SudoCue Users Forum Index SudoCue Users
A forum for users of the SudoCue programs and the services of SudoCue.Net
 
 FAQFAQ   SearchSearch   UsergroupsUsergroups   RegisterRegister 
 ProfileProfile   Log in to check your private messagesLog in to check your private messages   Log inLog in 

nice loop help please

 
Post new topic   Reply to topic    SudoCue Users Forum Index -> Help Me! I'm stuck!
View previous topic :: View next topic  
Author Message
magician
Rookie
Rookie


Joined: 01 Apr 2007
Posts: 5
Location: UK

PostPosted: Tue Apr 03, 2007 11:08 pm    Post subject: nice loop help please Reply with quote

I really need help with understanding the nice loop. I am using a program to help me get used to techniques, and when im stuck ti helps me. A lot of the time the nice loop is the answer, but i am no where near getting this. Please explain the following. Please also explain in laymans terms so I get it. I would really appreciate it not to be in complex notation



[/img]
for example in the first one, I dont understand why the 7 is highlighted, and then again in the next cell, and then for a third time in the 3rd cell. please help me understand all the ones i have posted so i can nail these once and for all.Also how do you spot them, and how do you kno wwhich direction to go in? And how does it eliminate a candidte.
Back to top
View user's profile Send private message
magician
Rookie
Rookie


Joined: 01 Apr 2007
Posts: 5
Location: UK

PostPosted: Wed Apr 04, 2007 11:43 am    Post subject: Reply with quote

PLEASE HELP
Back to top
View user's profile Send private message
mhparker
Grandmaster
Grandmaster


Joined: 20 Jan 2007
Posts: 345
Location: Germany

PostPosted: Wed Apr 04, 2007 1:17 pm    Post subject: Reply with quote

For an introduction to nice loops, I would recommend looking here first:

http://www.paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm

As regards your screenshots, the arrows are a bit confusing at first sight. Take the first screenshot for example. It would have been better for the programmer to have linked the 6 in r1c2 with the 6 in r1c5 (instead of the 7). Similarly, the two "3"s should be linked in r1c12 and the two "1"s in r12c1. In other words, the candidate used for a link is not necessarily the candidate used for the predecessor link (if any), as the graphic appears to imply. In addition, if the polarity (true/false) of the ends of each link would have been represented in a different color, the illustration would be much more understandable. As it is, we just have to keep in mind that the candidate used for a link is the candidate highlighted for the end cell of that link, and keep track of the polarity ourselves.

It also appears that continuous arrows are being used to represent strong links (i.e., between conjugate pairs) and broken arrows for the weak links. But here there is something I don't fully understand. The first screenshot shows a strong link on candidate 3 between r1c1 and r1c2, even though the "3"s in these cells do not form a conjugate pair in row 1 or box 1. My previous understanding was that the strong and weak links are identified in advance and then joined up to form a loop. But this can't be the case here. Instead, it looks like the programmer is making use of the fact that the loop is discontinous and that the inference chain asserts r1c5 = 7, and hence not 3, thus dynamically making the "3"s in r1c12 a strongly linked pair, which is necessary here to complete the loop. Because of this, I'm wondering whether the first example is really a valid nice loop. Maybe someone else can answer this?

The implications are valid though:

r2c1 = 7 --> r2c5 <> 7 --> r1c5 = 7 --> r1c2 = 6 --> r1c1 = 3 --> r2c1 = 1

In other words, r2c1 = 7 --> r2c1 <> 7, which is a logical contradiction. Therefore the original hypothesis (r2c1 = 7) must be incorrect and that we can delete 7 as a candidate from r2c1.

In the second example the implications are:

r3c2 = 6 --> r1c2 <> 6 --> r1c5 = 6 --> r1c8 = 8 --> r3c9 = 6 --> r3c2 <> 6

Again, this is a logical contradiction, implying that the original hypothesis (r3c2 = 6) must be incorrect and that we can delete 6 as a candidate from r3c2.

Hopefully, others on this forum can elaborate on this, and/or answer your other questions (as well as mine on nice loop validity above).
_________________
Cheers,
Mike
Back to top
View user's profile Send private message
GreenLantern
Regular
Regular


Joined: 30 May 2006
Posts: 14

PostPosted: Wed Apr 04, 2007 11:55 pm    Post subject: Reply with quote

Into Sudoku (from which these screenshots came) is a good program, but obviously the diagrams aren't as clear as they could be. I think the two Nice Loops that the program is trying to point out are the following:

  • [r2c5]=7=[r1c5]-7-[r1c7]-1-[r1c1]=1=[r2c1]=7=[r2c5] => r2c5=7
  • [r3c2]-6-[r1c2]=6=[r1c5]=8=[r1c8]-8-[r3c9]-6-[r3c2] => r3c2<>6


In the first loop, the initial assumption is that r2c5<>7 => r1c5=7 => r1c7=1 => r1c1=3 => r2c1=1 => r2c5=7 (contradiction). Therefore, r2c5=7. The confusing part of the first diagram is that it correctly shows that r1c2=6 even though this has nothing to do with the nice loop.

In the second loop, the initial assumption is r3c2=6 => r1c2=3 => r1c5=6 => r1c8=8 => r3c9=6 (contradiction). Therefore, r3c2<>6.

The link that mhparker gives for the Nice Loop tutorial is a good one. In fact, I would also recommend Paul's program, SudokuXP5, as it gives excellent Nice Loop hints which include diagrams as well as the actual Nice Loop notation.
Back to top
View user's profile Send private message
Display posts from previous:   
Post new topic   Reply to topic    SudoCue Users Forum Index -> Help Me! I'm stuck! All times are GMT
Page 1 of 1

 
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