The New Sudoku Players' Forum

[re'born]

Here we have Two Incompatible Unique Patterns, one in cells r56c349 and other in cells r45c19. But if r5c1~2 then the naked pair in r45c1 makes r5c3<>1 and so (because of the UP in r56c349) r5c9=1 => r4c7=9 => r4c9<>9. In other words, from the condition "r5c1=2 or r5c3=1 or r4c9=9" we now have showed that if r5c1~2 then also r5c3<>1 and r4c9<>9. So, r5c1=2.

Ahh, mentioning the Two Incompatible Unique Patterns did the trick for me. Thanks for explaining.

I see a UR like that as trivial as a naked pair. So I don't count it as a separate step.
Carcul

Fair enough.

[wapati]

I liked A-497 and B-58 the best. They are about as hard as it gets for pattern only. Sudoku Cue rates them around 3500

[Carcul]

Puzzle B10:

Code: Select all

 *--------------------------------------------------------*
 | 12    4689  1689 | 28    49    3    | 469   7     5    |
 | 69    7     3    | 1     5     49   | 8     2     469  |
 | 5     2489  289  | 7     6     28   | 1     49    3    |
 |------------------+------------------+------------------|
 | 7     89    5    | 6     2     1    | 3     489   49   |
 | 4     268   268  | 9     3     7    | 5     68    1    |
 | 13    369   169  | 4     8     5    | 7     69    2    |
 |------------------+------------------+------------------|
 | 23    39    7    | 28    1     6    | 49    5     489  |
 | 69    1     4    | 5     79    89   | 2     3     6789 |
 | 8     5     269  | 3     479   249  | 69    1     79   |
 *--------------------------------------------------------*


Solution 1:

If r9c5~4 then the emergent naked pair r89c5 makes r8c6=8. But this cannot be, because the ALS-xz rule A(689)=[r8c19], B(2,3,8,9)=[r7c124], x=9, z=8, tells us that r8c6<>8. So r9c5=4. After that, the same ALS-xz rule makes r8c6<>8 solving the puzzle.

Solution 2:

A(6,9)=[r2c1], B(4,6,8,9)=[r247c9], C(2,3,8,9)=[r7c124], => r8c1<>9.

Carcul

[wapati]

A 501 is probably good for EEs thread as an ER.

To me that is all that I see, and no shortcut.

Code: Select all

7..19.2..........38....6.7..8.37.....9..8..5.....19.4..3.5....24..........6.32..8

[wapati]

This one has many paths. Swordfish is in most of them.

Code: Select all

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

[daj95376]

A 501 is probably good for EEs thread as an ER. To me that is all that I see, and no shortcut.

Code: Select all

7..19.2..........38....6.7..8.37.....9..8..5.....19.4..3.5....24..........6.32..8

Code: Select all

# Although the following eliminations can be obtained with a complex Kraken X-Wing,
# I prefer the simplicity of a DIC on [r9].

# [r9c8]=1 =>              [r2c8]<>1,               [r78c7]<>1, [r8c9]<>1
# [r9c2]=1 => [r2c13]=1 => [r2c8]<>1 => [r7c8]=1 => [r78c7]<>1, [r8c9]<>1
 *-----------------------------------------------------------*
 | 7     6     5     | 1     9     3     | 2     8     4     |
 | 129   4     129   | 78    25    78    | 156   6-1   3     |
 | 8     12    3     | 4     25    6     | 159   7     159   |
 |-------------------+-------------------+-------------------|
 | 16    8     4     | 3     7     5     | 19    2     169   |
 | 126   9     127   | 26    8     4     | 3     5     167   |
 | 3     5     27    | 26    1     9     | 8     4     67    |
 |-------------------+-------------------+-------------------|
 | 19    3     189   | 5     4     178   | 67-1  169   2     |
 | 4     127   1289  | 789   6     178   | 57-1  3     5-1   |
 | 5    *17    6     | 79    3     2     | 4    *19    8     |
 *-----------------------------------------------------------*


[Carcul]

This one has many paths. Swordfish is in most of them.

Code: Select all

 *------------------------------------------------------*
 | 37    4     379  | 5     39    2  | 8     16    16   |
 | 2     1369  1369 | 13    1369  8  | 7     45    45   |
 | 156   156   8    | 7     146   14 | 3     2     9    |
 |------------------+----------------+------------------|
 | 9     156   4    | 18    2     7  | 56    3     1568 |
 | 135   2     13   | 4     18    6  | 9     58    7    |
 | 167   8     167  | 9     5     3  | 4     16    2    |
 |------------------+----------------+------------------|
 | 4     7     369  | 2     38    5  | 1     89    68   |
 | 18    19    5    | 6     7     14 | 2     489   3    |
 | 1368  136   2    | 138   1348  9  | 56    7     4568 |
 *------------------------------------------------------*


r7c3=9 or r9c4=1, and so r9c1/r9c2<>1 (because of r8c2) solving the puzzle.

