The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..2|9..|...|
 |8..|...|94.|
 |..7|...|.6.|
 |---+---+---|
 |.71|8.3|..5|
 |...|...|.3.|
 |..6|...|..2|
 |---+---+---|
 |.38|.96|4..|
 |...|..1|...|
 |79.|...|5..|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*--------------------------------------------------------------*
|a46    1     2      | 9     368  b48     | 7     5     38     |
| 8     5-6   3      | 267   267   257    | 9     4     1      |
| 9     45    7      |e13    138   45     | 2     6     38     |
|--------------------+--------------------+--------------------|
| 24    7     1      | 8     24    3      | 6     9     5      |
| 5    h28    9      | 1267  1267  27     | 18    3     4      |
| 3    g48    6      |f14    5     9      | 18    7     2      |
|--------------------+--------------------+--------------------|
| 1     3     8      | 5     9     6      | 4     2     7      |
| 2-6  i26    5      | 47    47    1      | 3     8     9      |
| 7     9     4      |d23    238  c28     | 5     1     6      |
*--------------------------------------------------------------*

xy chain: (6=4) r1c1 - (4=8) r1c6 - (8=2) r9c6 - (2=3) r9c4 - (3=1) r3c4 - (1=4) r6c4 - (4=8) r6c2 - (8=2) r5c2 - (2=6) r8c2 => -6 r2c2, r8c1; stte

Leren

[JC Van Hay]

Obsevations : The set of unsolved cells in B13467+R46 has only 2 solutions as it contains only bivalues.
Analysis : r1c1=4->r9c46=2, while r1c1=6->r9c6=8 and ste :=> 4r1c1 or 2r9c6 is false.
Interpretation :

Code: Select all

+--------------+------------------+-----------+
| 6-4  1     2 | 9     368   (48) | 7   5  38 |
| 8    56    3 | 267   267   257  | 9   4  1  |
| 9    5(4)  7 | (13)  138   5-4  | 2   6  38 |
+--------------+------------------+-----------+
| 24   7     1 | 8     24    3    | 6   9  5  |
| 5    28    9 | 1267  1267  27   | 18  3  4  |
| 3    8(4)  6 | (14)  5     9    | 18  7  2  |
+--------------+------------------+-----------+
| 1    3     8 | 5     9     6    | 4   2  7  |
| 26   26    5 | 47    47    1    | 3   8  9  |
| 7    9     4 | (23)  238   (28) | 5   1  6  |
+--------------+------------------+-----------+

Chain[6] : (4=82)r19c6-(2=314)r936c4-4r6c2=4r3c2 :=> -4r1c1.r3c6;ste
or

Code: Select all

+---------------+-------------------+-----------+
| 6(4)  1     2 | 9     368   (48)  | 7   5  38 |
| 8     56    3 | 267   267   257   | 9   4  1  |
| 9     5(4)  7 | (13)  138   45    | 2   6  38 |
+---------------+-------------------+-----------+
| 24    7     1 | 8     24    3     | 6   9  5  |
| 5     28    9 | 1267  1267  27    | 18  3  4  |
| 3     8(4)  6 | (14)  5     9     | 18  7  2  |
+---------------+-------------------+-----------+
| 1     3     8 | 5     9     6     | 4   2  7  |
| 26    26    5 | 47    47    1     | 3   8  9  |
| 7     9     4 | (23)  238   -2(8) | 5   1  6  |
+---------------+-------------------+-----------+

Chain[6] : 8r9c6=(8-4)r1c6=4r1c1-4r3c2=4r6c2-(4=132)r639c4 :=> -2r9c6;ste

[ArkieTech]

