The New Sudoku Players' Forum

[ixsetf]

This is my first attempt at making a sudoku puzzle, please provide feedback wherever possible.

Code: Select all

 *-----------*
 |.2.|6..|.7.|
 |..6|..7|...|
 |7.9|...|.35|
 |---+---+---|
 |8.2|.13|...|
 |..5|..6|1..|
 |..1|..5|.92|
 |---+---+---|
 |6..|8.4|9..|
 |...|.6.|...|
 |.1.|...|.8.|
 *-----------*


Play it online.

[ArkieTech]

Puzzle was a little too complex for me. Did you solve it?

here is my attempt -- someone will likely find a simpler route.

Code: Select all

 *-----------*
 |.2.|6..|.7.|
 |..6|..7|...|
 |7.9|...|.35|
 |---+---+---|
 |8.2|.13|...|
 |..5|..6|1..|
 |..1|..5|.92|
 |---+---+---|
 |6..|8.4|9..|
 |...|.6.|...|
 |.1.|...|.8.|
 *-----------*

a long chain proves 8r8c3
w-wing sets 3r1c3
another chain sets 4r8c9
another chain sets 8r3c2 and 4r3c5
another chain sets 2r5c4
an xy-chain sets 9r1c9
w-wing sets 2r9c1
 *--------------------------------------------------*
 | 1    2    3    | 6    5    8    | 4    7    9    |
 | 45   45   6    | 39   39   7    | 28   12   18   |
 | 7    8    9    | 1    4    2    | 6    3    5    |
 |----------------+----------------+----------------|
 | 8    49   2    | 49   1    3    | 5    6    7    |
 | 39   7    5    | 2    89   6    | 1    4    38   |
 | 34   6    1    | 47  *78   5    |*38   9    2    |
 |----------------+----------------+----------------|
 | 6    35   7    | 8    2    4    | 9    15   13   |
 | 59   359  8    | 37   6    1    | 237  25   4    |
 | 2    1    4    | 5    3-7  9    |*37   8    6    |
 *--------------------------------------------------*
an xy-wing finishes it off


[ixsetf]

I used http://www.sudokuwiki.org/sudoku.htm to make sure that my puzzle remained valid and non-trivial as I was building it. So I ended up spoiling myself a bit with the solution.

[SteveG48]

I wouldn't want to run into it in a dark alley!

[Leren]

I was about as (un)successful as Dan. My best attempt had 7 non-basic moves, the longest chains having 4 Strong links :

1. H3 Wing => - 4 r2c9
2. H2 Wing =>- 4 r1c3
3. 3/4 SIS AIC => - 34 r9c3
4. M Wing Type 7B => - 5 r8c4
5. 4 SIS AIC => - 3 r7c3
6. 4 SIS AIC => - 5 r7c5
7. H2 Wing => - 3 r6c7; stte

Code: Select all

*--------------------------------------------------------------*
| 145   2     38     | 6     3459  89     | 48    7     1489   |
| 145   3458  6      | 3459  3459  7      | 248   12    189    |
| 7     48    9      | 124   24    128    | 6     3     5      |
|--------------------+--------------------+--------------------|
| 8     49    2      | 49    1     3      | 5     6     7      |
| 39    7     5      | 29    289   6      | 1     4     38     |
| 34    6     1      | 47   c478   5      |d8-3   9     2      |
|--------------------+--------------------+--------------------|
| 6     35    7      | 8     23    4      | 9     125   13     |
| 259   3589  38     | 12379 6     129    | 2347  25    34     |
| 29    1     4      | 357  b357   29     |a37    8     6      |
*--------------------------------------------------------------*

The PM shows the last move.

