The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |4..|...|..2|
 |..8|.9.|3..|
 |.5.|...|.9.|
 |---+---+---|
 |.7.|...|.6.|
 |..4|7.2|8..|
 |5..|...|..1|
 |---+---+---|
 |...|4.8|...|
 |...|6.9|...|
 |..1|.7.|5..|
 *-----------*


Play/Print this puzzle online

[SpAce]

Code: Select all

.--------------.-----------.------------.
| 4   39  79+3 | 38  6  5  | 1   78  2  |
| 2   6   8    | 1   9  47 | 3   47  5  |
| 1   5   7-3  | 38  2  47 | 6   9   48 |
:--------------+-----------+------------:
| 39  7   29+3 | 5   8  1  | 24  6   34 |
| 6   1   4    | 7   3  2  | 8   5   9  |
| 5   8   2-3  | 9   4  6  | 7   23  1  |
:--------------+-----------+------------:
| 37  2   6    | 4   5  8  | 9   1   37 |
| 78  34  5    | 6   1  9  | 24  23  78 |
| 89  49  1    | 2   7  3  | 5   48  6  |
'--------------'-----------'------------'


BUG+2: (3)r14c3 => -3 r36c3; stte

[Ngisa]

Code: Select all

+-------------------+-----------------+------------------+
| 4      39     379 | 38     6     5  | 1      78     2  |
| 2      6      8   | 1      9     47 | 3      47     5  |
| 1      5     a37  | 38     2    a47 | 6      9     a48 |
+-------------------+-----------------+------------------+
|e39     7     f239 | 5      8     1  | 24     6      34 |
| 6      1      4   | 7      3     2  | 8      5      9  |
| 5      8     g2-3 | 9      4     6  | 7      23     1  |
+-------------------+-----------------+------------------+
| 37     2      6   | 4      5     8  | 9      1      37 |
| 78     34     5   | 6      1     9  | 24     23    b78 |
|d89     49     1   | 2      7     3  | 5     c48     6  |
+-------------------+-----------------+------------------+


(3=748)r3c369 - (8)r8c9 = r9c8 - (8=9)r9c1 - r4c1 = (9-2)r4c3 = (2)r6c3 => - 3r6c3; stte

Clement

[SteveG48]

Can't beat a BUG+2, but:

Code: Select all

.-------------.-----------.------------.
| 4   9-3 379 |c38  6  5  | 1  c78  2  |
| 2   6   8   | 1   9  47 | 3   47  5  |
| 1   5   37  | 38  2  47 | 6   9   48 |
:-------------+-----------+------------:
| 39  7   239 | 5   8  1  | 24  6   34 |
| 6   1   4   | 7   3  2  | 8   5   9  |
| 5   8   23  | 9   4  6  | 7   23  1  |
:-------------+-----------+------------:
| 37  2   6   | 4   5  8  | 9   1   37 |
| 78 a34  5   | 6   1  9  | 24  23  78 |
|a89 a49  1   | 2   7  3  | 5  b48  6  |
'-------------'-----------'------------'


(3=489)b7p578 - 8r9c8 = (38)r1c38 => -3r1c2 ; stte

[SpAce]

(3=748)r3c369 - (8)r8c9 = r9c8 - (8=9)r9c1 - r4c1 = (9-2)r4c3 = (2)r6c3 => - 3r6c3; stte

Hi Clement! That works nicely, but you could cut out some of the tail part:

(3=748)r3c369 - (8)r8c9 = r9c8 - (8=9)r9c1 - (9=3)r4c1 => -3 r46c3; stte

You could also shortcut to this:

(3=748)r3c369 - (8)r8c9 = (893)r894c1 => -3 r46c3; stte

[rjamil]

Code: Select all

4.......2..8.9.3...5.....9..7.....6...47.28..5.......1...4.8......6.9.....1.7.5..
 +-----------------+-------------+--------------+
 | 4     39  379   | 38    6  5  | 1   78  2    |
 | 2     6   8     | 1     9  47 | 3   47  5    |
 | 1     5   7-3   | (38)  2  47 | 6   9   (48) |
 +-----------------+-------------+--------------+
 | [3]9  7   2(3)9 | 5     8  1  | 24  6   (34) |
 | 6     1   4     | 7     3  2  | 8   5   9    |
 | 5     8   2[3]  | 9     4  6  | 7   23  1    |
 +-----------------+-------------+--------------+
 | 37    2   6     | 4     5  8  | 9   1   37   |
 | 78    34  5     | 6     1  9  | 24  23  78   |
 | 89    49  1     | 2     7  3  | 5   48  6    |
 +-----------------+-------------+--------------+

XY-Wing Transport: 348 @ r3c49 r4c9 ERI 3 @ b4r4c3 => -3 @ r3c3; stte

R. Jamil

[Sudtyro2]

Code: Select all

+--------------+--------------+--------------+
| 4  a39 a39-7 | b38  6   5   | 1   78  2    |
| 2   6   8    |  1   9   47  | 3   47  5    |
| 1   5  e37   | c38  2   47  | 6   9  c48   |
+--------------+--------------+--------------+
| 39  7   239  |  5   8   1   | 24  6  d34   |
| 6   1   4    |  7   3   2   | 8   5   9    |
| 5   8  e23   |  9   4   6   | 7  d23  1    |
+--------------+--------------+--------------+
| 37  2   6    |  4   5   8   | 9   1   37   |
| 78  34  5    |  6   1   9   | 24  23  78   |
| 89  49  1    |  2   7   3   | 5   48  6    |
+--------------+--------------+--------------+

AHP(39)r1c23 = 3r1c4 - (3=84)r3c49 - (4=32)b6p38 - (2=37)r36c3 => -7r1c3; stte

Added: Just curious...should a "pattern" and its "spoiler" be more properly linked as above with "=" or with "=="?

