## Nice loop problem

Advanced methods and approaches for solving Sudoku puzzles

### Nice loop problem

Below is a nice loop on (6's). The loop is" r2c1,r2c7, r4c7, r5c2, r5c9.

I was of the opinion that a (6) could be placed at r2c1 because it is at the intersection of two strong links. Can someone please tell me the error of my thinking? Thanks.

Code: Select all
`   *-----------------------------------------------------------* | 1     369   37    | 67    5     8     | 4     2     679   | | 26    8     27    | 4     79    3     | 5     679   1     | | 5     69    4     | 2     79    1     | 689   3     6789  | |-------------------+-------------------+-------------------| | 7     136   23    | 16    8     56    | 1269  1569  4     | | 26    16    5     | 3     4     9     | 7     168   268   | | 9     4     8     | 167   2     567   | 16    15    3     | |-------------------+-------------------+-------------------| | 48    7     1     | 5     6     24    | 3     89    289   | | 3     5     9     | 8     17    27    | 126   4     267   | | 48    2     6     | 9     3     47    | 18    178   5     | *-----------------------------------------------------------*`
Jasper32

Posts: 60
Joined: 04 January 2008

I am sorry, but I don't understand your notation. First of all [r2c7] is already set to 5, do you mean [r2c8]? How do you get from [r4c7] ([r4c8]?) to [r5c2] (the cells don't see each other)? How do you get from [r5c9] back to [r2c1]? It would be helpful if you could provide your complete chain.

For candidate 6 in [r2c1] I get:
Discontinuous Nice Loop [r2c1]=2=[r2c3]-2-[r4c3]=2=[r4c7]=9=[r3c7]-9-[r3c2]-6-[r2c1] => [r2c1]<>6

The grid contains simpler steps too, for example:
Hidden Single: [r1c4]=6
Hidden Single: [r8c5]=1
Hidden Pair: 5,6 in [r46c6] => [r46c4]<>6, [r6c6]<>7
and some more.
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

Jasper, I don't understand your question either. In the future, please ask for help on the Help with particular puzzles forum, as you've done in the past.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Sorry, I should have posted,  r2c1, r2c8, r4c8, r5c1, r5c9. It was late when I posted this and didn't get it correct. No, I wasn't drunk but much as I hate to admit it, I guess being 75 might have something to do with it.

I will post it the proper group next time ....another apology.

It was a "bad hair day" for me yesterday...

Thanks for your indulgences and replies.
Jasper32

Posts: 60
Joined: 04 January 2008

You don't have to apologize, everybody makes mistakes (especially me!). But unfortunately I still can't follow your chain. I guess you go:

r2c1=6=r2c8-6-r4c8

but now I am stuck. To continue you would need a strong link on 6, which I can't see. Could you please tell us, how you get from r4c8 to r5c1?
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

I don't know if this helps but there are some easy steps undone to get to here:

Code: Select all
`.------------------.------------------.------------------.| 1     39    37   | 6     5     8    | 4     2     79   || 26    8     27   | 4     79    3    | 5     679   1    || 5     69    4    | 2     79    1    | 689   3     6789 |:------------------+------------------+------------------:| 7     36    23   | 1     8     56   | 269   569   4    || 26    1     5    | 3     4     9    | 7     68    268  || 9     4     8    | 7     2     56   | 16    15    3    |:------------------+------------------+------------------:| 48    7     1    | 5     6     24   | 3     89    289  || 3     5     9    | 8     1     27   | 26    4     267  || 48    2     6    | 9     3     47   | 18    178   5    |'------------------'------------------'------------------'`

This has no bearing on nice loops but a single xy-wing wraps things up for some of us. (r69c7 with r5c8)
wintder

Posts: 297
Joined: 24 April 2007