Code: Select all

 *-----------------------------------------------------------*
 | 46    1     2     | 9     368  b48    | 7     5     38    |
 | 8     56    3     | 267   267   257   | 9     4     1     |
 | 9    a45    7     |c13    138  b45    | 2     6     38    |
 |-------------------+-------------------+-------------------|
 | 24    7     1     | 8     24    3     | 6     9     5     |
 | 5     28    9     | 1267  1267  27    | 18    3     4     |
 | 3     8-4   6     |c14    5     9     | 18    7     2     |
 |-------------------+-------------------+-------------------|
 | 1     3     8     | 5     9     6     | 4     2     7     |
 | 26    26    5     | 47    47    1     | 3     8     9     |
 | 7     9     4     |c23    238  b28    | 5     1     6     |
 *-----------------------------------------------------------*
als xy-wing
(4=5)r3c2-(5=2)r139c6-(2=4)r369c4 => -4r6c2; ste

[daj95376]

Obsevations : The set of unsolved cells in B13467+R46 has only 2 solutions as it contains only bivalues.
Analysis : r1c1=4->r9c46=2, while r1c1=6->r9c6=8 and ste :=> 4r1c1 or 2r9c6 is false.
Interpretation :

Code: Select all

+--------------+------------------+-----------+
| 6-4  1     2 | 9     368   (48) | 7   5  38 |
| 8    56    3 | 267   267   257  | 9   4  1  |
| 9    5(4)  7 | (13)  138   5-4  | 2   6  38 |
+--------------+------------------+-----------+
| 24   7     1 | 8     24    3    | 6   9  5  |
| 5    28    9 | 1267  1267  27   | 18  3  4  |
| 3    8(4)  6 | (14)  5     9    | 18  7  2  |
+--------------+------------------+-----------+
| 1    3     8 | 5     9     6    | 4   2  7  |
| 26   26    5 | 47    47    1    | 3   8  9  |
| 7    9     4 | (23)  238   (28) | 5   1  6  |
+--------------+------------------+-----------+

Chain[6] : (4=82)r19c6-(2=314)r936c4-4r6c2=4r3c2 :=> -4r1c1.r3c6;ste
or

Code: Select all

+---------------+-------------------+-----------+
| 6(4)  1     2 | 9     368   (48)  | 7   5  38 |
| 8     56    3 | 267   267   257   | 9   4  1  |
| 9     5(4)  7 | (13)  138   45    | 2   6  38 |
+---------------+-------------------+-----------+
| 24    7     1 | 8     24    3     | 6   9  5  |
| 5     28    9 | 1267  1267  27    | 18  3  4  |
| 3     8(4)  6 | (14)  5     9     | 18  7  2  |
+---------------+-------------------+-----------+
| 1     3     8 | 5     9     6     | 4   2  7  |
| 26    26    5 | 47    47    1     | 3   8  9  |
| 7     9     4 | (23)  238   -2(8) | 5   1  6  |
+---------------+-------------------+-----------+

Chain[6] : 8r9c6=(8-4)r1c6=4r1c1-4r3c2=4r6c2-(4=132)r639c4 :=> -2r9c6;ste

Okay, I'll bite. How does your observation have anything to do with either of your solutions since they both need two bivalue cells in [b2] that aren't in your observation set.

Code: Select all

 r1c1=4 and [b1467]+[r46] resolved ... [b3] extraneous
 *--------------------------------------------------*
 | 4    1    2    | 9    368  8    | 7    5    38   |
 | 8    6    3    | 27   27   257  | 9    4    1    |
 | 9    5    7    | 3    138  4    | 2    6    38   |
 |----------------+----------------+----------------|
 | 2    7    1    | 8    4    3    | 6    9    5    |
 | 5    8    9    | 267  267  27   | 1    3    4    |
 | 3    4    6    | 1    5    9    | 8    7    2    |
 |----------------+----------------+----------------|
 | 1    3    8    | 5    9    6    | 4    2    7    |
 | 6    2    5    | 47   7    1    | 3    8    9    |
 | 7    9    4    | 23   238  28   | 5    1    6    |
 *--------------------------------------------------*


