Almost locked sets

Advanced methods and approaches for solving Sudoku puzzles

Almost locked sets

Postby yasmin » Fri Mar 31, 2006 2:07 pm

Hi,

I've read about ALS's but haven't managed to apply them yet.

Can someone please explain:

1a. What exactly does it mean that a set is "locked" or "almost locked"?

1b. Am I supposed to be looking for sets with only 2 candidates in each in the X,Z version and for ones with 3 candidates each in the X,Y,Z version?

2. Can the sets include any number of cells or a specific number of cells in each case?

3. Am I looking for a particular shape in which the sets are ordered? or am I supposed to look for ANY odd combination of cells across the board which answers the conditions of "x = restricted common" and another common "z"?

In short, although I understood the example I read, I'm lost on how exactly to apply it. Perhaps I'm solving puzzles that don't have ALS's in them and therefore I just can't find any?

thanks in advance for some application tips...

Yasmin
yasmin
 
Posts: 20
Joined: 24 February 2006

Re: Almost locked sets

Postby Havard » Fri Mar 31, 2006 7:50 pm

yasmin wrote:Hi,

I've read about ALS's but haven't managed to apply them yet.

Can someone please explain:

1a. What exactly does it mean that a set is "locked" or "almost locked"?

1b. Am I supposed to be looking for sets with only 2 candidates in each in the X,Z version and for ones with 3 candidates each in the X,Y,Z version?

2. Can the sets include any number of cells or a specific number of cells in each case?

3. Am I looking for a particular shape in which the sets are ordered? or am I supposed to look for ANY odd combination of cells across the board which answers the conditions of "x = restricted common" and another common "z"?

In short, although I understood the example I read, I'm lost on how exactly to apply it. Perhaps I'm solving puzzles that don't have ALS's in them and therefore I just can't find any?

thanks in advance for some application tips...

Yasmin


Hm, I'm no expert, but I'll start you off, and then you should go back and read more about them!

A locked set is exactly n cells with exactly n different candidates.

So that if you have three cells, and they have some distribution of the candidates 1, 2 and 3 in them, you have a locked set:
examples are:
[12] [13] [23]
[123] [123] [123]
[123] [12] [13]

now a Almost locked set is exactly n cells with exactly n+1 different candidates... YES that means that any cell with two candidates in it is a ALS. So the simplest form of ALS is for example one cell with the numbers 1 and 2 in it!
Other examples would be two cells with three different candidates like this:
[12] [13]
[123] [12]
[123] [123]

so that should answer your 1a.

so about your 1b: You see, a set can be up to 8 cells with 9 different candidates in them. What a xz is concidering two sets, xyz is concidering THREE sets. Each set can be anything from 1 to 8 cells...
and that should answer your 2 ...

this should get you started! now go and look for examples of application of the ALS rule. This forum is full of them!:)

havard
Havard
 
Posts: 377
Joined: 25 December 2005

Postby yasmin » Sat Apr 08, 2006 3:05 pm

Hi Havard

Thanks for your explanation which clarifies a lot for me !

Yasmin
yasmin
 
Posts: 20
Joined: 24 February 2006


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