## AHS-notation? (Nightmare Nov 25 2007)

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

### AHS-notation? (Nightmare Nov 25 2007)

I have another notation question, this time regarding chains containing AHS-nodes (I guess).

Puzzle: 001000009004008000030900080306100007040000030700009602050002090000600100200000700

Grid after basic solving:
Code: Select all
`+-----------------+---------------------+------------------+| 568  2678 1     | 23457 234567 34567  | 2345 567  9      || 569  2679 4     | 2357  123567 8      | 235  1567 1356   || 56   3    257   | 9     124567 14567  | 245  8    1456   |+-----------------+---------------------+------------------+| 3    289  6     | 1     28     45     | 89   45   7      || 1589 4    2589  | 2578  25678  567    | 589  3    158    || 7    18   58    | 3458  3458   9      | 6    145  2      |+-----------------+---------------------+------------------+| 16   5    378   | 3478  13478  2      | 348  9    3468   || 4    789  3789  | 6     35789  357    | 1    2    358    || 2    16  389    | 3458  134589 1345   | 7    56   34568  |+-----------------+---------------------+------------------+`

My steps and questions:

Hidden Text: Show
1) (1)r5c1=r5c9-(1=4=5)r46c8-(5=6)r9c8-(6=1)r9c2-r7c1=(1)r5c1 => 1r5c1
2) (8)r79c4=(89-5)r89c5=r8c9-(5=8)r5c9-r5c4=(8)r79c4 => 8r79c4
3) W-Wing: (2=7)r2c3-r7c3=r7c4-(7=2)r5c4 => -2 r5c3; stte

Mostly I'm interested in step 2 with the AHS node, but please let me know if you see other problems. A general question: what should I call steps 1 and 2 and similar chains that loop back to themselves? I guess one name for them would be Discontinuous Nice Loop Type 2 (ANS / Grouped AHS), but I don't see nice loop terms used here a lot (and they're awfully long too). Also, please correct my grid markings if they're not standard or otherwise correct. I'm trying to use those for the first time.

Step 2:
Code: Select all
`+---------------+--------------------------+-----------------+| 8   267 1     | 23457    234567     3467 | 2345 567 9      || 9   267 4     | 2357     23567      8    | 235  567 1      || 5   3   27    | 9        2467       1    | 24   8   46     |+---------------+--------------------------+-----------------+| 3   29  6     | 1        28         5    | 89   4   7      || 1   4   29    | e27-8    2678       67   | 589  3   d58    || 7   8   5     | 34       34         9    | 6    1   2      |+---------------+--------------------------+-----------------+| 6   5   378   | fa347+8  1          2    | 48   9   348    || 4   79  3789  | 6        b357(9-8)  37   | 1    2   c358   || 2   1   389   | fa345+8  b345(9-8)  34   | 7    56  34568  |+---------------+--------------------------+-----------------+`

(8)r79c4=(89-5)r89c5=r8c9-(5=8)r5c9-r5c4=(8)r79c4 => 8r79c4 (=> -8 r5c4, r89c5)

Is my notation for the AHS(?) node ok? Specifically, does it make sense backwards as well:

(8)r79c4=r5c4-(8=5)r5c9-r8c9=(5-98)r89c5=(8)r79c4 ?

That doesn't look quite right to me as the (5-98)r89c5 seems like both 9 and 8 were eliminated from those cells (but only 8 is eliminated from both). Can it still be interpreted correctly? Or is there a way to improve the notation to make it clearer both ways (but hopefully not much more complicated)? Is there something like JC's trick with ANS nodes (like seen in step 1)?
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2582
Joined: 22 May 2017

### Re: AHS-notation? (Nightmare Nov 25 2007)

In general :
1. The less the number of native constraints in a step, the best.
2. A step can eventually contain a derived constraint from another flightless or not step.

Therefore,

step 1 can be indifferently written as
[(1=4=5)r46c8-(5=6)r9c8-(6=1)r9c2]-1r6c2=1r5c1 [Internal = sign]
[1r6c8=NP(45)r46c8-(5=6)r9c8-(6=1)r9c2]-1r6c2=1r5c1
Code: Select all
` 1r6c8|4r6c8 5r6c8|      |4r4c8 5r4c8|             5r9c8 6r9c8 1r9c2             6r9c2  |  V-1r6c2`
ALS-XZ Rule[(1=4=5)r46c8-(5=6=1)r9c82]-1r6c2=1r5c1

step2, can be written as
[(8)r79c4=HP(89)r89c5-5r8c5=r8c9-(5=8)r5c9]-8r5c4=8r79c4-8r89c5 [External - sign]
Code: Select all
` 8r79c4|8r9c5 8r8c5|       |9r9c5 9r8c5|              5r8c5 5r8c9 8r5c9              5r5c9  |  V-8r5c4`
or
using the ALS(34578)b8p1679 -> 8r79c4==5r9c4 or NQ(3478)b8p1679=5r9c4 or 8r79c4=NQ(3457)b8p1679 or (8=347=5)b8p9617
W-Wing[(8=347=5)b8p9617-5r8c5=5r8c9-(5=8)r5c9]-8r5c4=8r79c4-8r89c5
Code: Select all
`|      3r9c6 4r9c6      ||      3r8c6       7r8c6||8r7c4 3r7c4 4r7c4 7r7c4||8r9c4 3r9c4 4r9c4      |5r9c4                         5r8c5 5r8c9 8r5c9                         5r5c9  |  V-8r5c4`
JC Van Hay

Posts: 719
Joined: 22 May 2010

### Re: AHS-notation? (Nightmare Nov 25 2007)

Thanks, JC! That was very instructive again!

JC Van Hay wrote:In general :
1. The less the number of native constraints in a step, the best.

I think I see what you mean but I also think "the best" is somewhat subjective. I personally prefer clarity over brevity. I do agree, however, that my first chain may be unnecessarily long, which is also bad for clarity. I just wrote it the way I found it without too much thinking. Its one benefit is that its logic should be pretty easy to follow even for an ALS-novice (because one wrote it). Still, I'd probably do it this way now (because the elimination has the same effect with a shorter chain):

(1=4=5)r46c8-(5=6)r9c9-(6=1)r9c2 => -1 r6c2

Of course it can also be seen as an ALS-XZ (or several) but I'm not very good at thinking in those terms. A chain is a chain, and it's much easier for me to see it as such instead of thinking of patterns and restricted common candidates and so on. But, if I do choose to view it as an ALS-XZ (or simply as a chain of two ALSs, which is more natural for me) isn't there at least two ways we can do it:

1) ANS-1: r46c8{145} and ANS-2: r9c28{156}, where the RCC is 5 and the chain is: (1=4=5)r46c8-(5=6=1)r9c82 (like you wrote it).

2) ANS-1: r469c8{1456} and ANS-2: r9c2{16}, where the RCC is 6 and the chain is: (1=45=6)r469c8-(6=1)r9c2

Have I understood that correctly? The problem with many ALS nodes and especially big ones is that it gets harder and harder to see what's going on just by reading the chain without seeing the grid (and even then it's sometimes hard). Simpler chains can be followed more easily in one's head, even if they have more nodes, because one can see the effects on cell level. That's why I tend to prefer chains with as few and small ALS nodes as possible, even if they're a bit longer. I bet they're more intuitive for a novice than ALS patterns anyway, but it may just be my own bias.

I haven't yet digested what you said about step 2.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2582
Joined: 22 May 2017