Code: Select all

 r1c1=6 and [b1467]+[r46] resolved ... [b3] extraneous
 *--------------------------------------------------*
 | 6    1    2    | 9    38   48   | 7    5    38   |
 | 8    5    3    | 267  67   27   | 9    4    1    |
 | 9    4    7    | 13   138  5    | 2    6    38   |
 |----------------+----------------+----------------|
 | 4    7    1    | 8    2    3    | 6    9    5    |
 | 5    2    9    | 167  167  7    | 8    3    4    |
 | 3    8    6    | 4    5    9    | 1    7    2    |
 |----------------+----------------+----------------|
 | 1    3    8    | 5    9    6    | 4    2    7    |
 | 2    6    5    | 7    47   1    | 3    8    9    |
 | 7    9    4    | 23   38   28   | 5    1    6    |
 *--------------------------------------------------*


I don't see any commonality. However, the second grid has a UR Type 1 that forces r3c5=1 and results in r3c4,r5c5<>1 ... as in the first grid. An equivalent chain:

Code: Select all

 (1=4)r6c4 - (4=2)r4c5 = (2=4)r4c1 - (4=6)r1c1 - (6)r1c5 =UR= (1)r3c5  =>  r3c4,r5c5<>1


[Marty R.]

Code: Select all

+---------+---------------+---------+
| 46 1  2 | 9    368  48  | 7  5 38 |
| 8  56 3 | 267  267  257 | 9  4 1  |
| 9  45 7 | 13   138  45  | 2  6 38 |
+---------+---------------+---------+
| 24 7  1 | 8    24   3   | 6  9 5  |
| 5  28 9 | 1267 1267 27  | 18 3 4  |
| 3  48 6 | 14   5    9   | 18 7 2  |
+---------+---------------+---------+
| 1  3  8 | 5    9    6   | 4  2 7  |
| 26 26 5 | 47   47   1   | 3  8 9  |
| 7  9  4 | 23   238  28  | 5  1 6  |
+---------+---------------+---------+


Play this puzzle online at the Daily Sudoku site

Type 3 UR 38 r13c59 external analysis c5: (3=8)r9c5

R9c5=3-(3=2)r9c4-(2=8)r9c6-(8=4)r1c6-r1c1=r3c2-(4=8)r6c2
R9c5=8-(8=2)r9c6-(2=3)r9c4-(3=1)r3c4-(1=4)r6c4-(4=8)r6c2=>r6c2=8

Is there a way to notate this in one string?

[David P Bird]

Marty, here's a straight AIC based on your UR:

(1=4)r6c4 - (4)r6c2 = (4)r3c2 - (4)r1c1 = (4-8)r1c6 = (38)r1c59 -[UR]- (38)r3c59 = (3)r3c4 => r3c4 <> 1

The blue characters are my way of indicating the weak link between the pairs (38)r1c59 & (38)r3c59 resulting from the UR pattern.

Using the disrupting candidates internal to the UR cells rather than the external ones:

(1=4)r6c4 - (4)r6c2 = (4)r3c2 - (4=6)r1c1 - (6=38)r1c59 -[UR]- (38=1)r3c59 => r3c4 <> 1

[Marty R.]

Thank you David. Unfortunately, that's a little complex for me and I don't think I could pull it off if faced with a similar situation.

[daj95376]

Code: Select all

+---------+---------------+---------+
| 46 1  2 | 9    368  48  | 7  5 38 |
| 8  56 3 | 267  267  257 | 9  4 1  |
| 9  45 7 | 13   138  45  | 2  6 38 |
+---------+---------------+---------+
| 24 7  1 | 8    24   3   | 6  9 5  |
| 5  28 9 | 1267 1267 27  | 18 3 4  |
| 3  48 6 | 14   5    9   | 18 7 2  |
+---------+---------------+---------+
| 1  3  8 | 5    9    6   | 4  2 7  |
| 26 26 5 | 47   47   1   | 3  8 9  |
| 7  9  4 | 23   238  28  | 5  1 6  |
+---------+---------------+---------+


Type 3 UR 38 r13c59 external analysis c5: (3=8)r9c5

R9c5=3-(3=2)r9c4-(2=8)r9c6-(8=4)r1c6-r1c1=r3c2-(4=8)r6c2
R9c5=8-(8=2)r9c6-(2=3)r9c4-(3=1)r3c4-(1=4)r6c4-(4=8)r6c2=>r6c2=8

Is there a way to notate this in one string?