Carcul

[Del]

[/code]
r7c3=9 or r9c4=1, and so r9c1/r9c2<>1 (because of r8c2) solving the puzzle.

Carcul[/quote]

Would you please enlighten me as to the logic which allows you to select "r7c3=9 or r9c4=1" when there are other possibilities for these two cells.
Regards,
Del.

[Carcul]

Puzzle A317:

Code: Select all

 *------------------------------------------------------------*
 | 2      1467   134 | 8      39     69 | 46     467    5     |
 | 56     9      58  | 67     4      1  | 2      3      678   |
 | 46     4678   348 | 367    5      2  | 1      46789  46789 |
 |-------------------+------------------+---------------------|
 | 1456   1456   2   | 9      16     8  | 7      46     3     |
 | 3      468    48  | 2      7      5  | 4689   4689   1     |
 | 9      168    7   | 4      16     3  | 5      2      68    |
 |-------------------+------------------+---------------------|
 | 147    3      6   | 5      2      49 | 489    14789  4789  |
 | 47     2      9   | 1      8      46 | 3      5      467   |
 | 8      145    145 | 36     39     7  | 469    1469   2     |
 *------------------------------------------------------------*


Because of the ALS's A(3,4,6,7,8)=[r3c1234] and B(5,6,8)=[r2c13] we must have r3c1=1 or r3c2=4 or r3c3=4. So, r1c23/r3c89<>4.
After that: A(4,5,8)=[r29c3], B(4,6,8,9)=[r5c378], C(6,8)=[r6c9], => r2c9<>8.

Puzzle A324:

Code: Select all

 *----------------------------------------------------*
 | 2     1     4   | 56    7     8   | 9     3     56 |
 | 6     9     58  | 4     235   235 | 12    128   7  |
 | 57    3     578 | 1     2569  259 | 24    248   56 |
 |-----------------+-----------------+----------------|
 | 1     4     57  | 259   259   6   | 3     27    8  |
 | 3     8     2   | 7     1     4   | 6     5     9  |
 | 57    6     9   | 3     8     25  | 127   127   4  |
 |-----------------+-----------------+----------------|
 | 8     5     1   | 69    369   39  | 47    47    2  |
 | 4     7     6   | 25    25    1   | 8     9     3  |
 | 9     2     3   | 8     4     7   | 5     6     1  |
 *----------------------------------------------------*


Note how the AUR in cells [r26c78] functions as an ALS. So, we have A(5,7,8)=[r2c3|r3c1], B(1,2,7,8)=AUR, x=8, z=7, => r6c1<>7.

Carcul

[Carcul]

Puzzle A218:

Code: Select all

 *-----------------------------------------------------*
 | 3     5     79   | 4     79    1  | 6     8     2   |
 | 489   6     4789 | 38    79    2  | 1     37    5   |
 | 2     1     78   | 5     36    68 | 9     4     37  |
 |------------------+----------------+-----------------|
 | 89    78    3589 | 6     2     4  | 3578  1379  178 |
 | 1     248   348  | 7     5     9  | 348   23    6   |
 | 469   247   4569 | 1     8     3  | 457   279   47  |
 |------------------+----------------+-----------------|
 | 5     9     2    | 38    46    68 | 347   137   147 |
 | 7     48    1    | 9     34    5  | 2     6     348 |
 | 468   3     468  | 2     1     7  | 48    5     9   |
 *-----------------------------------------------------*


If r5c3=3 then because of r5c8 we must have r9c1=6 and r8c9=3. But that cannot be, because of the Unique Rectangle in cells r12c35. So, r5c3<>3 and the puzzle is solved.

Carcul

[Carcul]

Would you please enlighten me as to the logic which allows you to select "r7c3=9 or r9c4=1" when there are other possibilities for these two cells.

In that grid you have an XY-Wing. So, what happens if the condition above is not met?

Regards, Carcul

[wapati]

Swordfish, and several more patterns.

Code: Select all

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


[wapati]

An xyz will shorten the path, it is still long enough to be fun!

Code: Select all

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


[wapati]

This one was odd for me. I didn't know what BUG2 was. I don't like it but it can be used here. I used finned-x, finned-sword and BUG1.

Code: Select all

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


[wapati]

UR and 3 patterns.

Code: Select all

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