The New Sudoku Players' Forum

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 1     g689    7      | 69     269    5      | 4      3      28     |
 |b3-8    5      239    | 4      239  cd78     | 1      79     6      |
 | 4     g689   f239    |e37     12369 d178    | 5      79    e28     |
 *----------------------+----------------------+----------------------|
 | 2      4      6      | 1      7      3      | 9      8      5      |
 |a38     1-8    5      | 2      4      9      | 7      6      13     |
 | 9      7      13     | 5      8      6      | 2      4      13     |
 *----------------------+----------------------+----------------------|
 | 5      19     8      | 69     169    4      | 3      2      7      |
 | 7      3      4      | 8      5      2      | 6      1      9      |
 | 6      2      19     | 37     139    17     | 8      5      4      |
 *--------------------------------------------------------------------*


OK, I think I'm happy with it now, and it reads right in both directions.

8r5c1 = r2c1 - 8r2c6 = (HP(7&8))r23c6 - (7|8=2&3)r3c49 - (2|3=9)r3c3 - (9=6&8)r13c2 => -8 r2c1,r5c2 ; stte

[David P Bird]

Steve your first chain simply did not parse.

1) Whenever you notate a link you should ensure that it would be impossible for two weakly linked terms ever to be true together or two strongly linked terms ever to be false together. For example (8)r2c1 - (8)r239c6 is not a valid weak link as (8)r2c1 & (8)r3c6 can be true at the same time.

2) If you have an almost-almost naked set such as (2369=78)r3c2349, (2369) will be false if EITHER of (7) or (8) is true in the node. The next weak link must then ensure that it would make BOTH (7) and (8) false in the node, not just one of them. Reversing your chain for this puzzle, it would need (2369=78)r3c2349 - (78)r3c68.

I far prefer to use (2369=7|8) or (2369=78#1) to show the inference in an AANS because it helps prevent logical errors being made when composing a chain and makes the meaning clear to the improving players who read it.

Sorry I'm off to bed now and don't have time to inspect your latest one.

DPB
.

[SteveG48]

Dang!

Thanks, David. I thought I was getting it. Give me awhile to figure out what you just told me.

Wait. I think you were responding to my earlier offering, which I knew to be deficient. What about my latest, 2 minutes before yours?

Looks like we're crossing messages. Tomorrow, then. Thanks for your help.

[David P Bird]

8r5c1 = r2c1 - 8r2c6 = (HP(7&8))r23c6 - (7|8=2&3)r3c49 - (2|3=9)r3c3 - (9=6&8)r13c2 => -8 r2c1,r5c2 ; stte

I like your latest chain as it is very ingenious, but (8)r2c6 is a member of both terms connected by the red link. When (8)r2c6 is false two strong links are being followed a) (8=7)r2c6 and (8)r2c6 = (8)r3c6 to force (7,8)r2c6,r3c6. Now the next weak link (78)r23c6 - (7|8)r3c49 is dependent on that distribution because if the digits were swapped over it wouldn't be valid.

Ah! you say but they aren't swapped over! To which I stand on my high horse and tell you that every link in a Eureka AIC chain must be independent and stand on its own, but your chain is remembering what went on before.

Fortunately there is a way out of this by using a 'split' node.
(8)r5c1 = (8)r2c1 - (8)r2c6 = (7,8)HP:r2c6,r3c6 - (7|8=2&3)HP:r3c49 - (2|3=9)r3c3 - (9=6&8)HP:r13c2 => r2c1,r5c2 <>8; stte

The Boolean term (7,8)HP:r2c6,r3c6 is true when cells occupied by the digits match according to their listing orders and false otherwise. I have no problems with this because I believe that within reason we should be able to use any True/False condition we want in a chain provided it's clear what's needed to make it true. Others may differ however as split notes amount to concealed branching. That's true, but the branching involved will be no worse than what we accept in an ALS.

Note now that (8)r2c6 is no longer a possibility in two successive terms as it was before, which makes the chain far more digestible. Note too that the chain can be read backwards.

DPB.

