The New Sudoku Players' Forum

[eleven]

bye

[StrmCkr]

When i look at your

whip[6]: r7c1{n3 n9} - r8n9{c3 c4} - c4n6{r8 r2} - c9n6{r2 r5} - r5n3{c9 c8} - r2c8{n3 .} ==> r4c1≠3

i don't see the link r8n9{c3 c4}, cause there is a 9 in r8c1.

You don't see the link because it is not a link but a CSP-Variable and its values content. In r8n9 (not in r8c1), the c1 (not the 9), i.e. n9r8c1, is t-candidate, linked to the previous right-linking one (n9r7c1).

When i replace it by c4n9{r7 r8} it would work for my understanding of your chains.

It works also with that way.

Then the chain uses 9 cells, 5 strong and 5 weak links. Additionally you need the hidden memory links 3r4c1-r5c12 and 6r2c4-r2c8.

There are neither strong nor weak links, let alone hidden ones. There are only csp-variables and links. There's no pure logic way of defining a rating based on the number of links (which amounts to counting the number of inferences in the mesozoic view of chains as networks of inferences).

My solution needs 7 cells, 3 strong and 2 weak links - and nothing hidden.

Nothing hidden? How do you count all the hidden "strong" and "weak" links inside the Subsets? If you count them, you have to add 2+3+4=9 "strong" links plus as many "weak" ones (and that is counting only 1 link for each base or cover set).

You don't count the internals as it's already noted in the strong link
a=b
All other information of internal cell interaction isn't used as its of set(j) set a has n candidate then set b doesn't

Aic don't have carry over information (csp) of what z truth means to placements of x in the following links. (hidden)

The metric for ours based on aics is easy
cell, strong links, weak links

Number of digits or interactions isn't measured.
path length and cell size only.

For our aics to match your chain the csp hidden cells are included the extras digit and all applicable cells at each link
makes for a bigger cell count and potentially extra strong weak links.
That's the point elevens mentioned over and over.

And it makes for absolute Clarity over having to know which of your chain classes use memory or don't.

[denis_berthier]

My solution needs 7 cells, 3 strong and 2 weak links - and nothing hidden.

Nothing hidden? How do you count all the hidden "strong" and "weak" links inside the Subsets? If you count them, you have to add 2+3+4=9 "strong" links plus as many "weak" ones (and that is counting only 1 link for each base or cover set).

You don't count the internals as it's already noted in the strong link
a=b
All other information of internal cell interaction isn't used as its of set(j) set a has n candidate then set b doesn't

Not counting the "internals", i.e. red the inner Subsets, is absurd. They have their own complexity and these should obviously be added when defining the global complexity of the chain.
They are not already counted in the "strong" links, which count only 1 whatever they link. What I say is instead of 1, it should be 2 for a Pair, 3 for a Tripet...
So, what's really added to the usual strong links count is 2-1=1 for a Pair, 3-1=2 for a swordfish...
This is old stuff (HLS, 2007).
That's the only way to have a consistent definition, between chains and Subsets (e.g. when a Pair can be considered as a Pair or as a bivalue-chain[2]).

[StrmCkr]

How do you find it absurd when the only data used is the interaction of. N through the subset?
When building the network and not how all other digits operate with in said sets.

What your saying would also then by all means should scale for using 3 of x digits, = 3 of x digits (grouped links)
Which uses the space of a sector 9 cells in which 2 of 3 mini sectors(3cells) are used.
Vs the space of a set of n cells with n+1 digits

All bivalves are Is 1 cell with 2 digits.

the metric is consistant as cell counts scale with n cell scaling at each strong link.
Total:
Cell count
Strong link
Weak links

Your argument for pairs is moot, as they are only usable as 2 distinct bivavle cells for the n cells. With n+1digit context rule for als.
Thus the applicable AIC chain is the Same as the bivavle Chain

[denis_berthier]

.
A bivalue-chain[2] requires 2 cells, like a Pair.
Anyone who has tried to implement ALS-chains knows that including a Quad is not the same thing as a mere candidate.

[StrmCkr]

hidden pair: {you can also swap 8 = 0 instead of 0 = 8 creating 2 more versions of the list below:4 WAYS TO VIEW IT)
(2)0=8(2) - (1)8=0(1)
Or
(1)0=8(1) - (2)8=0(2)

VS

Naked pair:( aKA als size 1 ) {you can also swap 8 for 0 and 0 for 8 creating 2 more versions of the list below: 4 WAYS TO VIEW IT)
(1)8=8(2) - (2)0=0(1)
Or
(2)8=8(1) - (1)0=0(2)


Compared to a single link has no meaning.
So let's make it have 2 links { x-wing} { this constructively also has 4 view points }

(1) r1c1= r1c9 (1) - (1)r4c9 =R4c1 (1)

{naked / hidden}
2 cells
2 strong links
1 weak link

x wing:
4 cells
2 strong links
1 weak link

metrically the x wing is harder to use as it has 2x the cells.

