The New Sudoku Players' Forum

[SteveG48]

Here's another from our local newspaper:

Code: Select all

 *-----------*
 |...|7..|...|
 |58.|.19|.26|
 |32.|.4.|...|
 |---+---+---|
 |...|..4|37.|
 |2..|...|..5|
 |.38|5..|...|
 |---+---+---|
 |...|.6.|.59|
 |95.|43.|.62|
 |...|..1|...|
 *-----------*


[JC Van Hay]

Code: Select all

+--------------------+---------------+--------------------+
| 14     149    6    | 7    28   258 | 59   348     348   |
| 5      8      47   | 3    1    9   | 47   2       6     |
| 3      2      (79) | 6    4    58  | 59   18      (178) |
+--------------------+---------------+--------------------+
| (16)   (169)  5    | 128  289  4   | 3    7       (18)  |
| 2      1479   4-9  | 18   789  3   | 6    148(9)  5     |
| 47(1)  3      8    | 5    79   6   | 2    4(19)   4(1)  |
+--------------------+---------------+--------------------+
| 478    47     3    | 28   6    278 | 1    5       9     |
| 9      5      1    | 4    3    78  | 78   6       2     |
| 678    67     2    | 9    5    1   | 478  34      347   |
+--------------------+---------------+--------------------+


1. 1R6 -> [9r4c2==9r5c8==9r3c3]-9r5c3; 21 singles
||1r6c1-(1=69)r4c12
||1r6c8-9r6c8=9r5c8
||1r6c9-(1=87)r43c9-(7=9)r3c3

Code: Select all

+-------------+-----------+---------------+
| 14  14    6 | 7  2    5 | 9  38    38   |
| 5   8     7 | 3  1    9 | 4  2     6    |
| 3   2     9 | 6  4    8 | 5  1     7    |
+-------------+-----------+---------------+
| 6   (19)  5 | 2  89   4 | 3  7     (18) |
| 2   7-9   4 | 1  789  3 | 6  (89)  5    |
| 17  3     8 | 5  79   6 | 2  49    14   |
+-------------+-----------+---------------+
| 47  47    3 | 8  6    2 | 1  5     9    |
| 9   5     1 | 4  3    7 | 8  6     2    |
| 8   6     2 | 9  5    1 | 7  34    34   |
+-------------+-----------+---------------+


2. XYWing(189)r4c29.r5c8-9r5c2; stte

[Leren]

1.

Code: Select all

*--------------------------------------------------------------*
| 14    149   6      | 7     28    258    | 59    348   348    |
| 5     8     7-4    | 3     1     9      | 47    2     6      |
| 3     2     79     | 6     4     58     | 59    18    178    |
|--------------------+--------------------+--------------------|
| 16    169   5      | 128   289   4      | 3     7     18     |
| 2     1479  49     | 18    789   3      | 6     1489  5      |
| 147   3     8      | 5     79    6      | 2     149   14     |
|--------------------+--------------------+--------------------|
| 478   47    3      | 28    6     278    | 1     5     9      |
| 9     5     1      | 4     3     78     | 78    6     2      |
| 678   67    2      | 9     5     1      | 478   34    347    |
*--------------------------------------------------------------*

Kraken Column 9 Digit 4:

4r2c3 - 4r2c7 = 4r9c7 - (4=3) r9c8 - 3r9c9 = 3 r1c9 - 4 r1c9;

4r2c3 - (4=1) r1c1            - 1  r6c1
4r2c3 - (4=9) r5c3 - 9r5c8 = (9-1) r6c8 = 1r6c9     - 4 r6c9;

4r2c3 - 4r2c7 = 4r9c7                               - 4 r9c9;

2.

Code: Select all

*--------------------------------------------------------------*
| 14    14    6      | 7     2     5      | 9     38    38     |
| 5     8     7      | 3     1     9      | 4     2     6      |
| 3     2     9      | 6     4     8      | 5     1     7      |
|--------------------+--------------------+--------------------|
| 6    a19    5      | 2     8-9   4      | 3     7     18     |
| 2     79    4      | 1    *9-78  3      | 6     89    5      |
|b17    3     8      | 5    c79    6      | 2     49    14     |
|--------------------+--------------------+--------------------|
| 47    47    3      | 8     6     2      | 1     5     9      |
| 9     5     1      | 4     3     7      | 8     6     2      |
| 8     6     2      | 9     5     1      | 7     34    34     |
*--------------------------------------------------------------*

BUG+1 => - 78 r5c5; stte or XY Wing (9=1) r4c2 - (1=7) r6c1 - (7=9) r6c5 => - 9 r4c5; stte

Eliminating 1 from r1c1 => single stepper stte finish but it's too messy to prove. I'll leave it as a challenge for the resident geniuses. Since JC Van Hay didn't post a single stepper I don't feel so bad

Leren

[pjb]

Good one Steve, at present I can only find multi step solutions which I won't bore you with.
Phil

[SteveG48]

I didn't find a single-stepper either!

