The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |1..|8.2|..3|
 |..2|.4.|7..|
 |.3.|.1.|.5.|
 |---+---+---|
 |5..|...|..1|
 |.17|...|39.|
 |3..|...|..4|
 |---+---+---|
 |.8.|.9.|.2.|
 |..5|.6.|4..|
 |9..|5.8|..7|
 *-----------*


Play/Print this puzzle online

[pjb]

Code: Select all

 1     a57     6      | 8      7-5    2      | 9      4      3     
 8      59     2      | 39     4      359    | 7      1      6     
b47     3      49     | 679    1      679    | 28     5      28     
 ---------------------+----------------------+---------------------
 5      269    489    | 2479   3      479    | 28     67     1     
c24     1      7      | 246   e58     456    | 3      9     d28     
 3      269    89     | 1279   78     179    | 5      67     4     
 ---------------------+----------------------+---------------------
 6      8      3      | 47     9      47     | 1      2      5     
 27     27     5      | 13     6      13     | 4      8      9     
 9      4      1      | 5      2      8      | 6      3      7     


(5=7)r1c2 - (7=4)r3c1 - (4=2)r5c1 - (2=8)r5c9 - (8=5)r5c5 => -5 r1c5; stte

Phil

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 1     57    6      | 8     57    2      | 9     4     3      |
| 8     59    2      | 39    4     359    | 7     1     6      |
| 47    3     49     | 679   1     679    | 28    5     28     |
|--------------------+--------------------+--------------------|
| 5     269  d89-4   | 2479  3     479    |c28    67    1      |
|a24    1     7      | 246   58    456    | 3     9    b28     |
| 3     269   89     | 1279  78    179    | 5     67    4      |
|--------------------+--------------------+--------------------|
| 6     8     3      | 47    9     47     | 1     2     5      |
| 27    27    5      | 13    6     13     | 4     8     9      |
| 9     4     1      | 5     2     8      | 6     3     7      |
*--------------------------------------------------------------*

H2 Wing: (4=2) r5c1 - r5c9 = (2-8) r4c7 = (8) r4c3 => - 4 r4c3; stte

Leren

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 1    c57    6     |  8   d57    2     | 9     4     3     |
 | 8     59    2     |  39   4    e359   | 7     1     6     |
 |b47    3     49    |  679  1     679   | 28    5     28    |
 *-------------------+-------------------+-------------------|
 | 5     269   489   |  2479 3     479   | 28    67    1     |
 |a24    1     7     | f246  58   f456   | 3     9     8-2   |
 | 3     269   89    |  1279 78    179   | 5     67    4     |
 *-------------------+-------------------+-------------------|
 | 6     8     3     |  47   9     47    | 1     2     5     |
 | 27    27    5     |  13   6     13    | 4     8     9     |
 | 9     4     1     |  5    2     8     | 6     3     7     |
 *-----------------------------------------------------------*


OK, let me try Danny's notation for a networking solution, except this one starts with a strong link:

(2=4*)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (*45=26)r5c46 => -2 r5c9 ; stte

[ArkieTech]

Code: Select all

 *-----------------------------------------------------------*
 | 1     5-7   6     | 8    a57    2     | 9     4     3     |
 | 8     59    2     | 39    4     359   | 7     1     6     |
 |c47    3     49    | 679   1     679   | 28    5     28    |
 |-------------------+-------------------+-------------------|
 | 5     269   489   | 2479  3     479   | 28    67    1     |
 |b24    1     7     | 246  b58    456   | 3     9    b28    |
 | 3     269   89    | 129-7 78    19-7  | 5     67    4     |
 |-------------------+-------------------+-------------------|
 | 6     8     3     | 47    9     47    | 1     2     5     |
 | 27    27    5     | 13    6     13    | 4     8     9     |
 | 9     4     1     | 5     2     8     | 6     3     7     |
 *-----------------------------------------------------------*
(7=5)r1c5-(5=4)r5c159-(4=7)r3c1 => -7r1c2,r3c46; ste