Leren

[Leren]

Just for fun I brought out the heavy artillery and reduced the solution to 4 non-basic moves:

1. W Wing (48) r1c7 + r3c2 Grouped S/L on 8 Row 2 => - 4 r1c13;
2. Forcing Chain Contradiction in Column 6 Digit 8 => - 5 r1c1;
3. Forcing Chain Contradiction in Row 6 Digit 3 => - 9 r1c6;
4. Forcing Chain Contradiction in Row 9 Digit 3 => - 5 r2c1; stte

Code: Select all

*--------------------------------------------------------------*
| 1     2     3      | 6     5     8      | 4     7     9      |
|a4-5aA 45    6      | 39    39    7      | 28    12    18     |
| 7     8     9      | 124   24    12     | 6     3     5      |
|--------------------+--------------------+--------------------|
| 8     49    2      | 49    1     3      | 5     6     7      |
| 39    7     5      | 29    289   6      | 1     4     38     |
| 34bB  6     1      | 47c   478d  5      | 38C   9     2      |
|--------------------+--------------------+--------------------|
| 6     35    7      | 8     23    4      | 9     125   13     |
| 259   359   8      | 12357 6     129    | 237   25    4      |
|b259   1     4      |c2357  237e  29     | 237D  8     6      |
*--------------------------------------------------------------*

Forcing Chain Contradiction in Row 9 Digit 3:

5r2c1 - 5r9c1                              = (5-3) r9c4
5r2c1 - 4r2c1 = 4r6c1 - (4=7) r6c4 - 7r6c5 = (7-3) r9c5
5r2c1 - 4r2c1 = (4-3) r6c1 = 3r6c7            - 3  r9c7.

I've documented the 4th move in the PM.

Leren

[daj95376]

_

Normally, my solver would take several steps to resolve your puzzle. However, there is a two-step solution.

Code: Select all

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

 after basics
 +--------------------------------------------------------------------------------+
 |  145     2       348     |  6       3459    89      |  48      7       1489    |
 |  145     3458    6       |  3459    3459    7       |  248     12      1489    |
 |  7       48      9       |  124     24      128     |  6       3       5       |
 |--------------------------+--------------------------+--------------------------|
 |  8       49      2       |  49      1       3       |  5       6       7       |
 |  39      7       5       |  29      289     6       |  1       4       38      |
 |  34      6       1       |  47      478     5       |  38      9       2       |
 |--------------------------+--------------------------+--------------------------|
 |  6       35      37      |  8       2357    4       |  9       125     13      |
 |  2459    34589   3478    |  123579  6       129     |  2347    25      34      |
 |  2459    1       347     |  23579   23579   29      |  2347    8       6       |
 +--------------------------------------------------------------------------------+
 # 94 eliminations remain

 (3=9)r1c367 - (9=2)r9c6 - (2=1)r7c2359 - (1=489)r1c679  =>  -48 r1c3

 after more basics
 +--------------------------------------------------------------------------------+
 |  145     2       3       |  6       459     89      |  48      7       1489    |
 |  145     458     6       |  3459    3459    7       |  248     12      1489    |
 |  7       48      9       |  124     24      128     |  6       3       5       |
 |--------------------------+--------------------------+--------------------------|
 |  8       49      2       |  49      1       3       |  5       6       7       |
 |  39      7       5       |  29      289     6       |  1       4       38      |
 |  34      6       1       |  47      478     5       |  38      9       2       |
 |--------------------------+--------------------------+--------------------------|
 |  6       35      7       |  8       235     4       |  9       125     13      |
 |  259     359     8       |  123579  6       129     |  2347    25      34      |
 |  259     1       4       |  23579   23579   29      |  237     8       6       |
 +--------------------------------------------------------------------------------+
 # 78 eliminations remain

 (3=4)r6c1 - (4=15)r12c1 - (5=29)r9c16
              ||                        \
           - (4=7)r6c4 - r6c5 = (7)r9c5  - (27=3)r9c7  =>  -3 r6c8


[Edit: upgraded network step.]

