The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |65.|...|42.|
 |3..|.75|...|
 |.72|...|...|
 |---+---+---|
 |7..|...|8..|
 |.18|6.4|73.|
 |..3|...|..2|
 |---+---+---|
 |...|...|35.|
 |...|45.|..1|
 |.35|...|.98|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 6       5       19       | 1389    1389    189      | 4       2       7        |
| 3     b48      14        | 2       7       5        | 19      168     69       |
|a89      7       2        | 19      4       6        | 5       18      3        |
|--------------------------+--------------------------+--------------------------|
| 7     c2469    469       | 1359    1239    129      | 8       146     569      |
| 25-9    1       8        | 6       29      4        | 7       3       59       |
| 5-9     46      3        | 15789   189     1789     | 19      46      2        |
|--------------------------+--------------------------+--------------------------|
| 1       26      7        | 89      2689    289      | 3       5       4        |
| 289   d2689    69        | 4       5       3        | 26      7       1        |
| 4       3       5        | 17      126     127      | 26      9       8        |
*--------------------------------------------------------------------------------*

M Wing (9=8)r3c1 - r2c2 = (8-9)r8c2 = r4c2 => r56c1 <9>

Leren

[SudoQ]

Another one:

Code: Select all

|-----------------|-------------------|--------------|
| 6     5     19  | 1389   1389  189  | 4   2    7   |
| 3     48    14  | 2      7     5    | 19  168  69  |
| 89    7     2   | 19     4     6    | 5   18   3   |
|-----------------|-------------------|--------------|
| 7    46(29) 469 | 1359   1239  129  | 8   146  569 |
| 259   1     8   | 6      29    4    | 7   3    59  |
| 59    46    3   | 15789  189   1789 | 19  46   2   |
|-----------------|-------------------|--------------|
| 1     (2)6   7  | 89     2689  289  | 3   5    4   |
|(8)9-2 (289)6 69 | 4      5     3    | 26  7    1   |
| 4      3     5  | 17     126   127  | 26  9    8   |
|-----------------|-------------------|--------------|

/SudoQ

[Marty R.]

M Wing (9=8)r3c1 - r2c2 = (8-9)r8c2 = r4c2 => r1c56 <9>

I think Leren meant his elimination to be typed as r56c1 rather than r1c56.

Code: Select all

+--------------+-----------------+------------+
| 6   5    19  | 1389  1389 189  | 4  2   7   |
| 3   48   14  | 2     7    5    | 19 168 69  |
| 89  7    2   | 19    4    6    | 5  18  3   |
+--------------+-----------------+------------+
| 7   2469 469 | 1359  1239 129  | 8  146 569 |
| 259 1    8   | 6     29   4    | 7  3   59  |
| 59  46   3   | 15789 189  1789 | 19 46  2   |
+--------------+-----------------+------------+
| 1   26   7   | 89    2689 289  | 3  5   4   |
| 289 2689 69  | 4     5    3    | 26 7   1   |
| 4   3    5   | 17    126  127  | 26 9   8   |
+--------------+-----------------+------------+


Play this puzzle online at the Daily Sudoku site

I used a chain to make the same eliminations as Leren.

(9=8)r3c1-(8=4)r2c2-(4=6)r6c2-(6=2)r7c2-(462=9)r4c2-->r56c1<>9. (Not sure about the last term in the notation).

[ArkieTech]

(9=8)r3c1-(8=4)r2c2-(4=6)r6c2-(6=2)r7c2-(462=9)r4c2-->r56c1<>9. (Not sure about the last term in the notation).

I would show it this way:

(9=8)r3c1-(8r2c2=9r4c2)als:r24678c2 => -9r56c1; stte

[Leren]

Marty R Wrote: I think Leren meant his elimination to be typed as r56c1 rather than r1c56.

Thanks for spotting that error Marty, I've edited the post accordingly.

Leren

[David P Bird]

The English language is full of redundancies and can still be understood if many of the letters are omitted – as witnessed by the texting styles of mobile phone users. Mobile phones have limited display space and small key pads, so there are good reasons for using abbreviations. However readers who are unaccustomed to a texter's style can struggle to make sense of their messages.

These justifications don't carry over to notating AICs on a computer screen though. The aim is to get the reader to accept that a chain of logic is valid. Having taken the effort to find the chain, surely it's worth the extra seconds it takes to ensure every notated node is indeed a stand-alone Boolean that can either be true or false. This also proves to be very useful when trying to verify to oneself that the logic followed is indeed water-tight.

