | 2   5  7   |
+------------+-----------+------------+
| 5   3  1   |A28 B48 29 | 46  7  469 |
| 8   7  2   | 6  C49 3  | 49  1  5   |
| 69  4  69  | 1   7  5  | 8   3  2   |
+------------+-----------+------------+
Back to top
View user's profile Send private message Send e-mail
TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Fri Aug 17, 2007 10:32 pm    Post subject: Reply with quote

klimke,

Welcome to the forum.

klimke wrote:
I'm still stuck on the pincer argument. I see the convergence of the two pincer cells at r1c3 but do not understand how a conclusion that they are opposites is arrived at.


The conclusion is that if r1c3 were 5 the chain would work it's way back in both directions to the point where there would be a contradiction, in this case that both r4c2 and r4c8 would have to be 9.

Nice chain: -5- R1C7 -9- R3C8 -4- R4C8 -9- R4C2 -2- R2C2 -9- R2C3 -5-

Johan notation: [59][94][49][92][29][95]

Code:
 
 *--------------------------------------------------*
 | 4    6    58   | 3    89   7    | 59A  2    1    |
 | 3    29E  59F  | 25   1    4    | 7    6    8    |
 | 27   1    578  | 258  6    29   | 345  49B  349  |
 |----------------+----------------+----------------|
 | 269  29D  3    | 7    5    8    | 1    49C  469  |
 | 67   5    679  | 4    2    1    | 36   8    369  |
 | 1    8    4    | 9    3    6    | 2    5    7    |
 |----------------+----------------+----------------|
 | 5    3    1    | 28   48   29   | 46   7    469  |
 | 8    7    2    | 6    49   3    | 49   1    5    |
 | 69   4    69   | 1    7    5    | 8    3    2    |
 *--------------------------------------------------*


Last edited by TKiel on Fri Aug 17, 2007 10:41 pm; edited 2 times in total
Back to top
View user's profile Send private message
keith



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

PostPosted: Fri Aug 17, 2007 10:37 pm    Post subject: Reply with quote

Quote:
Keith, I looked at that rectangle and realized that one had to be 3 or the other one 6, but I didn't go forward with it. I haven't settled on an opinion as to whether that's rectangle theory or a forcing chain. Actually, it's using rectangle theory to steer one towards a forcing chain. How do you view it re: its degree of trial-and-error?

Marty,

This is philosophy and personal opinion:

My complaint about chains is there is not a systematic way to find them.

At the lower limit, every pattern is a chain. (A naked single is a chain of length zero?)

Anyway, the UR gives you a place to start. I do not think what I described is trial and error.

So, in my opinion: Recognize a pattern, and explore the implications, is quite acceptable.

Keith
Back to top
View user's profile Send private message
klimke



Joined: 17 Aug 2007
Posts: 5

PostPosted: Fri Aug 17, 2007 11:15 pm    Post subject: Reply with quote

Thanks for the info on the xy-chains, however, I am still confused.

In the Johan post, I don't see how E-F is a conjugate pair in 5's.

In the TKiel post, I don't see how C-D is a conjugate pair in 9's.

In both cases, it appears there are more than 2 candidates per row or column. Any clarification would be welcome.

Also, going back to the original Mogulmeister reply, it was implied that 2 simple pincers (r2c3 & r1c7) could cause an exclusion at r1c3. While elegant, I can not justify that move logically. Clarification there would be appreciated also.

Klimke
Back to top
View user's profile Send private message
TKiel



Joined: 22 Feb 2006
Posts: 292
Location: Kalamazoo, MI

PostPosted: Sat Aug 18, 2007 12:49 am    Post subject: Reply with quote

klimke,

An XY-chain involves only bi-value cells. They do not have to be conjugates, but the values within the cells are strongly linked (i.e. if X, then not Y; if not X, then Y.

In my post above, I said the conclusion was that if r1c3 were <5> then the chain would lead back to a contradiction in that there would be two <9>'s in row 4. It is not true that the contradiction would have to be in row 4 (it could be elsewhere in the chain) but let's look at how that would happen.

If r1c3 were <5>, then r1c9 would not be <5>, would have to be <9>.
If r1c9 were <9>, then r3c8 would not be <9>, would have to be <4>.
If r3c8 were <4>, then r4c8 would not be <4>, would have to be <9>.

If r1c3 were <5>, then r2c3 would not be <5>, would have to be <9>.
If r2c3 were <9>, then r2c2 would not be <9>, would have to be <2>.
If r2c2 were <2>, then r4c2 would not be <2>, would have to be <9>.

So even though the cells in the chain are not conjugates, the values within the cells are strongly linked, because an XY-chain uses only bi-value cells.
Back to top
View user's profile Send private message
Marty R.



