The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |8..|754|...|
 |6.9|.1.|...|
 |...|...|..2|
 |---+---+---|
 |53.|4..|12.|
 |..2|...|7..|
 |.71|..9|.35|
 |---+---+---|
 |1..|...|...|
 |...|.7.|2.6|
 |...|391|..7|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *--------------------------------------------------*
 | 8    2    3    | 7    5    4    | 69   69   1    |
 | 6    4    9    | 2-8  1    23   | 5    7   e38   |
 | 7    1    5    | 9   a68   36   |d348  48   2    |
 *----------------+----------------+----------------|
 | 5    3    68   | 4   b68   7    | 1    2    9    |
 | 9    68   2    | 1    3    5    | 7    68   4    |
 | 4    7    1    |c68   2    9    |d68   3    5    |
 *----------------+----------------+----------------|
 | 1    58   7    | 26   4    26   | 389  589  38   |
 | 3    9    4    | 5    7    8    | 2    1    6    |
 | 2    568  68   | 3    9    1    |d48   458  7    |
 *--------------------------------------------------*


(8)r3c5 = r4c5 - (8=6)r6c4 - (6=348)r369c7 - (3=8)r2c9 => -8 r2c4 ; stte

After looking at Leren's, I realize that the first two terms in mine are unnecessary:

(8=6)r6c4 - (6=348)r369c7 - (3=8)r2c9 => -8 r2c4 ; stte

[Leren]

Code: Select all

*--------------------------------------------------------------*
| 8     2     3      | 7     5     4      | 69    69    1      |
| 6     4     9      |d28    1     23     | 5     7    e38     |
| 7     1     5      | 9     68    36     |f3-48  48    2      |
|--------------------+--------------------+--------------------|
| 5     3     68     | 4     68    7      | 1     2     9      |
| 9     68    2      | 1     3     5      | 7     68    4      |
| 4     7     1      |c68    2     9      |b68    3     5      |
|--------------------+--------------------+--------------------|
| 1     58    7      | 26    4     26     | 389   589   38     |
| 3     9     4      | 5     7     8      | 2     1     6      |
| 2     568   68     | 3     9     1      |a48    458   7      |
*--------------------------------------------------------------*

Embedded chains : (4=8) r9c7 [ - r6c7 = r6c4 - r2c4 = (8-3) r2c9 = (3) r3c7 ] = - 48 r3c7; stte

Leren

[tlanglet]

Code: Select all

 *--------------------------------------------------*
 | 8    2    3    | 7    5    4    | 69   69   1    |
 | 6    4    9    | 28   1    23   | 5    7    38   |
 | 7    1    5    | 9    68   36   | 348  48   2    |
 |----------------+----------------+----------------|
 | 5    3    68   | 4    68   7    | 1    2    9    |
 | 9    68   2    | 1    3    5    | 7    68   4    |
 | 4    7    1    | 68   2    9    | 68   3    5    |
 |----------------+----------------+----------------|
 | 1    58   7    | 26   4    26   | 389  589  38   |
 | 3    9    4    | 5    7    8    | 2    1    6    |
 | 2    568  68   | 3    9    1    | 48   458  7    |
 *--------------------------------------------------*


Almost "Simple coloring (8)" with extra 8r3c8

Coloring (8) => r2c4,r3c7,r4c5,r5c2,r6c7,r7c9,r9c3<>8
||
(8-4)r3c8=(4-5)r9c8=(5-9)r7c8=(9-3)r7c7=3r7c9-(3=8)r2c9 Contradiction => r3c8<>8

Ted

[daj95376]

Code: Select all

 *--------------------------------------------------*
 | 8    2    3    | 7    5    4    | 69   69   1    |
 | 6    4    9    | 28   1    23   | 5    7    38   |
 | 7    1    5    | 9    68   36   | 348  48   2    |
 |----------------+----------------+----------------|
 | 5    3    68   | 4    68   7    | 1    2    9    |
 | 9    68   2    | 1    3    5    | 7    68   4    |
 | 4    7    1    | 68   2    9    | 68   3    5    |
 |----------------+----------------+----------------|
 | 1    58   7    | 26   4    26   | 389  589  38   |
 | 3    9    4    | 5    7    8    | 2    1    6    |
 | 2    568  68   | 3    9    1    | 48   458  7    |
 *--------------------------------------------------*


Almost "Simple coloring (8)" with extra 8r3c8

Coloring (8) => r2c4,r3c7,r4c5,r5c2,r6c7,r7c9,r9c3<>8
||
(8-4)r3c8=(4-5)r9c8=(5-9)r7c8=(9-3)r7c7=3r7c9-(3=8)r2c9 Contradiction => r3c8<>8

Ted, I'm not picking on you. Your solution just happens to be the most recent example of a situation that bothers me.

