The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |...|5..|.1.|
 |.1.|...|9..|
 |3..|..8|265|
 |---+---+---|
 |84.|...|...|
 |..6|..1|3..|
 |...|...|.82|
 |---+---+---|
 |279|8..|..1|
 |..1|...|.4.|
 |.6.|..9|...|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 67      8-2    a28     | 5      9      36     | 47     1      347   
 67      1       5      | 2346   2346   2346   | 9      37     8     
 3       9       4      | 17     17     8      | 2      6      5     
------------------------+----------------------+---------------------
 8       4       37-2   | 237    2357   2357   | 1      9      6     
 9      f25      6      | 247    8      1      | 3     e57     47     
 1       35      37     | 9      3467   3467   | 457    8      2     
------------------------+----------------------+---------------------
 2       7       9      | 8      3456   3456   | 56    d35     1     
 5       38      1      | 2367   2367   2367   | 678    4      9     
 4       6      b38     | 137    1357   9      | 578    2     c37     


(2=8)r1c3 - (8=3)r9c3 - r9c9 = (3-5)r7c8 = r5c8 - (5=2)r5c2 => -2 r1c2, r4c3; stte

Phil

[SpAce]

Code: Select all

.--------------.------------------.----------------.
| 67  28   28  | 5     9     36   | 47   1     347 |
| 67  1    5   | 2346  2346  2346 | 9    37    8   |
| 3   9    4   | 17    17    8    | 2    6     5   |
:--------------+------------------+----------------:
| 8   4    237 | 237   2357  2357 | 1    9     6   |
| 9   25   6   | 247   8     1    | 3   b57    47  |
| 1  d35   37  | 9     3467  3467 |c457  8     2   |
:--------------+------------------+----------------:
| 2   7    9   | 8     3456  3456 | 56  a(3)5  1   |
| 5  e38   1   | 2367  2367  2367 | 678  4     9   |
| 4   6  f(3)8 | 137   1357  9    | 578  2     7-3 |
'--------------'------------------'----------------'

W-Wing (35) with transport:

(3=5)r7c8 - r5c8 = r6c7 - (5=3)r6c2 - r8c2 = (3)r9c3 => -3 r9c9; stte

[Ngisa]

Code: Select all

+---------------------+------------------------+--------------------+
| 67     a28     b28  | 5        9        36   | 47      1      347 |
| 67      1       5   | 2346     2346     2346 | 9       37     8   |
| 3       9       4   | 17       17       8    | 2       6      5   |
+---------------------+------------------------+--------------------+
| 8       4      c237 |d237     d2357    d2357 | 1       9      6   |
| 9       25      6   |e247      8        1    | 3       57    f4*7 |
| 1       35     d37* | 9        3467     3467 |g457     8      2   |
+---------------------+------------------------+--------------------+
| 2       7       9   | 8        3456     3456 |h56     i35     1   |
| 5       3-8     1   | 2367     2367     2367 | 678     4      9   |
| 4       6      k38  | 137      1357     9    |h578     2     j37  |
+---------------------+------------------------+--------------------+


A net
(8=2)r1c2 - r1c3 = [(2)r4c3/(2-7)] - r4c456 = (2-4)r5c4 = (4*)r5c9
______________=(7*)r6c3 - (4*7*=5)r6c7 - r79c7 = (5-3)r7c8 = r9c9 - (3=8)r9c3 => - 8r8c2; stte

Clement

[SpAce]

A net
(8=2)r1c2 - r1c3 = [(2)r4c3/(2-7)] - r4c456 = (2-4)r5c4 = (4*)r5c9
______________=(7*)r6c3 - (4*7*=5)r6c7 - r79c7 = (5-3)r7c8 = r9c9 - (3=8)r9c3 => - 8r8c2; stte

Nice, I love nets! This one was a bit hard to read for me, though, so I redrew it for myself:

Code: Select all

(8=2)r1c2 - r1c3 = (2)r4c3 - r5c2 = (2-4)r5c4 = r5c9 - (4|7=5)r6c7 - r5c8 = (5-3)r7c8 = r9c9 - (3=8)r9c3
                    |                                     |
                   (7)r4c3 = r6c3 ------------------------

A matter of taste, of course, but that way it works easily backwards as well. Anyway, I think you should have a "|" in this node: (4*|7*=5)r6c7 to make it correct (something that I found unintuitive for a long time). Would you agree?