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

PostPosted: Sat Aug 18, 2007 12:56 am    Post subject: Reply with quote

Quote:
Also, going back to the original Mogulmeister reply, it was implied that 2 simple pincers (r2c3 & r1c7) could cause an exclusion at r1c3. While elegant, I can not justify that move logically. Clarification there would be appreciated also.


Klimke, I can't speak for others, but if I considered a move "elegant", it would be justifiable to me. What sort of clarification are you looking for?

I don't know if I'm answering anything, but if you look at the implications of a 9 in r2c3 and work from box 1 to box 4 to box 6 and box 3, then r1c7 must be=5, thus the pincer effect.
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Sat Aug 18, 2007 10:38 am    Post subject: Reply with quote

Hello Klimke,

Sometimes a picture is worth a thousand words. The pincers are in green and the steps between them shown in pink. The eliminated 5 in yellow.

A quick look at x-y chains in sudopedia should help but as Tracy and others have shown, the 5 in r1c3 can not endure because there will always be a situation where one of the pincers will always contain 5.



[Edited to replace original image which was lost when Tinypic folded]


Last edited by Mogulmeister on Thu Jul 01, 2021 2:48 pm; edited 2 times in total
Back to top
View user's profile Send private message
klimke



Joined: 17 Aug 2007
Posts: 5

PostPosted: Sat Aug 18, 2007 1:01 pm    Post subject: Reply with quote

The picture was worth it, I see it now.

Thanks for all the assistance from the group. Very helpful.
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Sun Aug 19, 2007 11:25 am    Post subject: Reply with quote

The philosophy of sudoku is very interesting and I find myself seeing that a cut and dried position is not so easy for me personally. Why ?

Simply that when I tackle extreme puzzles I will use anything in my armoury because they are so darned hard to begin with.

Under normal circumstances and in attempting puzzles that are sub-diabolical I will eschew forcing chains and unique rectangles. As Keith mentioned it's a personal choice but the first one feels like nishio (trial and error/bifurcation) and UR's feel like a backdoor cheat (to me anyway).

Needless to say when I'm up against it I use both methods! Smile
Back to top
View user's profile Send private message
Marty R.



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

PostPosted: Sun Aug 19, 2007 4:00 pm    Post subject: Reply with quote

Quote:
and UR's feel like a backdoor cheat (to me anyway).


MM, like you, I'm interested in the philosophy, although I don't understand it nearly as well as many on this forum.

I'd be interested in hearing in more detail the objections to URs. I know you're not the only one, but I don't understand why, since it seems to be based on pattern recognition, as are many other techniques which are much more readily accepted.
Back to top
View user's profile Send private message
keith



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

PostPosted: Sun Aug 19, 2007 4:15 pm    Post subject: Reply with quote

After my UR elimination above, there are four 5-link chains that make the following eliminations:

R2C2 is not <9>.
R2C3 is not <5>.
R3C3 is not <7>.
R3C4 is not <5>.

You only need the first one to solve the puzzle. Easy to see, once you know it's there!
Back to top
View user's profile Send private message
keith



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

PostPosted: Sun Aug 19, 2007 9:15 pm    Post subject: Reply with quote

Quote:
I'd be interested in hearing in more detail the objections to URs.

I'd like to hear them too. Rolling Eyes

Is it because you like to solve puzzles that have multiple solutions?

Or, is it like my mother-in-law, who won't drive to any place on a route that involves a left turn?

Keith
Back to top
View user's profile Send private message
Mogulmeister



Joined: 03 May 2007
Posts: 1151

PostPosted: Sun Aug 19, 2007 10:06 pm    Post subject: Reply with quote

Your mother-in-law sounds like a real purist Keith - I can assure you I'm not one of those ! Smile No, my reason for not going to a UR as an immediate technique is personal philosophical sentiment and not based on some lofty logical standpoint.

Whilst acknowledging (and sometimes using) URs, I feel they are like an external agent - a get out of jail card. I'm not as extreme as Glassman but don't really care if a puzzle has one solution - albeit that these days the best ones do seem to.

It's more to do with a feeling that the UR is like a gamer's trapdoor - that it is not really an intrinsic part of the game - more like penalties after extra time in football* (or rushing the goal-tender 1-on-1 after regulation in an ice-hockey game). The after extra time penalties are really nothing to do with football. The UR to my mind takes advantage of uniqueness, a global given, rather than logical interplay between the candidates.

Incidentally, I'd be interested to see if anyone has been able to create a puzzle that could only be solved if a UR was used.

It's a powerful technique but it sometimes feels as if someone has brought a pump action shotgun grouse shooting.


*The game known as "soccer" in the US.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    dailysudoku.com Forum Index -> Other puzzles All times are GMT
Goto page 1, 2  Next
Page 1 of 2

 
Jump to:  
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum


Powered by phpBB © 2001, 2005 phpBB Group