Original forcing chain streams/lines:

Code: Select all

r9c5=3-(3=2)r9c4-(2=8)r9c6-(8=4)r1c6-r1c1=r3c2-(4=8)r6c2

r9c5=8-(8=2)r9c6-(2=3)r9c4-(3=1)r3c4-(1=4)r6c4-(4=8)r6c2=>r6c2=8


Write the first line as it would be read from r-to-l, and clean up the start of the second line:

Code: Select all

(8=4)r6c2-r3c2=r1c1-(4=8)r1c6-(8=2)r9c6-(2=3)r9c4-(3)r9c5

(8)r9c5-(8=2)r9c6-(2=3)r9c4-(3=1)r3c4-(1=4)r6c4-(4=8)r6c2=>r6c2=8


Combine the last term from the first line with the first term of the second line and include the reason:

Code: Select all

(8=4)r6c2-r3c2=r1c1-(4=8)r1c6-(8=2)r9c6-(2=3)r9c4-(3=ext_UR=8)r9c5 ...

 -(8=2)r9c6-(2=3)r9c4-(3=1)r3c4-(1=4)r6c4-(4=8)r6c2  =>  r6c2=8


Note: I normally don't include the conclusion in a discontinuous loop like this, but I did so for Marty.

[Leren]

Code: Select all

*--------------------------------------------------------------*
|a46    1     2      | 9     38-6  48     | 7     5     38     |
| 8     56    3      | 267  c267   257    | 9     4     1      |
| 9     45    7      | 13    138   45     | 2     6     38     |
|--------------------+--------------------+--------------------|
|a24    7     1      | 8    c24    3      | 6     9     5      |
| 5    b28    9      | 1267 c1267  27     |b18    3     4      |
| 3     48    6      | 14    5     9      | 18    7     2      |
|--------------------+--------------------+--------------------|
| 1     3     8      | 5     9     6      | 4     2     7      |
| 26    26    5      | 47   c47    1      | 3     8     9      |
| 7     9     4      | 23    238   28     | 5     1     6      |
*--------------------------------------------------------------*

als xy-wing: (6=2) r14c1 - (2=1) r5c27 - (1=6) r2458c5 => r1c5 <> 6; stte

Leren

[JC Van Hay]

How does your observation have anything to do with either of your solutions since they both need two bivalue cells in [b2] that aren't in your observation set.

Danny, sorry if my comments confused you.
The observation only gives me the best starting point of an analysis of the puzzle in order to find the next best elimination.
Therefore, the solutions are not interpretations of the observation, but of the subsequent analysis.
So you did to find your "equivalent chain"!
To be noted in your two diagrams : in the first (r1c1=4), 3r3c4->r9c4=2! and 8r4c6->r9c6=2! while in the second (r1c1=6), r1c6=8->r9c6=8.
Best Regards, JC.

[daj95376]

Danny, sorry if my comments confused you.
The observation only gives me the best starting point of an analysis of the puzzle in order to find the next best elimination.
Therefore, the solutions are not interpretations of the observation, but of the subsequent analysis.
So you did to find your "equivalent chain"!
To be noted in your two diagrams : in the first (r1c1=4), 3r3c4->r9c4=2! and 8r4c6->r9c6=2! while in the second (r1c1=6), r1c6=8->r9c6=8.

Okay, you were just indicating how you took advantage of the bivalue cells to set up links that led to a conclusion. Yes, I followed your conclusion.

Thanks for the explanation!

Regards, Danny