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 67    28    28    | 5     9     36    | 47    1     347   |
 | 67    1     5     | 2346  2346  2346  | 9     37    8     |
 | 3     9     4     | 17    17    8     | 2     6     5     |
 *-------------------+-------------------+-------------------|
 | 8     4     237   | 237   2357  2357  | 1     9     6     |
 | 9     25    6     | 247   8     1     | 3     57   d47    |
 | 1     5-3  e37    | 9     3467  3467  |e457   8     2     |
 *-------------------+-------------------+-------------------|
 | 2     7     9     | 8     3456  3456  |d56    35    1     |
 | 5   ab38    1     | 2367  2367  2367  |c678   4     9     |
 | 4     6    b8-3   | 137   1357  9     | 578   2    c37    |
 *-----------------------------------------------------------*


3r8c2 = (8r8c2)&(3r9c3) - (3|8=67)b9p49 - (6|7=45)r5c9,r7c7 - (4|5=37)r6c37 => -3 r6c2,r9c3 ; stte

[eleven]

Code: Select all

 *--------------------------------------------------------------*
 |  67   28   28    |  5      9      36     |  47    1    347   |
 |  67   1    5     |  2346   2346   2346   |  9     37   8     |
 |  3    9    4     |  17     17     8      |  2     6    5     |
 |------------------+-----------------------+-------------------|
 |  8    4    237   |  237    2357   2357   |  1     9    6     |
 |  9    25   6     |  247    8      1      |  3     57   47    |
 |  1   c35   37    |  9      3467   3467   |  47-5  8    2     |
 |------------------+-----------------------+-------------------|
 |  2    7    9     |  8      3456   3456   | a56    35   1     |
 |  5   c38   1     |  2367   2367   2367   | b6+78  4    9     |
 |  4    6   b38    |  137    1357   9      |  578   2   b37    |
 *--------------------------------------------------------------*

Almost xy-wing cells b.
(5=6)r7c7 - (6=8)r8c7,r9c38 - (8=5)r68c2 => -5r6c7, stte

[Ngisa]

A net
(8=2)r1c2 - r1c3 = [(2)r4c3/(2-7)] - r4c456 = (2-4)r5c4 = (4*)r5c9
______________=(7*)r6c3 - (4*7*=5)r6c7 - r79c7 = (5-3)r7c8 = r9c9 - (3=8)r9c3 => - 8r8c2; stte

Nice, I love nets! This one was a bit hard to read for me, though, so I redrew it for myself:

Code: Select all

(8=2)r1c2 - r1c3 = (2)r4c3 - r5c2 = (2-4)r5c4 = r5c9 - (4|7=5) - r5c8 = (5-3)r7c8 = r9c9 - (3=8)r9c3
                    |                                     |
                   (7)r4c3 = r6c3 ------------------------

A matter of taste, of course, but that way it works easily backwards as well. Anyway, I think you should have a "|" in this node: (4*|7*=5)r6c7 to make it correct (something that I found unintuitive for a long time). Would you agree?

No "|" is for an Unordered group in a box. Any way, I had a trouble in making it understandable. However,I have found that a net was not actually necessary, only an AIC: (8=2)r1c2 - r1c3 = r4c3 - (2=5)r5c2 - r5c8 = r6c7 -r79c7 = (5-3)r7c8 = r9c9 - (3=8)r9c3 => - 8r8c2; stte

[SpAce]

No "|" is for an Unordered group in a box.