I don't see why this should be considered a single step. The coloring on <8> has nothing in common with r3c8<>8 deduction. It could easily be viewed as two, independent steps w/o a contradiction or partitioning on <8>:

Code: Select all

Step 1:  (4)r3c8=(4-5)r9c8=(5-9)r7c8=(9-3)r7c7=3r7c9-(3=8)r2c9  =>  r3c8<>8

Step 2:  Coloring (8) => r2c4,r3c7,r4c5,r5c2,r6c7,r7c9,r9c3<>8


BTW: My favorite solution is a three-stepper that uses uniqueness:

Code: Select all

 +-----------------------+
 | 8 . . | 7 5 4 | . . . |
 | 6 . 9 | . 1 . | . . . |
 | . . . | . . . | . . 2 |
 |-------+-------+-------|
 | 5 3 . | 4 . . | 1 2 . |
 | . . 2 | . . . | 7 . . |
 | . 7 1 | . . 9 | . 3 5 |
 |-------+-------+-------|
 | 1 . . | . . . | . . . |
 | . . . | . 7 . | 2 . 6 |
 | . . . | 3 9 1 | . . 7 |
 +-----------------------+

 r1  b3  Naked  Pair                     <> 69   r3c78
 r7  b8  Naked  Pair                     <> 26   r7c2

 r39c78  <48> UR Type 6.2233             <> 8    r3c8,r9c7

 r79c28  <58> UR Type 6.2233             <> 8    r7c2,r9c8

         BUG+1                           =  8    r7c7


[tlanglet]

Code: Select all

 *--------------------------------------------------*
 | 8    2    3    | 7    5    4    | 69   69   1    |
 | 6    4    9    | 28   1    23   | 5    7    38   |
 | 7    1    5    | 9    68   36   | 348  48   2    |
 |----------------+----------------+----------------|
 | 5    3    68   | 4    68   7    | 1    2    9    |
 | 9    68   2    | 1    3    5    | 7    68   4    |
 | 4    7    1    | 68   2    9    | 68   3    5    |
 |----------------+----------------+----------------|
 | 1    58   7    | 26   4    26   | 389  589  38   |
 | 3    9    4    | 5    7    8    | 2    1    6    |
 | 2    568  68   | 3    9    1    | 48   458  7    |
 *--------------------------------------------------*


Almost "Simple coloring (8)" with extra 8r3c8

Coloring (8) => r2c4,r3c7,r4c5,r5c2,r6c7,r7c9,r9c3<>8
||
(8-4)r3c8=(4-5)r9c8=(5-9)r7c8=(9-3)r7c7=3r7c9-(3=8)r2c9 Contradiction => r3c8<>8

Ted, I'm not picking on you. Your solution just happens to be the most recent example of a situation that bothers me.

I don't see why this should be considered a single step. The coloring on <8> has nothing in common with r3c8<>8 deduction. It could easily be viewed as two, independent steps w/o a contradiction or partitioning on <8>:

Code: Select all

Step 1:  (4)r3c8=(4-5)r9c8=(5-9)r7c8=(9-3)r7c7=3r7c9-(3=8)r2c9  =>  r3c8<>8

Step 2:  Coloring (8) => r2c4,r3c7,r4c5,r5c2,r6c7,r7c9,r9c3<>8


BTW: My favorite solution is a three-stepper that uses uniqueness:

Code: Select all

 +-----------------------+
 | 8 . . | 7 5 4 | . . . |
 | 6 . 9 | . 1 . | . . . |
 | . . . | . . . | . . 2 |
 |-------+-------+-------|
 | 5 3 . | 4 . . | 1 2 . |
 | . . 2 | . . . | 7 . . |
 | . 7 1 | . . 9 | . 3 5 |
 |-------+-------+-------|
 | 1 . . | . . . | . . . |
 | . . . | . 7 . | 2 . 6 |
 | . . . | 3 9 1 | . . 7 |
 +-----------------------+

 r1  b3  Naked  Pair                     <> 69   r3c78
 r7  b8  Naked  Pair                     <> 26   r7c2

 r39c78  <48> UR Type 6.2233             <> 8    r3c8,r9c7

 r79c28  <58> UR Type 6.2233             <> 8    r7c2,r9c8

         BUG+1                           =  8    r7c7


Danny,
I believe we had this conversation before where I agreed that "almost" type solutions involving a contradiction are two steps solutions. I agree again. Hopefully, I have not posted anything that implies otherwise.

I look for solutions that are different than those already posted which, many times, results in almost type solutions that I think are interesting; otherwise I simply do not bother to post anything.

Ted

[Marty R.]

Code: Select all

+----------+----------+------------+
| 8 2   3  | 7  5  4  | 69  69  1  |
| 6 4   9  | 28 1  23 | 5   7   38 |
| 7 1   5  | 9  68 36 | 348 48  2  |
+----------+----------+------------+
| 5 3   68 | 4  68 7  | 1   2   9  |
| 9 68  2  | 1  3  5  | 7   68  4  |
| 4 7   1  | 68 2  9  | 68  3   5  |
+----------+----------+------------+
| 1 58  7  | 26 4  26 | 389 589 38 |
| 3 9   4  | 5  7  8  | 2   1   6  |
| 2 568 68 | 3  9  1  | 48  458 7  |
+----------+----------+------------+


Play this puzzle online at the Daily Sudoku site

This looked like a puzzle that I could find a one-stepper to in 30 seconds, but alas, I couldn't find one at all although there were several moves I could see.

1) Type 6 UR (48), r39c78=>r3c8,r9c7=4
2) Remote Pairs (68), (8=6)r3c5-r4c5=r6c4-(6=8)r6c7=>r3c7<>8

[daj95376]

Danny,
I believe we had this conversation before ...

Sorry Ted,

My swiss cheese memory let me down again.

Regards, Danny

[Marty R.]

I look for solutions that are different than those already posted which, many times, results in almost type solutions that I think are interesting; otherwise I simply do not bother to post anything.

Ted, I post a lot of duplicate solutions for no other purpose than providing feedback to Dan to let him know who's doing his puzzles.