[Leren]

I've now managed to get a solution in 2 non-basic moves:

1. Forcing Chain Contradiction in Row 5 Digit 9:

Code: Select all

1r2c1 - 1r2c8 = 1r7c8 - (1=3) r7c9 - 3r5c9                = (3-9) r5c1;
1r2c1 - (1=2) r2c8 - 2r7c8 = 2r7c5 - 2r5c5                = (2-9) r5c4;
1r2c1 - (1=2) r2c8 - 2r7c8 = 2r7c5 - (2=4) r3c5 - (4=9) r1c5 - 9  r5c5; => - 1 r2c1

2. Forcing Chain Contradiction in Row 9 Digit 3 (same as the 4th move in my previous attempt) :

Code: Select all

5r2c1 - 5r9c1                              = (5-3) r9c4;
5r2c1 - 4r2c1 = 4r6c1 - (4=7) r6c4 - 7r6c5 = (7-3) r9c5;
5r2c1 - 4r2c1 = (4-3) r6c1 = 3r6c7            - 3  r9c7; => - 5 r2c1; stte

When will the fun ever stop !

Leren

[JC Van Hay]

How is it possible to resist the call of the cell r7c8

So, the simplest "solution" : 8 Singles; r7c8=1or2->contradiction :=> r7c8=5; ste.

OR

Code: Select all

+--------------------+----------------------+----------------------+
| 1345   2      348  | 6       34589    189 | 48       7      1489 |
| 1345   3458   6    | 123459  234589   7   | 248      12     1489 |
| 7      48     9    | 124     248      128 | 6        3      5    |
+--------------------+----------------------+----------------------+
| 8      49     2    | 49      1        3   | 5        6      7    |
| 39     7      5    | 29      289      6   | 1        4      38   |
| 34     6      1    | 47      4(78)    5   | (38)     9      2    |
+--------------------+----------------------+----------------------+
| 6      35     37   | 8       35(27)   4   | 9        15(2)  13   |
| 23459  34589  3478 | 123579  6        129 | 4-2(37)  125    134  |
| 23459  1      347  | 23579   2359(7)  29  | 24(37)   8      6    |
+--------------------+----------------------+----------------------+


#1a. Kraken 7C5 :=> [HP(37)r89c7==2r7c8==7r8c7]-2r8c7

7r6c5-8r6c5=(8-3)r6c7=HP(37)r89c7
||
7r7c5-2r7c5=2r7c8
||
7r9c5-7r9c7=7r8c7

Code: Select all

+----------------------+-------------------------+--------------------+
| 1345     2      348  | 6         34589   189   | 48    7       1489 |
| 1345     3458   6    | 123459    234589  7     | 248   12      1489 |
| 7        48     9    | 124       248     128   | 6     3       5    |
+----------------------+-------------------------+--------------------+
| 8        49     2    | 49        1       3     | 5     6       7    |
| (39)     7      5    | 29        289     6     | 1     4       8(3) |
| 34       6      1    | 47        478     5     | 38    9       2    |
+----------------------+-------------------------+--------------------+
| 6        35     37   | 8         357(2)  4     | 9     -1(25)  (13) |
| 345(29)  34589  3478 | 13579(2)  6       19(2) | 347   1(25)   134  |
| 2345(9)  1      347  | 23579     23579   (29)  | 2347  8       6    |
+----------------------+-------------------------+--------------------+


#1b. Kraken 2R8+9C1 :=> [2r7c8==1r7c9==5r7c8]-1r7c8; 9 Singles

2r8c1-9r8c1=*[2r7c8=2r7c5-(2=9)r9c6-9r9c1=*(9-3)r5c1=3r5c9-(3=1)r7c9]
||
2r8c46-2r7c5=2r7c8
||
2r8c8-5r8c8=5r7c8