Which dialect of AICs is that? In this forum "|" means OR and "&" means AND. If neither is explicitly used, AND is usually assumed. In ALS nodes and multi-digit cells it's an important distinction whether the digits are ANDed or ORed, and here you need an OR, I think. The reason is that the preceding weak link is really a logical NAND. Without the explicit "|" (OR), "&" (AND) is implied, and your chain translates into: if both 4r5c9 and 7r4c3 are true, then both 4r5c9 and 7r4c3 can't be true -- but one of them can, which breaks the intended logic because the following strong link no longer works.

What you really want to say is: if both 4r5c9 and 7r4c3 are true, then neither 4r6c7 nor 7r6c7 can be true (which implies that 5r6c7 must be true), and that requires the explicit "|". Another way to see it is that two digits can't both be true at the same time in a single cell, so they need an OR between them -- that's easy to see if you try to read your net backwards.

It's a subtle distinction, which took me a while to understand. Thankfully I got help, especially from eleven. I still make mistakes with this myself, and might have made one here as well, so anyone is free to chime in if I got something wrong.

Steve's chain is a good example of how it works:

3r8c2 = (8r8c2)&(3r9c3) - (3|8=67)b9p49 - (6|7=45)r5c9,r7c7 - (4|5=37)r6c37 => -3 r6c2,r9c3 ; stte

[Ngisa]

No "|" is for an Unordered group in a box.

Which dialect of AICs is that? In this forum "|" means OR and "&" means AND. If neither is explicitly used, AND is usually assumed. In ALS nodes and multi-digit cells it's an important distinction whether the digits are ANDed or ORed, and here you need an OR, I think. The reason is that the preceding weak link is really a logical NAND. Without the explicit "|" (OR), "&" (AND) is implied, and your chain translates into: if both 4r5c9 and 7r4c3 are true, then both 4r5c9 and 7r4c3 can't be true -- but one of them can, which breaks the intended logic because the following strong link no longer works.

What you really want to say is: if both 4r5c9 and 7r4c3 are true, then neither 4r6c7 nor 7r6c7 can be true (which implies that 5r6c7 must be true), and that requires the explicit "|". Another way to see it is that two digits can't both be true at the same time in a single cell, so they need an OR between them -- that's easy to see if you try to read your net backwards.

It's a subtle distinction, which took me a while to understand. Thankfully I got help, especially from eleven. I still make mistakes with this myself, and might have made one here as well, so anyone is free to chime in if I got something wrong.

Steve's chain is a good example of how it works:

3r8c2 = (8r8c2)&(3r9c3) - (3|8=67)b9p49 - (6|7=45)r5c9,r7c7 - (4|5=37)r6c37 => -3 r6c2,r9c3 ; stte

It is a dialect of Eureka notation. I use * to attract attention to the cells I am referring to.

[SpAce]

It is a dialect of Eureka notation. I use * to attract attention to the cells I am referring to.

I didn't mention the "*" so your point is lost on me. Never mind. Your sudoku logic was correct and your notation got understood, so all is well.

[rjamil]

Code: Select all

...5...1..1....9..3....826584.........6..13.........822798....1..1....4..6...9...
 +-----------+-----------------+----------------+
 | 67 28 28  | 5    9    (3)6  | 47  1    (3)47 |
 | 67 1  5   | 2346 2346 2346  | 9   (3)7 8     |
 | 3  9  4   | 17   17   8     | 2   6    5     |
 +-----------+-----------------+----------------+
 | 8  4  237 | 237  2357 2357  | 1   9    6     |
 | 9  25 6   | 247  8    1     | 3   57   47    |
 | 1  35 37  | 9    3467 3467  | 457 8    2     |
 +-----------+-----------------+----------------+
 | 2  7  9   | 8    3456 456-3 | 56  (3)5 1     |
 | 5  38 1   | 2367 2367 2367  | 678 4    9     |
 | 4  6  38  | 137  1357 9     | 578 2    37    |
 +-----------+-----------------+----------------+

2-String Kite: r1c69 & r27c8 => -3 @ r7c6; lclste

R. Jamil