[SteveG48]

Eliminating 1 from r1c1 => single stepper stte finish but it's too messy to prove. I'll leave it as a challenge for the resident geniuses. Since JC Van Hay didn't post a single stepper I don't feel so bad

Leren

I explored that one for awhile with no luck.

[keith]

Code: Select all

+----------------+----------------+----------------+
| 14   149  6    | 7    28   258  | 59   348  348  |
| 5    8    47   | 3    1    9    | 47   2    6    |
| 3    2    79   | 6    4    58   | 59   18   178  |
+----------------+----------------+----------------+
| 16   169  5    | 128  289  4    | 3    7    18   |
| 2    1479 49   | 18   789  3    | 6    1489 5    |
| 147  3    8    | 5    79   6    | 2    149  14   |
+----------------+----------------+----------------+
| 478  47   3    | 28   6    278  | 1    5    9    |
| 9    5    1    | 4    3    78   | 78   6    2    |
| 678  67   2    | 9    5    1    | 478  34   347  |
+----------------+----------------+----------------+


Note the DP 34 in R19C89.
R1C89=8 and R9C9=7 have a common outcome, R8C7=8. That leads to a BUG+1.

Keith

[Leren]

keith wrote : That leads to a BUG+1.

I found that solving a lot of cells, or uncovering a lot of hidden singles, leads to the same BUG+1 / XY Wing position that both I and JC Van Hay mentioned.

The one exception is to eliminate 1 in r1c1, which solves in singles, but it seems to be too hard to prove by human friendly methods.

Leren

[SteveG48]

The one exception is to eliminate 1 in r1c1, which solves in singles, but it seems to be too hard to prove by human friendly methods.

Leren

I don't think it's quite that bad. My best effort used Keith's UR, an embedded kite, and a bunch of stars to show that r6c1 has to be a 1. It's just no fun.

[keith]

R5C5=9 nails it. (It's the BUG+1 cell.)

Tell me how.

Keith

[SteveG48]

R5C5=9 nails it. (It's the BUG+1 cell.)

Tell me how.

Keith

(7*)r5c5 - (7=9*)r6c5 - r6c8 = (9*)r5c8 - (9=4)rr5c3 - (4*7*9)r5c2 = (169)b4p125 - (1|9=4)r1c2 - (4=238)r1c589 - (2*9=8)r4c5 - 8r4c9 => contradiction 8b6
8r5c5 - b5p124 = ((1279)b5p1248)&((8*)r4c9) - (7|9=164*)b4p127 - (4=79)r35c3 - (7*8=1)r3c9 - (1=4)r6c9 => contradiction 4r6

Therefore, r5c5=9

Another "solution" that's no fun.

[bat999]

Code: Select all

.-------------------.-----------------.------------------.
|  14     149    6  | 7     28    258 | 59   348    348  |
|  5      8      47 | 3     1     9   | 47   2      6    |
|  3      2     c79 | 6     4     58  | 59   18    b178  |
:-------------------+-----------------+------------------:
| d16B   d169B   5  | 128   28-9  4   | 3    7     b18   |
|  2      1479  c49 | 18    789   3   | 6    1489   5    |
| d147B   3      8  | 5    d79B   6   | 2    149   a14A  |
:-------------------+-----------------+------------------:
|  478    47     3  | 28    6     278 | 1    5      9    |
|  9      5      1  | 4     3     78  | 78   6      2    |
|  678    67     2  | 9     5     1   | 478  34     347  |
'-------------------'-----------------'------------------'

(1)r6c9 - (1=7)r34c9 - (7=4)r35c3 - (4=9)r4c12,r6c15
(4)r6c9 - (4=9)r4c12,r6c15
=> -9 r4c5; stte

Those four cells r4c12,r6c15 have five candidates 14679.
Knock out the 4 to leave the four candidates 1679 in the four cells r4c12,r6c15.
the four cells r4c12,r6c15 restricted to 1679, one or two of the cells will contain a 9.

Edited because the four cells might include two 9s with one of the other candidates not used.

[pjb]

Bat999 wrote:
(1)r6c9 - (1=7)r34c9 - (7=4)r35c3 - (4=9)r4c12,r6c15
(4)r6c9 - (4=9)r4c12,r6c15
=> -9 r4c5; stte

I'm Impressed, well done
Phil

[SteveG48]

Me, too. Wow.