[daj95376]

Code: Select all

 *-----------------------------------------------------------*
 | 1    c57    6     |  8   d57    2     | 9     4     3     |
 | 8     59    2     |  39   4    e359   | 7     1     6     |
 |b47    3     49    |  679  1     679   | 28    5     28    |
 *-------------------+-------------------+-------------------|
 | 5     269   489   |  2479 3     479   | 28    67    1     |
 |a24    1     7     | f246  58   f456   | 3     9     8-2   |
 | 3     269   89    |  1279 78    179   | 5     67    4     |
 *-------------------+-------------------+-------------------|
 | 6     8     3     |  47   9     47    | 1     2     5     |
 | 27    27    5     |  13   6     13    | 4     8     9     |
 | 9     4     1     |  5    2     8     | 6     3     7     |
 *-----------------------------------------------------------*


OK, let me try Danny's notation for a networking solution, except this one starts with a strong link:

(2=4*)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (*45=26)r5c46 => -2 r5c9 ; stte

Steve, looks okay, but the network logic forces the user to pause and recall an earlier relationship on <4>. Not desirable ... unless necessary.

When I wrote my first solver, I inadvertantly included network logic in my chains() routine. I learned a lot about chains before writing my second solver. Now, let's consider turning your network expression into a chain.

What if you didn't remember that the <4> in r5c1 was set true and, thus, didn't remember that it forced <4> false in r5c46? You would then end up with <246> in cells r5c46 after "(5)r2c6 - (5)r5c6". However, you started off with <24> in r5c1 ... and can reuse it.

Code: Select all

(2=4)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (5=246)r5c146 => -2 r5c9 ; stte


You now have a chain that's easier for everyone to follow!

[tlanglet]

Code: Select all

 *-----------------------------------------------------------*
 | 1    c57    6     |  8   d57    2     | 9     4     3     |
 | 8     59    2     |  39   4    e359   | 7     1     6     |
 |b47    3     49    |  679  1     679   | 28    5     28    |
 *-------------------+-------------------+-------------------|
 | 5     269   489   |  2479 3     479   | 28    67    1     |
 |a24    1     7     | f246  58   f456   | 3     9     8-2   |
 | 3     269   89    |  1279 78    179   | 5     67    4     |
 *-------------------+-------------------+-------------------|
 | 6     8     3     |  47   9     47    | 1     2     5     |
 | 27    27    5     |  13   6     13    | 4     8     9     |
 | 9     4     1     |  5    2     8     | 6     3     7     |
 *-----------------------------------------------------------*


OK, let me try Danny's notation for a networking solution, except this one starts with a strong link:

(2=4*)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (*45=26)r5c46 => -2 r5c9 ; stte

Steve, looks okay, but the network logic forces the user to pause and recall an earlier relationship on <4>. Not desirable ... unless necessary.

When I wrote my first solver, I inadvertantly included network logic in my chains() routine. I learned a lot about chains before writing my second solver. Now, let's consider turning your network expression into a chain.

What if you didn't remember that the <4> in r5c1 was set true and, thus, didn't remember that it forced <4> false in r5c46? You would then end up with <246> in cells r5c46 after "(5)r2c6 - (5)r5c6". However, you started off with <24> in r5c1 ... and can reuse it.

Code: Select all

(2=4)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (5=246)r5c146 => -2 r5c9 ; stte


You now have a chain that's easier for everyone to follow!

Another view of this logic is to reverse the order of the chain.........

ANT(246=5)r5c146-5r2c6=5r1c5-(5=7)r1c2-(7=4)r3c1-(4=2)r5c1 => r5c9<>2

Ted

[Sudtyro2]

Another view of this logic is to reverse the order of the chain.........

