How to spot nice loops?

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How to spot nice loops?

Postby Sam Kennedy » Wed Jun 15, 2016 11:37 am

I followed the bivalue/bilocation plot guide (here: http://forum.enjoysudoku.com/nice-loops-for-advanced-level-players-b-b-plot-t2143.html) and ended up with this:
Image (thick black = strong link, thin grey = weak link)

I've read this guide: http://paulspages.co.uk/sudokuxp/howtosolve/niceloops.htm on the theory of nice loops, and understand it, however what I'm struggling with is how to actually find nice loops looking at a mess of lines like above. I've been using the online pixlr image editor to do this, is there any sudoku software which allows you to annotate links yourself?

I would be grateful if someone could point out any nice loops/aic in the above puzzle so I can get a better idea of how to find them.

Thank you :)
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Re: How to spot nice loops?

Postby SteveG48 » Wed Jun 15, 2016 1:39 pm

It would appear from the graphic that you're using Hodoku. Just go to the all possible steps tab and list the available steps. The list will include Nice loops.

Hodoku is also a good program for annotating things yourself. Set the coloring to "candidate" rather than "cell" and you can color candidates in each cell to show links and so forth in any way you wish.
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Re: How to spot nice loops?

Postby pjb » Wed Jun 15, 2016 1:41 pm

Code: Select all
 5       8       1      | 9      6      47     | 347    2      37     
 79      49      47     | 1      3      2      | 8      6      5     
 36     a26     b23-6   | 458    48     4578   | 479    19     17     
------------------------+----------------------+---------------------
 1       45      9      | 6      248    458    | 23     7      238   
 2       3       58     | 58     7      1      | 6      4      9     
 468     7       468    | 3      248    9      | 1      5      28     
------------------------+----------------------+---------------------
 368    d56-2   c35-268  | 248    9      48     | 27     18     1267   
 468     1       2468   | 7      5      3      | 29     89     26     
 79      29      278    | 28     1      6      | 5      3      4     

Here's a nice little 'continuous nice loop'
(2)r3c2 = (2-3)r3c3 = (3-5)r7c3 = (5-6)r7c2 = r3c2 => -6 r3c3, -268 r7c3, -2 r7c2
Here's a 'discontinuous nice loop' which solves the puzzle in one:
(7)r9c3 = (7-4)r2c3 = r2c2 - (4=5)r4c2 - (5=8)r5c3 => -8 r9c3; stte

Getting away from loops, here's an AIC which solves the puzzle in one:
(5=4)r4c2 - (4=9)r2c2 - (9=2)r9c2 - (2=8)r9c4 - (8=5)r5c4 => -5 r4c6, r5c3; stte

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Re: How to spot nice loops?

Postby Sam Kennedy » Thu Jun 16, 2016 7:30 am

Thank you so much for the replies, I used candidate colouring and it was so much easier to make loops around the board. This is a new puzzle but I think I found my first loop! :D
Image

The loop is: [r3c4]-3-[r3c2]=3=[r8c2]=1=[r9c2]=6=[r7c1]-6-[r7c4]=6=[r3c4] (Sorry if this notation is standard, I'm still learning this!)
Pretty much, if r3c4 is 3, it would have to be 6, therefore it cannot be 3. There's probably a much simpler way of coming to that same conclusion, but this way was a lot more satisfying.

Is that a valid nice loop? It doesn't appear to break any of the propagation rules but I was able to use the rules for a discontinuous loop to eliminate the 3 from the cell?

Thank you again :)
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Re: How to spot nice loops?

Postby SteveG48 » Thu Jun 16, 2016 2:52 pm

Sam Kennedy wrote:The loop is: [r3c4]-3-[r3c2]=3=[r8c2]=1=[r9c2]=6=[r7c1]-6-[r7c4]=6=[r3c4] (Sorry if this notation is standard, I'm still learning this!)


Hi, Sam.

What you've got is definitely a valid chain giving the elimination you've indicated. Well done! I don't know if it's technically a Nice loop (some of the distinctions baffle me), but it does the job.

Here in the forum we generally use Eureka notation. Written that way, your loop would be written:

3r3c4 - r3c2 = (3-1)r8c2 = (1-6)r9c2 = r7c1 - r7c4 = 6r3c4 => -3 r3c4

Note that you can also shorten it by dropping the first term and it will still be perfectly valid:

3r3c2 = (3-1)r8c2 = (1-6)r9c2 = r7c1 - r7c4 = 6r3c4 => -3 r3c4

The logic of this is that if r3c2 is not a 3, then r3c4 is a 6 (which isn't a 3!). If r3c2 is a 3, then r3c4 can't be a 3. Either way, r3c4 is not a 3 and you have your elimination.
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