In this case the Almost Locked Set in question consists of the three cells r4c23,r6c2 that must contain (4) and (6) and so can only hold one of (2) or (9). This is usually notated as (246=9)r4c23,r6c2
This signifies the two Booleans [these cells contain the triple (246)] and [(9) is true in one of these cells] that are strongly linked.
It could also be expressed the other way around (2=469)r4c23,r6c2.

This still requires that the reader verifies for himself that the linking cells see all instances of (2) in the ALS on one side and all instances of (9) on the other, but that's easier to do than working out the composition of an unspecified cell set.

[Marty R.]

The English language is full of redundancies and can still be understood if many of the letters are omitted – as witnessed by the texting styles of mobile phone users. Mobile phones have limited display space and small key pads, so there are good reasons for using abbreviations. However readers who are unaccustomed to a texter's style can struggle to make sense of their messages.

These justifications don't carry over to notating AICs on a computer screen though. The aim is to get the reader to accept that a chain of logic is valid. Having taken the effort to find the chain, surely it's worth the extra seconds it takes to ensure every notated node is indeed a stand-alone Boolean that can either be true or false. This also proves to be very useful when trying to verify to oneself that the logic followed is indeed water-tight.

In this case the Almost Locked Set in question consists of the three cells r4c23,r6c2 that must contain (4) and (6) and so can only hold one of (2) or (9). This is usually notated as (246=9)r4c23,r6c2
This signifies the two Booleans [these cells contain the triple (246)] and [(9) is true in one of these cells] that are strongly linked.
It could also be expressed the other way around (2=469)r4c23,r6c2.

This still requires that the reader verifies for himself that the linking cells see all instances of (2) in the ALS on one side and all instances of (9) on the other, but that's easier to do than working out the composition of an unspecified cell set.

David,

Thank you for your comments. As you've undoubtedly noticed, I'm a notation (and ALS) newbie. I don't understand why the ALS is in r4c23,r6c2. Would it also be valid to say the ALS is in r467c2?

[David P Bird]

Thank you for your comments. As you've undoubtedly noticed, I'm a notation (and ALS) newbie.

That's why I'm trying to show you, and whoever else will listen, to the path of righteousness.

I don't understand why the ALS is in r4c23,r6c2. Would it also be valid to say the ALS is in r467c2?

I too had trouble at the start which I remember well.

Here's your chain with the ALS fully specified as you suggest:

Code: Select all

+--------------+-----------------+------------+
| 6   5    19  | 1389  1389 189  | 4  2   7   |
| 3   48   14  | 2     7    5    | 19 168 69  |
| 89  7    2   | 19    4    6    | 5  18  3   |
+--------------+-----------------+------------+
| 7   2469 469 | 1359  1239 129  | 8  146 569 |
| 259 1    8   | 6     29   4    | 7  3   59  |
| 59  46   3   | 15789 189  1789 | 19 46  2   |
+--------------+-----------------+------------+
| 1   26   7   | 89    2689 289  | 3  5   4   |
| 289 2689 69  | 4     5    3    | 26 7   1   |
| 4   3    5   | 17    126  127  | 26 9   8   |
+--------------+-----------------+------------+

(9=8)r3c1 - (8=4)r2c2 - (4=6)r6c2 - (6=2)r7c2 – (462=9)r467c2

Now check that weak link into the ALS. The two Booleans are (2)r7c2 and the triplet(246)r467c2. As they are weakly linked it should be impossible for them both to be true together, but as (2)r7c2 is inside the ALS that inference doesn't hold. (See footnote 1.)

But your ALS is usable provided it is entered from an external cell:

(9=8)r3c1 - (8=4)r2c2 – (246=9)r467c2 => r56c1 <> 9.

Perhaps now you see why I assumed you were using the ALS in box 4.

Footnote 1
The validity of any "pure" AIC can tested by checking which nodes will be true and false firstly when the opening node is false reading left to right and secondly when the final node is false reading from right to left. This should then show that it's impossible for both end nodes to be false. The question to ask at each step is whether there are any circumstances that would allow two linked nodes both to be false for strong links, or true for weak links.

Footnote 2
Some more on notation!
1. Some redundancy in a notation assists readers to spot typing errors so should not be completely shunned.
2. White space between words in a sentence not only helps readers to absorb the contents but also to re-find their place again when they have been distracted. This should be noted considering that we expect our readers to check the grid quite frequently when reading our chains.

[Marty R.]

Thank you.