## Small patterns

Advanced methods and approaches for solving Sudoku puzzles

### Small patterns

Is there any agreement on what constitutes the full set of all "small patterns"? I'm thinking things like naked pairs, 2-string kites and really short chains, excluding uniqueness techniques.

Thanks.
Red Ed

Posts: 633
Joined: 06 June 2005

### Re: Small patterns

Red Ed wrote:Is there any agreement on what constitutes the full set of all "small patterns"? I'm thinking things like naked pairs, 2-string kites and really short chains, excluding uniqueness techniques.

With a "really short" limit of seven links (3 strong and 4 weak) for chains, the list of "small patterns" is ... well, small. Within that limit, I think there would be consensus but, then again, sudokuists are often an eclectic group.
ronk
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Joined: 02 November 2005
Location: Southeastern USA

### Re: Small patterns

I was thinking even narrower, restricting to just two base sets (or strong sets, constraints, whatever). I think there are 14 distinct patterns - here - though I'm sure players would argue they're all just fish in disguise. How does it look to you?

The list is generated semi-automatically. If I'm not miles off with what I've done so far then I'll finish my code and see what I can find up to and including four base sets.
Red Ed

Posts: 633
Joined: 06 June 2005

### Re: Small patterns

Red Ed wrote:I think there are 14 distinct patterns - here - though I'm sure players would argue they're all just fish in disguise. How does it look to you?

Completeness always seems to be one of the more difficult things to prove, but I'm not aware of any that are missing. If anything, there might be a few too many, since some have co-existing smaller patterns, e.g., locked candidates in patterns 2-3-x and 2-5-1.

you wrote: 12 = 1 and 2 are possibly candidates in this cell
*12 = 1 and 2 are the only candidates in this cell

Shouldn't these be reversed? If so, then the '*' is a little similar to "x*" in a regular expression. Also, were you expecting help with the missing names?
ronk
2012 Supporter

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

### Re: Small patterns

ronk wrote:If anything, there might be a few too many, since some have co-existing smaller patterns, e.g., locked candidates in patterns 2-3-x and 2-5-1.
Can you say more about that? I can't see how these smaller patterns make any of the 14 elimination patterns redundant, bearing in mind the maximality bit described in the preamble on that page. (Keep it simple, please; I don't actually play sudoku, so don't know solving terminology.)

ronk wrote:Also, were you expecting help with the missing names?
That would be welcome - either here on on the wiki (but if the latter, please tip me off here). Thanks.
Red Ed

Posts: 633
Joined: 06 June 2005

your "2-3-1" is indeed an X-wing -- r12\c14

but
b3\r3 provides the exclusions in r3;
following which,
b1\c1 and b2\c4 provide the exclusions in c1 and in c4 respectively

Pat

Posts: 3784
Joined: 18 July 2005

### Re:

Pat wrote:b3\r3 provides the exclusions in r3

Here's the pattern:
Code: Select all
`   1 /1 /1 |  1 /1 /1 | /1 /1 /1   1 /1 /1 |  1 /1 /1 | /1 /1 /1  -1 -1 -1 | -1 -1 -1 |  .  .  .  ---------+----------+---------  -1  .  . | -1  .  . |  .  .  .  -1  .  . | -1  .  . |  .  .  .  -1  .  . | -1  .  . |  .  .  .  ---------+----------+---------  -1  .  . | -1  .  . |  .  .  .  -1  .  . | -1  .  . |  .  .  .  -1  .  . | -1  .  . |  .  .  .`
Yep, I see your point. Hmm... that's interesting. It's reducible not because either of the original base sets (1r1 or 1r2) is redundant, but rather because there's another base set (1b3) that can make some eliminations all by itself.

That rather messes things up. I need to have a long think now.
Red Ed

Posts: 633
Joined: 06 June 2005

i used (1)b3\r3 but if you prefer you can do it with your (1)r12\b12
to get the exclusions in r3

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will you be doing other box-sizes ?
( e.g. 2x4 )

Pat

Posts: 3784
Joined: 18 July 2005

### Re: Small patterns

Red Ed wrote:
ronk wrote:Also, were you expecting help with the missing names?
That would be welcome - either here on on the wiki (but if the latter, please tip me off here). Thanks.

Here are four of them (I didn't address the reducible patterns):

Pattern number 2-2-1: empty rectangle
Pattern number 2-4-2: skyscraper
Pattern number 2-4-3: finned x-wing
Pattern number 2-6-1: locked pair

In case you're not aware, sudopedia.org is in big trouble: no Ruud, no active admin, images missing since the last site crash, and even worse, a continual "heavy" spambot attack (as of your click, a list of the the last 500 changes).
ronk
2012 Supporter

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Joined: 02 November 2005
Location: Southeastern USA

### Re: Small patterns

Thanks ronk. I was aware that sudopedia was in a mess; I decided to use it just as a temporary dumping-ground.

I'll give my "small patterns" fun a break for a bit while I ponder how best to remove sub-patterns. I need to be a bit clearer in my own mind about exactly what I mean by "pattern".

(One year later ... now superseded by "holes beget holes")
Red Ed

Posts: 633
Joined: 06 June 2005