Code: Select all

+-----------------+-------------------+---------------+
| 1     2       3 | 6       5     89  | 48   7   489  |
| 45    458     6 | 349     3489  7   | 2    1   489  |
| 7     48      9 | 124     248   128 | 6    3   5    |
+-----------------+-------------------+---------------+
| 8     4(9)    2 | 49      1     3   | 5    6   7    |
| (39)  7       5 | 29      289   6   | 1    4   8(3) |
| 34    6       1 | 47      478   5   | 38   9   2    |
+-----------------+-------------------+---------------+
| 6     35      7 | 8       23    4   | 9    25  1    |
| 2359  5-3(9)  8 | 123579  6     129 | 347  25  4(3) |
| 2359  1       4 | 23579   2379  29  | 37   8   6    |
+-----------------+-------------------+---------------+


#2. [9r8c2=9r4c2-(9=3)r5c1-3r5c9=3r8c9]-3r8c2; ste

[Leren]

My version of JC's single move solution:

Forcing Chain Contradiction in Row 8 Digit 2:

Code: Select all

 - 5r7c8 = (5-3) r7c2 = (3-9) r8c2 ----------------------------------------------------------------------------|
 - 5r7c8 = 5r7c2 - 5r89c1 = (5-4) r2c1 = (4-3) r6c1 = 3r6c7 - 3r9c7 *= 3r9c5 - (3=2) r7c5 - (2=9) r9c6 - 9r8c4 *= 9r8c1  -2  r8  c1;
 - 5r7c8 = 5r7c2 - 5r9c1 = (5-3) r9c4 ------------------------------|
 - 5r7c8 = 5r7c2 - 5r89c1 = (5-4) r2c1 = (4-3) r6c1 = 3r6c7 - 3r9c7 *= 3r9c5 - (3=2) r7c5                                -2  r8 c46;
 - 5r7c8 = 5r7c2 - 5r89c1 = (5-4) r2c1 = 4r6c1 - (4=7) r6c4 - 7r8c4                                                  = (7-2) r8  c7;
 - 5r7c8                                                                                                             = (5-2) r8  c8; => -12 r7c8; stte

Simple when you know what to look for ! I'm starting to wonder whether JC's father is a carpenter

Leren

[denis_berthier]

I had missed that puzzle.
It has a solution using only very simple rules:

Code: Select all

*******************************************************************************************************
***  SudoRules 20.0.s based on CSP-Rules 2.0.s, using CLIPS 6.30-r152, config = gW-S
*******************************************************************************************************
.2.6...7...6.7....7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8.
27 givens, 198 candidates
singles ==> r5c8 = 4, r4c8 = 6, r4c9 = 7, r4c7 = 5, r6c2 = 6, r5c2 = 7, r6c4 = 7, r7c3 = 7, r9c9 = 6, r3c7 = 6
whip[1]: b8n1{r8c6 .} ==> r8c9 ≠ 1, r8c8 ≠ 1
whip[1]: c6n8{r3 .} ==> r3c5 ≠ 8
whip[1]: b3n2{r2c8 .} ==> r2c6 ≠ 2, r2c4 ≠ 2
whip[1]: c6n8{r1 .} ==> r1c5 ≠ 8
whip[1]: b4n3{r6c1 .} ==> r9c1 ≠ 3, r8c1 ≠ 3, r2c1 ≠ 3, r1c1 ≠ 3
whip[1]: r3n1{c6 .} ==> r2c6 ≠ 1, r2c4 ≠ 1, r1c6 ≠ 1
naked-pairs-in-a-column: c6{r1 r2}{n8 n9} ==> r9c6 ≠ 9, r8c6 ≠ 9, r3c6 ≠ 8
whip[1]: c6n9{r2 .} ==> r1c5 ≠ 9, r2c4 ≠ 9
singles ==> r3c2 = 8, r8c3 = 8
whip[1]: r3n4{c5 .} ==> r2c4 ≠ 4, r1c5 ≠ 4
biv-chain[2]: b2n3{r2c4 r1c5} - c3n3{r1 r9} ==> r9c4 ≠ 3
whip[2]: r9n5{c5 c1} - r1n5{c1 .} ==> r7c5 ≠ 5
biv-chain[3]: b3n9{r2c9 r1c9} - r1c6{n9 n8} - r1c7{n8 n4} ==> r2c9 ≠ 4
biv-chain[2]: c9n4{r8 r1} - c3n4{r1 r9} ==> r9c7 ≠ 4
whip[1]: r9n4{c3 .} ==> r8c1 ≠ 4, r8c2 ≠ 4
biv-chain[3]: b7n2{r8c1 r9c1} - r9c6{n2 n7} - r8n7{c6 c7} ==> r8c7 ≠ 2
biv-chain[3]: b7n2{r9c1 r8c1} - r8c8{n2 n5} - r7n5{c8 c2} ==> r9c1 ≠ 5
whip[1]: r9n5{c5 .} ==> r8c4 ≠ 5
biv-chain[3]: b8n5{r9c4 r9c5} - c5n9{r9 r5} - r5c4{n9 n2} ==> r9c4 ≠ 2
biv-chain[3]: r6n4{c1 c5} - r6n8{c5 c7} - r1c7{n8 n4} ==> r1c1 ≠ 4
biv-chain[4]: c4n3{r2 r8} - c4n1{r8 r3} - c4n4{r3 r4} - c2n4{r4 r2} ==> r2c2 ≠ 3
singles ==> r1c3 = 3, r1c5 = 5, r1c1 = 1, r2c4 = 3, r9c3 = 4, r9c4 = 5
whip[1]: r1n4{c9 .} ==> r2c7 ≠ 4
biv-chain[3]: b8n9{r8c4 r9c5} - b8n3{r9c5 r7c5} - c2n3{r7 r8} ==> r8c2 ≠ 9
singles
123658479
546379821
789142635
892413567
375296148
461785392
657824913
238961754
914537286