ANT(246=5)r5c146-5r2c6=5r1c5-(5=7)r1c2-(7=4)r3c1-(4=2)r5c1 => r5c9<>2

Ted

Code: Select all

 *-----------------------------------------------------------*
 | 1    c57    6     |  8   d57    2     | 9     4     3     |
 | 8     59    2     |  39   4     359   | 7     1     6     |
 |b47    3     49    |  679  1     679   | 28    5     28    |
 *-------------------+-------------------+-------------------|
 | 5     269   489   |  2479 3     479   | 28    67    1     |
 |a24    1     7     |  246 e58    456   | 3     9     8-2   |
 | 3     269   89    |  1279 78    179   | 5     67    4     |
 *-------------------+-------------------+-------------------|
 | 6     8     3     |  47   9     47    | 1     2     5     |
 | 27    27    5     |  13   6     13    | 4     8     9     |
 | 9     4     1     |  5    2     8     | 6     3     7     |
 *-----------------------------------------------------------*

Or maybe a simple XY-Chain...

(2=4)r5c1-(4=7)r3c1-(7)r1c2=(7-5)r1c5=(5-8)r5c5=(8)r5c9 => r5c9<>2

[Marty R.]

Code: Select all

+------------+-------------+----------+
| 1  57  6   | 8    57 2   | 9  4  3  |
| 8  59  2   | 39   4  359 | 7  1  6  |
| 47 3   49  | 679  1  679 | 28 5  28 |
+------------+-------------+----------+
| 5  269 489 | 2479 3  479 | 28 67 1  |
| 24 1   7   | 246  58 456 | 3  9  28 |
| 3  269 89  | 1279 78 179 | 5  67 4  |
+------------+-------------+----------+
| 6  8   3   | 47   9  47  | 1  2  5  |
| 27 27  5   | 13   6  13  | 4  8  9  |
| 9  4   1   | 5    2  8   | 6  3  7  |
+------------+-------------+----------+


Play this puzzle online at the Daily Sudoku site

Potential DP 67-46-47, r357c46, using externals.

7r3c1=4r5c1-(4=7)r3c1=>r3c1=7

[daj95376]

Or maybe a simple XY-Chain...

(2=4)r5c1-(4=7)r3c1-(7)r1c2=(7-5)r1c5=(5-8)r5c5=(8)r5c9 => r5c9<>2

Sudtyro2: Your chain is correct, but it's not an XY-Chain. An XY-Chain is a sequence of bivalue cells containing a strong link within each cell and weak links between the cells. Example: Phil's post at the top of this thread.


Marty: Beautiful !


[Edit: Corrected personal reference. I thought SteveG48 had made the post.]

[SteveG48]

What if you didn't remember that the <4> in r5c1 was set true and, thus, didn't remember that it forced <4> false in r5c46? You would then end up with <246> in cells r5c46 after "(5)r2c6 - (5)r5c6". However, you started off with <24> in r5c1 ... and can reuse it.

Code: Select all

(2=4)r5c1 - (4=7)r3c1 - (7=5)r1c2 - r1c5 = r2c6 - (5=246)r5c146 => -2 r5c9 ; stte


You now have a chain that's easier for everyone to follow!

Wow!!!! Danny, if I'd come up with that on my own (not likely), I'd have thought that it would never be accepted. Then I look at it again and I can't see why I thought that. It just works. So at this point, would it be considered a networked solution or not? Apparently not.

Ted, Steve, thanks for your thoughts as well. If I'm not careful, I'm going to learn something from this.

[Sudtyro2]

Or maybe a simple XY-Chain...
(2=4)r5c1-(4=7)r3c1-(7)r1c2=(7-5)r1c5=(5-8)r5c5=(8)r5c9 => r5c9<>2

Steve: Your chain is correct, but it's not an XY-Chain. An XY-Chain is a sequence of bivalue cells containing a strong link within each cell and weak links between the cells. Example: Phil's post at the top of this thread.

Thx, Danny, for the correction! Would it be safe just to call it an AIC?

SteveC

[daj95376]

Thx, Danny, for the correction! Would it be safe just to call it an AIC?

_

Yes, it's an AIC w/o any network extensions.