## A simple ALS with a hitch

Post the puzzle or solving technique that's causing you trouble and someone will help

### A simple ALS with a hitch

Code: Select all
`  *--------------------------------------------------------------------* | 9      245    2568   | 34     46x     345    | 1      3568   7      | | 56     57     1      | 379    8      2      | 4      356    359    | | 4568   3      5678   | 1      469x    4579   | 5689   2      589    | |----------------------+----------------------+----------------------| | 3468   47     3678   | 234    5      1      | 2368   9      2348   | | 2      459    359    | 6      49     8      | 357    3457   1      | | 34568  1      35689  | 29     7      349    | 23568  34568  23458  | |-----------99-----------+----------------------+----------------------| | 35     8      359    | 479    2      6      | 3579   1      3459   | | 1      6      4      | 5      3      79y     | 2789   78     289    | | 7      259    2359   | 8      1      49y     | 359    345    6      | *--------------------------------------------------------------------*`

The cell’s with (x) is an ALS as is the cell’s with a "y". At least, I think so. Here is the confusing part, the (4) in r1c6 is a restricted common, (4) in r3c6 looks like it could also be a restricted common and so is the (9) r3c6.

Here is the problem, it looks like either the (9) or the (4) could be the restricted common. You can exclude the (4) from r1c6 and the (4) from r3c6 but you cannot exclude the (9) from r3c6. In the future, how can I tell which candidate is the restricted candidate?. I must be missing something. Any help would be appreciated.
Jasper32

Posts: 60
Joined: 04 January 2008

A restricted common candidate for two sets of cells is a candidate common to the two sets which can actually be entered in only one of them. Your two sets are almost locked but they have no restricted common candidate.

You might like to check the sets A and B in columns 1 and two.

Code: Select all
` *-----------------------------------------------------------------*  |  9       245    2568   | 34    46     345   | 1      3568   7   |  | A56     B57     1      | 379   8      2     | 4      356    359 |  |  4568    3      5678   | 1     469    4579  | 5689   2      589 |  |------------------------+---------------------+------------------|  | A3468   B47     3678   | 234   5      1     | 2368   9      2348|  |  2       459    359    | 6     49     8     | 357    3457   1   |  | A34568   1      35689  | 29    7      349   | 23568  34568  458 |  |------------------------+--------------------+-------------------|  | A35      8      359    | 479   2      6     | 3579   1      3459|  |  1       6      4      | 5     3      79    | 2789   78     289 |  |  7       259    2359   | 8     1      49    | 359    345    6   |  *-----------------------------------------------------------------*`

Each is almost locked and each has 4 as a candidate but it cannot be in both because only one 4 is allowed in box 4. So, 4 is restricted common.

A and B share another candidate: 5. If 5 were to be placed in r3c1, it would be eliminated from both A and B. But then both A and B would need a 4 to make up as many entries as cells. This contradiction to the meaning of restricted common means that 5 may be eliminated from r3c1.

Steve
Steve R

Posts: 74
Joined: 03 April 2006

### als

Steve R wrote:
A restricted common candidate for two sets of cells is a candidate common to the two sets which can actually be entered in only one of them. Your two sets are almost locked but they have no restricted common candidate.

Jasper32

Posts: 60
Joined: 04 January 2008

Jasper, in addition to Steve R's helpful reply (not to mention his good pickup of his ALS example), another way of expressing it: the digits of a restricted common of each ALS set in the typical ALS pattern must directly 'see' each other ie. be in the same row, column or box. Note in Steve's example how the restricted common digits (number 4) in each of the sets A & B 'see' each other because they are in the same box.

(Full disclosure : I say 'typical' ALS pattern, because restricted commons can also indirectly see each other thru conjugate links.)
DonM
2013 Supporter

Posts: 475
Joined: 13 January 2008

### ALS

Thanks DonM for your further clarification of how ALS. I was quite satisfied with everything until you wrote:

(Full disclosure : I say 'typical' ALS pattern, because restricted commons can also indirectly see each other thru conjugate links.)

Just when I thought I new everything about ALS's you have to come up with the “conjugate links" stuff….only kidding, I will explore that next.
Jasper32

Posts: 60
Joined: 04 January 2008