A.I.C with ALS components {n cells with n+1 digit}

isn't the same as:
als - chains: {these cant use a bi-local single digit that an AIC can}

Als A) n-cells with n+1 digits
ALS b) n-cells n+1 digits
AlS C .... >ALS xxx
where each als has 1 RC between the two so that the final ALS a = Als xxx and Z a mutual candidate in a & XXX can be eliminated for all cells seen by cells of a&xxx with z

Code: Select all

Anyone who has tried to implement ALS-chains knows that including a Quad is not the same thing as a mere candidate.

a quad isnt added directly to an aic chain what is added is:
3 cells with 4 digits
added to a set of
1 cell with 2 digits
the linkage is the same as adding 1 candidate as that's all its is doing A = B

Code: Select all

whip[6]: r7c1{n3 n9} - r8n9{c3 c4} - c4n6{r8 r2} - c9n6{r2 r5} - r5n3{c9 c8} - r2c8{n3 .} ==> r4c1≠3

Code: Select all

+---------------------+------------------+--------------------+
| 1       2      3    | 7      68    58  | 589  569    4      |
| 5       9      7    | 2(6)   2468  148 | 18   (36)   138(6) |
| 8       6      4    | 3      9     15  | 2    57     17     |
+---------------------+------------------+--------------------+
| 2-3     1358   6    | 4      7     9   | 158  235    138    |
| 47(3)   47(3)  19   | 8      5     2   | 19   67(3)  7(36)  | <----
| 279     578    259  | 1      3     6   | 4    2579   78     |
+---------------------+------------------+--------------------+
| (39)    35     8    | 59     1     7   | 6    4      2      |
| 247(9)  47     2(9) | 2(69)  2468  48  | 3    1      5      |
| 6       145    125  | 25     24    3   | 7    8      9      |
+---------------------+------------------+--------------------+


one of the problem converting this one to an aic is the
A = B for Row 5 digit 3

R5C34 = R6C89 there is no strong link for R6C89 to link to dead ending a normal aic chain.

instead we replace the R6C89 connection
with choices
: is 6 or isnt 6
R5C9 is 6 setting R5C8 as 3 which connects to a bivalve cell of 3/6 in R2C8 connecting to a bi local for digit 6.... {forms chain path}
R5C9 isnt 6 then R2C9 is 6 which connects to a bivalve cell for 3/6 in R2C8 & the same bi local seen by the bivalve cell {forms a chain path} of digit 6
which also means that R5C8 <> 3 thus R5C9 is 3.

i get that it works however its a directional chain and it cannot be reversed like an aic.
also don't get why this r8n9{c3 c4} isn't listing C1 when its part of the cells involved as a grouped link C13 -> C4
{ guessing you don't list as its automatically marked " off" by selecting the Col 1 as truth path when the next line search triggers.}
or
why R5C12 isnt listed as the other half of R5C89 as its the only part left on when the other 2 are off
which is what derives the eliminations it revealed.

the problem is most revealed herein
consider R2C8 is either 3 or a 6
on its own we can not use any of the chains listed to discern anything useful.

add some fun logic

IF 3 @ R5C12 is on then we know R4c1 <> 3
if 3 @ R5C12 is both off then we know R5C89 contains 3...

now we apply the logic of R2C8 is either 3 or 6 then the chain works

R5C12 = True
or R5C89 acts as a bi local choice

(6) R2C8 = R2C8 (3) - (3)R5C8 = R5C9(3) - (6)R5C9 = R2C9 (6) - (6) R2C4 = R8C4 (6) - (9)R8C4 = R8C13 (9) - (9) R7C1 (3)
|
(6) R2C4 = R8C4 (6) - (9)R8C4 = R8C13 (9) - (9) R7C1 (3)

thus
R4C1 <> 1

[Ngisa]

Code: Select all

+-------------------+-------------------+--------------------+
| 1      2      3   | 7     68     i58  | 589   569     4    |
| 5      9      7   | 26    2468    148 | 18    36      1368 |
| 8      6      4   | 3     9      i15  | 2     57     j17   |
+-------------------+-------------------+--------------------+
|e23    L1358   6   | 4     7       9   | 158  d235     138  |
| 347    347  ma1-9 | 8     5       2   |b19    367     367  |
| 279   k578    259 | 1     3       6   | 4    c2579   j78   |
+-------------------+-------------------+--------------------+
|e39     35     8   |f59    1       7   | 6     4       2    |
| 2479   47     29  |269    2468   h48  | 3     1       5    |
| 6      145    125 |f25   g24      3   | 7     8       9    |
+-------------------+-------------------+--------------------+


9r5c3 - (9)r5c7 = (9-2)r6c8 = r4c8 - (2=39)r47c1 - (9=52)r79cr79c4 - (2=4)r9c5 - (4=8)r8c6 - (8=51)r13c6 - (1=78)r36c9 - (8)r6c2 = (8-1)r4c2 = (1)r5c3 => - 9r5c3; stte

Clement