SteveC

[SpAce]

AHP(39)r1c23 = 3r1c4 - (3=84)r3c49 - (4=32)b6p38 - (2=37)r36c3 => -7r1c3; stte

Added: Just curious...should a "pattern" and its "spoiler" be more properly linked as above with "=" or with "=="?

Hi Steve! I think yours is fine as it is (in this regard; see below *) because it's a (sort of) native link. I'd reserve the "==" for derived strong links which require some sort of explanation, such as those between DP guardians, which explanation is usually given externally before the chain. The alternative is to inline the explanation between the two "=", like =UR= or =[UR]= (the latter being David's original style).

For example, my solution could (should?) have been written in any one of these ways:

BUG+2: (3)r1c3 == (3)r4c3 => -3 r36c3; stte

(3)r1c3 =BUG= (3)r4c3 => -3 r36c3; stte

(3)r1c3 =[BUG+2]= (3)r4c3 => -3 r36c3; stte

BUG+2: (3)r[1==4]c3 => -3 r36c3; stte (+ the same two variants)

A couple of real recent examples here and here. In both of those cases it was quite mandatory to mark (and explain) the special links, or they would be pretty hard to decipher. Here's one more with the inline variant, and below that Cenoman's much nicer solution with the normal one. You get the idea: mostly necessary with DPs; should be avoided with normal links to preserve its meaning.

The same principle holds for derived weak links but they're rarely seen.

----

* There's something else I'd change in your chain, though:

AHP(39)r1c23 = 3r1c4 ...

The "A" is actually incorrect because the link is between an HP (not almost-HP) and 3r1c4. Personally I'd leave out the "HP" too. I don't understand why hidden sets should be glorified any more than naked sets (**), even though many seem to do that. No one writes normal ALS nodes as NP(39) so why clutter these with unnecessary text?

Of course, the whole solution can be named "Almost Hidden Pair" or "AHP" if one wants to highlight the pattern, though. So, a couple of easy ways to fix your chain:

HP(39)r1c23 = 3r1c4 ... (my least favorite)

AHP: (39)r1c23 = 3r1c4 ... (no problem, as long as there's the colon and the space or it's on a separate line)

(39)r1c23 = 3r1c4 ... (my favorite)

** Just to clarify: I do prefer to see AHS solutions like yours (very nice!), but I just don't see any logical reason to treat them differently in the notation.

[Cenoman]

Added: Just curious...should a "pattern" and its "spoiler" be more properly linked as above with "=" or with "=="?

Hi Steve,
As a regular user of the '==' symbol, I have to break my decision to remain silent in notation discussions.
SpAce has already covered the subject extensively. I agree with almost every statement.
Only one slight difference, about the use of HP. I was once adviced (maybe by Leren ?) to reserve the use of HP in front of actual pairs, and to keep the (12) notation where a single instance of one digit is present in the AHP. Subtle nuance. Giving AHSs the same treatment as ALSs, mutatis mutandis, is also correct to me.

I reserve the '==' symbol to derived strong links, issued from deadly patterns, either uniqueness DPs, or solvability DPs (such as oddagons).
No need in your solution above, the extra candidate being in the same row as the HP.

In short: I reserve '==' to links between guardians.

[SpAce]

Only one slight difference, about the use of HP. I was once adviced (maybe by Leren ?) to reserve the use of HP in front of actual pairs, and to keep the (12) notation where a single instance of one digit is present in the AHP. Subtle nuance.

Not necessarily a bad nuance, but many subtleties tend to go unnoticed by casual observers and end up being misused, after which they lose their meaning. For example, I've missed this one, even though I'm not necessarily the worst case scenario about picking up such things. I still don't think it's necessary or overly helpful, as the logic works exactly the same in both cases. Nothing wrong with it either, though.

To me a slightly better distinction would be the way the pair (or other locked set) is being used. If its weak link is used against candidates within the set's own cells, then it's a classic hidden set operation (and I like those). It's true in Steve's chain, and in yours here as well. In those cases the HP-prefix makes the most sense, and perhaps provides some additional clarity, though it's still not necessary. However, what if we used Steve's pair for an external elimination instead:

(39)r1c23 = 3r1c4 - (3=84)r3c49 - (4=32)b6p38 - (2=3)r6c3 => -3 r3c3; stte

The pair is the same and both candidates are present, but would you now call it HP? Technically it is one, I guess, though it's behaving more like an NP (using an external weak link). (Never mind the fact that we don't need the 9 for anything and could simply use 3r1c23). A better example would be the other Steve's lovely mystery triple here which also spawned some related discussion. (Now that I look at it, it doesn't seem so mysterious at all, but I'm instead wondering why no one, including myself, suggested writing it as a quad (4582)r1c3467 and getting rid of one term).

Anyway, questions like that make accurate and consistent use of such prefixes difficult, so I think it's simpler to avoid them and think in terms of generic locked sets. Personally I like minimalism, so with any extra markings I must ask: 1) is it necessary for correctness or 2) does it significantly improve clarity. I come up negative with both in this case, though the latter is of course subjective.

Giving AHSs the same treatment as ALSs, mutatis mutandis, is also correct to me.

I'm also fine with both. Obviously there's nothing wrong with using the prefix when applicable, and I'm all for reasonable diversity. It'd be boring if everyone wrote their solutions exactly the same way. A bit of variety might also inspire new thinking and improvements.