[JC Van Hay]

Hi Denis,

May I draw your attention to the fact that the puzzle is
.2.6...7...6..7...7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8. and not
.2.6...7...6.7....7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8.

Best regards, JC.

[denis_berthier]

Hi Denis,
May I draw your attention to the fact that the puzzle is
.2.6...7...6..7...7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8. and not
.2.6...7...6.7....7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8.

Hi JC,

Thanks for noticing. It's strange indeed that the 7 can be moved by one place in the same row and the puzzle is still valid - with a similar path.
The good one is solved as follows. It's slightly harder, as it now requires a non-reversible chain: a whip[3] before the biv-chain[4] (or nice loop if you prefer).

Code: Select all

*********************************************************************************************************
***  SudoRules 20.0.s based on CSP-Rules 2.0.s, using CLIPS 6.30-r152, config = gW-S
*********************************************************************************************************
.2.6...7...6..7...7.9....358.2.13.....5..61....1..5.926..8.49......6.....1.....8.
27 givens, 202 candidates
singles ==> r5c8 = 4, r4c8 = 6, r4c9 = 7, r4c7 = 5
hidden-single-in-a-block ==> r6c2 = 6, r5c2 = 7, r9c9 = 6, r3c7 = 6
161 candidates, 835 csp-links and 835 links.
whip[1]: b8n1{r8c6 .} ==> r8c9 ≠ 1, r8c8 ≠ 1
whip[1]: c6n8{r3 .} ==> r3c5 ≠ 8
whip[1]: b3n2{r2c8 .} ==> r2c5 ≠ 2, r2c4 ≠ 2
whip[1]: c6n8{r1 .} ==> r1c5 ≠ 8
whip[1]: b4n3{r6c1 .} ==> r9c1 ≠ 3, r8c1 ≠ 3
whip[1]: b5n8{r6c5 .} ==> r2c5 ≠ 8
whip[1]: r3n1{c4 .} ==> r2c4 ≠ 1
whip[1]: b4n3{r6c1 .} ==> r2c1 ≠ 3, r1c1 ≠ 3
whip[1]: r3n1{c6 .} ==> r1c6 ≠ 1
whip[2]: r9n5{c5 c1} - r1n5{c1 .} ==> r7c5 ≠ 5
whip[2]: r4n4{c4 c2} - r3n4{c2 .} ==> r2c4 ≠ 4
biv-chain[3]: b3n9{r2c9 r1c9} - r1c6{n9 n8} - r1c7{n8 n4} ==> r2c9 ≠ 4
whip[2]: c3n4{r8 r1} - c9n4{r1 .} ==> r8c2 ≠ 4, r8c1 ≠ 4
biv-chain[3]: c9n4{r8 r1} - r1c7{n4 n8} - c3n8{r1 r8} ==> r8c3 ≠ 4
whip[1]: r8n4{c9 .} ==> r9c7 ≠ 4
biv-chain[3]: b7n2{r9c1 r8c1} - r8c8{n2 n5} - r7n5{c8 c2} ==> r9c1 ≠ 5
whip[1]: r9n5{c5 .} ==> r8c4 ≠ 5
biv-chain[3]: r1c7{n4 n8} - r6c7{n8 n3} - r6c1{n3 n4} ==> r1c1 ≠ 4, r1c3 ≠ 4
hidden-single-in-a-column ==> r9c3 = 4