TAGdpbSplitNodes

[JC Van Hay]

Steve's chain written as an exclusion matrix:

Code: Select all

+----------------------+--------------------+-------------+
| 1       (689)  7     | 69    269    5     | 4  3   28   |
| 3(-8)   5      239   | 4     239    (78)  | 1  79  6    |
| 4       (689)  (239) | (37)  12369  (178) | 5  79  (28) |
+----------------------+--------------------+-------------+
| 2       4      6     | 1     7      3     | 9  8   5    |
| -3(+8)  1-8    5     | 2     4      9     | 7  6   13   |
| 9       7      13    | 5     8      6     | 2  4   13   |
+----------------------+--------------------+-------------+
| 5       19     8     | 69    169    4     | 3  2   7    |
| 7       3      4     | 8     5      2     | 6  1   9    |
| 6       2      19    | 37    139    (17)  | 8  5   4    |
+----------------------+--------------------+-------------+
8r5c1 8r2c1
      8r2c6 7r2c6
            7r9c6 1r9c6
            7r3c6 1r3c6 8r3c6
                        8r3c9 2r3c9
            7r3c4                   3r3c4
                              2r3c3 3r3c3 9r3c3
                                          9r3c2 6r3c2 8r3c2
                                                6r1c2 8r1c2 :=> r2c1≠8, r5c2≠8, r5c1=8
or

+----------------------+--------------------+-------------+
| 1       (689)  7     | 69    269    5     | 4  3   28   |
| 3(-8)   5      239   | 4     239    (78)  | 1  79  6    |
| 4       (689)  (239) | (37)  12369  17(8) | 5  79  (28) |
+----------------------+--------------------+-------------+
| 2       4      6     | 1     7      3     | 9  8   5    |
| -3(+8)  1-8    5     | 2     4      9     | 7  6   13   |
| 9       7      13    | 5     8      6     | 2  4   13   |
+----------------------+--------------------+-------------+
| 5       19     8     | 69    169    4     | 3  2   7    |
| 7       3      4     | 8     5      2     | 6  1   9    |
| 6       2      19    | 37    139    17    | 8  5   4    |
+----------------------+--------------------+-------------+
8r5c1 8r2c1
      8r2c6 7r2c6
            ..... .....
            8r2c6 ..... 8r3c6
                        8r3c9 2r3c9
            7r3c4                   3r3c4
                              2r3c3 3r3c3 9r3c3
                                          9r3c2 6r3c2 8r3c2
                                                6r1c2 8r1c2 :=> r2c1≠8, r5c2≠8, r5c1=8


Advantages :

no need of symbols like - = | || & , ' [ ] ( ) { } * # $ ...
easy to learn, to read, to write, ...
readable from any constraint
easy to transform into any other notation
easy to check if it as an AIC of exclusion matrices
allows to find all the exclusions and placements from the same set of constraints
...

[SteveG48]

Thanks, all.

I really like JC's ingenious variant using the X-Y chain, but David's explanation is what I was really looking for: a way to write my own logic but do it right. One last question. David wrote:

(8)r5c1 = (8)r2c1 - (8)r2c6 = (7,8)HP:r2c6,r3c6 - (7|8=2&3)HP:r3c49 - (2|3=9)r3c3 - (9=6&8)HP:r13c2 => r2c1,r5c2 <>8; stte

Would it be equivalent (and correct) to write:

(8)r5c1 = (8)r2c1 - (8)r2c6 = [7r2c6]&[8r3c6] - (7|8=2&3)HPr3c49 - (2|3=9)r3c3 - (9=6&8)HP:r13c2 => r2c1,r5c2 <>8; stte ?

[David P Bird]

Would it be equivalent (and correct) to write:

(8)r5c1 = (8)r2c1 - (8)r2c6 = [7r2c6]&[8r3c6] - (7|8=2&3)HPr3c49 - (2|3=9)r3c3 - (9=6&8)HP:r13c2 => r2c1,r5c2 <>8; stte ?

When it comes to agreeing how to notate particular Booleans there are as many opinions as there are players. I'm obviously old school and am used to seeing digits in brackets followed by cells. Consequently I'll read chains which keep to that format quicker than those that don't. But any notation that is fairly intuitive and unambiguous, including your alternative, will work.

DPB
.

[SteveG48]

Thanks.

[DonM]

Steve's chain written as an exclusion matrix:

Code: Select all

+----------------------+--------------------+-------------+
| 1       (689)  7     | 69    269    5     | 4  3   28   |
| 3(-8)   5      239   | 4     239    (78)  | 1  79  6    |
| 4       (689)  (239) | (37)  12369  (178) | 5  79  (28) |
+----------------------+--------------------+-------------+
| 2       4      6     | 1     7      3     | 9  8   5    |
| -3(+8)  1-8    5     | 2     4      9     | 7  6   13   |
| 9       7      13    | 5     8      6     | 2  4   13   |
+----------------------+--------------------+-------------+
| 5       19     8     | 69    169    4     | 3  2   7    |
| 7       3      4     | 8     5      2     | 6  1   9    |
| 6       2      19    | 37    139    (17)  | 8  5   4    |
+----------------------+--------------------+-------------+
8r5c1 8r2c1
      8r2c6 7r2c6
            7r9c6 1r9c6
            7r3c6 1r3c6 8r3c6
                        8r3c9 2r3c9
            7r3c4                   3r3c4
                              2r3c3 3r3c3 9r3c3
                                          9r3c2 6r3c2 8r3c2
                                                6r1c2 8r1c2 :=> r2c1≠8, r5c2≠8, r5c1=8
or

