## CHAINS, not required. Good puzzles.

Post puzzles for others to solve here.
Carcul wrote: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.

Carcul wrote: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.
re'born

Posts: 551
Joined: 31 May 2007

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
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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
Carcul

Posts: 724
Joined: 04 November 2005

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
2010 Supporter

Posts: 527
Joined: 13 September 2006

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 .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

wapati wrote: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     | *-----------------------------------------------------------*`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Wapati wrote: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
Carcul

Posts: 724
Joined: 04 November 2005

[/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.
Del

Posts: 13
Joined: 27 October 2005

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
Last edited by Carcul on Fri Nov 10, 2006 6:30 am, edited 1 time in total.
Carcul

Posts: 724
Joined: 04 November 2005

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

Posts: 724
Joined: 04 November 2005

Del wrote: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
Carcul

Posts: 724
Joined: 04 November 2005

Swordfish, and several more patterns.

Code: Select all
`. 8 . | . 4 5 | 9 . 61 . . | . . . | . 8 .. . . | 9 . . | . . 4---------------------. . 6 | . 2 . | . . 78 . . | 5 . 4 | . . 94 . . | . 7 . | 5 . .---------------------2 . . | . . 6 | . . .. 6 . | . . . | . . 37 . 5 | 4 9 . | . 6 .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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
2010 Supporter

Posts: 527
Joined: 13 September 2006

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 . 11 . . | . . 6 | . . .. . 3 | 7 . . | . . 2---------------------. . 8 | . 2 7 | . 6 .. . . | 9 . 1 | . . .. 2 . | 4 6 . | 7 . .---------------------8 . . | . . 2 | 9 . .. . . | 5 . . | . . 79 . 4 | . . . | . 5 .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006

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 . .`
wapati
2010 Supporter

Posts: 527
Joined: 13 September 2006