naked-pairs-in-a-row: r9{c1 c6}{n2 n9} ==> r9c7 ≠ 2, r9c5 ≠ 9, r9c5 ≠ 2, r9c4 ≠ 9, r9c4 ≠ 2
whip[3]: r1c6{n8 n9} - c5n9{r1 r5} - r5n8{c5 .} ==> r1c9 ≠ 8
biv-chain[4]: r1n3{c3 c5} - r1n5{c5 c1} - r1n1{c1 c9} - r7c9{n1 n3} ==> r7c3 ≠ 3
naked-single ==> r7c3 = 7
biv-chain[3]: r6n8{c7 c5} - c5n7{r6 r9} - r9c7{n7 n3} ==> r6c7 ≠ 3
singles
123658479
456397218
789142635
842913567
975286143
361475892
637824951
598761324
214539786

[DonM]

How is it possible to resist the call of the cell r7c8

So, the simplest "solution" : 8 Singles; r7c8=1or2->contradiction :=> r7c8=5; ste.

JC, I've been taking a look at this puzzle and didn't hear r7c8 calling out to me. How did you come up with r7c8=1or2->contradiction? (ie. what chains were used?). I ask because a) Leren referred to it as a 'single-move' solution and b) the alternate solution required relatively complex network moves.

(Not to JC): While I'm at it , why did 2 posters just give summaries of solutions rather than full chains? When that happens, it raises doubts as to the accuracies of the moves.

[JC Van Hay]

How is it possible to resist the call of the cell r7c8

So, the simplest "solution" : 8 Singles; r7c8=1or2->contradiction :=> r7c8=5; ste.

JC, I've been taking a look at this puzzle and didn't hear r7c8 calling out to me.

r7c8 contains 3 candidates belonging to 3 bilocals (1r72c8,2r7c82,5r78c8).
It calls therefore the attention before the 2 solutions of B4R4 and the chain snippet of bilocals in R1 as a starting point to the analysis of the puzzle (SteveK's ~first empirical rule).

How did you come up with r7c8=1or2->contradiction? (ie. what chains were used?).

No chain(s) needed in the phase of analysis of the puzzle, like with any kind of coloring such as GEM, RGT, ...

I ask because a) Leren referred to it as a 'single-move' solution

The conséquences of r7c8=1,r7c8=2 and r7c8=5 have to be analyzed together independently of the fact that they could end up in a contradiction, solution.

and b) the alternate solution required relatively complex network moves.

Once such a phase is finished, whether the puzzle is completely solved or not, a set of "chains" can be builded according to some predefined properties.
Here, the shortest solution was looked for instead of a so-called "elegant solution" which is almost impossible to do otherwise, at least one of the best ones.