+----------------------+--------------------+-------------+
| 1       (689)  7     | 69    269    5     | 4  3   28   |
| 3(-8)   5      239   | 4     239    (78)  | 1  79  6    |
| 4       (689)  (239) | (37)  12369  17(8) | 5  79  (28) |
+----------------------+--------------------+-------------+
| 2       4      6     | 1     7      3     | 9  8   5    |
| -3(+8)  1-8    5     | 2     4      9     | 7  6   13   |
| 9       7      13    | 5     8      6     | 2  4   13   |
+----------------------+--------------------+-------------+
| 5       19     8     | 69    169    4     | 3  2   7    |
| 7       3      4     | 8     5      2     | 6  1   9    |
| 6       2      19    | 37    139    17    | 8  5   4    |
+----------------------+--------------------+-------------+
8r5c1 8r2c1
      8r2c6 7r2c6
            ..... .....
            8r2c6 ..... 8r3c6
                        8r3c9 2r3c9
            7r3c4                   3r3c4
                              2r3c3 3r3c3 9r3c3
                                          9r3c2 6r3c2 8r3c2
                                                6r1c2 8r1c2 :=> r2c1≠8, r5c2≠8, r5c1=8


Advantages :

no need of symbols like - = | || & , ' [ ] ( ) { } * # $ ...
easy to learn, to read, to write, ...
readable from any constraint
easy to transform into any other notation
easy to check if it as an AIC of exclusion matrices
allows to find all the exclusions and placements from the same set of constraints
...

Disadvantage:
It makes my brain hurt.

[ronk]

Code: Select all

+----------------------+--------------------+-------------+
| 1       (689)  7     | 69    269    5     | 4  3   28   |
| 3(-8)   5      239   | 4     239    (78)  | 1  79  6    |
| 4       (689)  (239) | (37)  12369  17(8) | 5  79  (28) |
+----------------------+--------------------+-------------+
| 2       4      6     | 1     7      3     | 9  8   5    |
| -3(+8)  1-8    5     | 2     4      9     | 7  6   13   |
| 9       7      13    | 5     8      6     | 2  4   13   |
+----------------------+--------------------+-------------+
| 5       19     8     | 69    169    4     | 3  2   7    |
| 7       3      4     | 8     5      2     | 6  1   9    |
| 6       2      19    | 37    139    17    | 8  5   4    |
+----------------------+--------------------+-------------+
8r5c1 8r2c1
      8r2c6 7r2c6
            ..... .....
            8r2c6 ..... 8r3c6
                        8r3c9 2r3c9
            7r3c4                   3r3c4
                              2r3c3 3r3c3 9r3c3
                                          9r3c2 6r3c2 8r3c2
                                                6r1c2 8r1c2 :=> r2c1≠8, r5c2≠8, r5c1=8

Advantages :

no need of symbols like - = | || & , ' [ ] ( ) { } * # $ ...
easy to learn, to read, to write, ...
readable from any constraint
easy to transform into any other notation
easy to check if it as an AIC of exclusion matrices
allows to find all the exclusions and placements from the same set of constraints
...

Disadvantage:
It makes my brain hurt.

With a little help from some software:

Code: Select all

     (8r2)  (8r3)  (7b2)  (2r3)  (3r3)  (9b1)  (6b1)
    +(8b1)
2N6: 8r2c6A========7r2c6                                     
       |             |                                       
8B2: 8r2c6A=8r3c6    |                                       
              |      |                                       
3N4:          |    7r3c4=========3r3c4                       
              |                    |                         
3N9:        8r3c9=========2r3c9    |                         
                            |      |                         
3N3:                      2r3c3==3r3c3==9r3c3               
                                          |                 
3N2: 8r3c2==============================9r3c2==6r3c2 
       |                                  |      |   
1N2: 8r1c2==============================9r1c2==6r1c2

                                                             
  (8)r2c6 = (68)r13c2  ==> r2c1<>8

It's also easy to see David P Bird's "split nodes" for derived strong inference 8r2c6 = 9r3c3. But all this requires a bit too much work for my taste. I'd rather just use this 3-line Kraken cell form of notation?

Code: Select all

9r3c3 - (9=68)r13c2
 ||
3r3c3 - (3=7)r3c4 - (7=8)r2c6
 ||
2r3c3 - (2=8)r3c9 - 8r3c6 = (8)r2c6 ==> r2c1<>8