The New Sudoku Players' Forum

[Cenoman]

Myth's CoALS rule:The number group A comes from the overlapping area, and the number group B comes from the non-overlapping area, then the numbers in A have a strong relationship with the numbers in B.
And you turn it into a strong relationship between A from the overlapping area and B from the non-overlapping area.
In fact, the strong relationship is for A and B in all cells of CoALS, not partitions. That is to say, the final solution 8 may not come from r4c6, and the strong relationship you wrote does not hold. Myth's CoALS rule can only provide the following strong Relationship 8 (r47c6, r5c5) = 9r5c5.

Full agreement with yzfwsf's statement.
I was just writing a similar draft !

[Sudtyro2]

Myth's CoALS rule:The number group A comes from the overlapping area, and the number group B comes from the non-overlapping area, then the numbers in A have a strong relationship with the numbers in B.
And you turn it into a strong relationship between A from the overlapping area and B from the non-overlapping area.
In fact, the strong relationship is for A and B in all cells of CoALS, not partitions. That is to say, the final solution 8 may not come from r4c6, and the strong relationship you wrote does not hold. Myth's CoALS rule can only provide the following strong Relationship 8 (r47c6, r5c5) = 9r5c5.

Thx, yzfwsf, for this amazing revelation! Just one request: Could you rewrite the CoALS Rule in general terms to reflect your findings? And how would that new Rule be applied to this particular puzzle?

Regards,
SteveC

PS. I may need another "vacation" much sooner than expected

[yzfwsf]

I don't think I proposed any new rules at all. I just repeated the CoALS Rule.
If you feel offended, please ignore my point of view. Best Regards.

[Sudtyro2]

I don't think I proposed any new rules at all. I just repeated the CoALS Rule.
If you feel offended, please ignore my point of view. Best Regards.

I'm certainly not offended, but rather feeling a bit ignorant...like exactly how you get only 8 (r47c6, r5c5) = 9r5c5 from CoALS Rule. On the other hand, I also think that JCO and Cenoman both already "got it". If anyone can further explain the details of the above logic, I would be most grateful!

Regards,
SteveC

[jco]

Hello,

That truth is a consequence of r5c5 being BVC. We don't need CoALS rule to infer it.
IMO the fact (from CoALS rule) that we have either 2 and 8 (somewhere) in the final structure OR 4 and 6 and 9 in the final structure (or both) does not give anything useful. It would be nice if a chain could be built from that available strong link, but unfortunately this does no seem possible here.

If r5c5 had more than 2 candidates (for instance, having 4 there too), then CoALS rule
is useful in order to show that (9)r5c5=(8)r47c6,r5c5, in the following way.
In this situation (no more BVC at r5c5), if 9 is not in the structure, then (469) is false, so
by CoAls rule, 2 and 8 must be there, so (8)r5c5,r7c6 => (8)r5c5,r6c47.
If (8)r5c5,r6c47 is not true, then (28) is not true in the structure, so again by CoALS rule
4,6 and 9 must be there, and this implies r5c5=9. This scenario being what yzfwsf and Cenoman
meant IMO.

Regards,
JCO

Edit: Deleted wrong explanation and then edited many times to improve the text for clarity.

[jco]

Hello,

Another way to reason, still in the more interesting situation that r5c5 is not just a BVC,
is to work with the idea of the proof of CoALS, instead of using the rule.
If 9 is false, then the ALS digits, that has it as a candidate, get locked and since 8 belongs to that
ALS (because 8 is in the intersection), it follows that 8 must be true in that ALS, and so
8 belongs to the combined ALSs.
If 8 is false for the combined ALSs, then the ALS digits, which have 9 as an candidate, also have 8 as
a candidate (8 being in the ALSs intersection), and so that digits are locked.
That implies that 9 is true in that ALS, so r5c5=9.

Regards,
JCO

Edit: I wrote this in another post because I had edited too many times the previous post.

[Sudtyro2]

Code: Select all

+--------------+-------------------+-----------------+
| 1   5   6    | 3    4      7     | 289  289   289  |
| 7   4   3    | 8    2      9     | 6    5     1    |
| 9   8   2    | 1    6      5     | 37   4     37   |
+--------------+-------------------+-----------------+
| 6   29  59   | 57   1    ab28    | 2389 23789 4    |
| 3   7   14   | 69  a9-8    2468  | 128  268   5    |
| 8   129 45   | 57   3     b46    | 129  67    29   |
+--------------+-------------------+-----------------+
| 5   139 179  | 69   789   b68    | 4    238   238  |
| 2   6   8    | 4    5      3     | 79   1     79   |
| 4   39  79   | 2    789    1     | 5    38    6    |
+--------------+-------------------+-----------------+

Perhaps this a good time to once again thank all for their helpful inputs to this posting. I realize now that my understanding of Myth's CoALS Rule was actually incomplete, as pointed out by both yzfwsf and Cenoman.

For this puzzle, I applied Myth's CoALS rule to my two overlapping ALS marked (a&b). Then, as illustrated in Myth's original posting's first three example grids, the rule states that the digits in the overlap cell(r4c6) are strongly linked to the digits in the non-overlap cells (r5c5,r67c6) that are NOT present in the overlap cell. This immediately and correctly gives us (82=469)r4c6,(r5c5,r67c6). However, the digits in the non-overlap cells are actually (4698)r5c5,r67c6. So, how is this handled? My interpretation was that the non-overlap 8s were to be ignored. However, Myth's later statement in his Rule's "proof " includes all digits in the entirety of the structure. I guess I misinterpreted the meaning of "entirety." In one case the 8s are excluded in defining the non-overlap digits. But in the next case the 8s are included in the "entirety." Unfortunately, I chose to apply the first case only. My bad!

Regards,
SteveC

[yzfwsf]

In other words, there is a strong relationship between the candidates that only appear in non overlapping cells and the remaining candidates.

[Cenoman]

Hi Steve,
I already told you in a previous post:
Happy to read you again in this forum !
I tell it again.
Happy also we are eventually in line for this puzzle.

We have missed you for seven long months, so when you write:

PS. I may need another "vacation" much sooner than expect

... I hope it was just a short moment of disappointment, and that you will not extend your silence another seven months

Please post on your nice CoALS, oddagon, 1-fish and other solutions !
Best regards.