Contrary "17" Puzzles

Everything about Sudoku that doesn't fit in one of the other sections

Puzzle #12481

Postby Draco » Thu Mar 20, 2008 5:48 pm

For #12481:
Code: Select all
. . . | 8 7 . | . 3 .
5 2 . | . . . | . . .
4 . . | . . . | . . .
------+-------+------
. . 3 | . 9 . | . 7 .
. . . | . . 5 | 4 . .
. 8 . | . . . | . . .
------+-------+------
2 . . | . . . | 5 . .
. . . | 3 . . | . . 9
. . . | 1 . . | . . .


1 69  69  | 8 7  4   | 2  3  5
5 2   7   | 9 6  3   | 8  4  1
4 3   8   | 5 2  1   | 9  6  7
----------+----------+--------
6 5   3   | 4 9  8   | 1  7  2
7 1   2   | 6 3  5   | 4  9  8
9 8   4   | 2 1  7   | 3  5  6
----------+----------+--------
2 469 169 | 7 48 69  | 5  18 3
8 467 156 | 3 45 26  | 67 12 9
3 679 569 | 1 58 269 | 67 28 4


Try:

r8c6=2 --> r8c8=1 --> r7c8=8 --> r7c3=1 ... and ...
r8c6=6 --> r9c6=2 --> r7c6=9

Which lets us state r7c3<>9. Then:

r8c5=4 --> r8c3=5 --> r8c8=1 ... and ...
r8c5=5 --> r9c5=8 --> r9c8=2

Ergo r8c8<>2. Puzzle reduces to singles.

Cheers...

- draco
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Postby Draco » Thu Mar 20, 2008 7:29 pm

Try #6550

Code: Select all
. . . | . 9 . | . 6 .
. 2 . | 7 . . | . . .
. 1 . | . . . | . . .
------+-------+------
6 . . | 2 . . | 8 3 .
9 . . | 5 . . | . . .
. . . | 1 . . | . . .
------+-------+------
. . . | . . . | 5 . 2
4 . . | . 6 . | . . .
. . . | . . . | 1 . .


5   3478 3478 | 38  9    2   | 37  6   1 
38  2    6    | 7   1    348 | 349 5   389
378 1    9    | 6   5    348 | 347 2   378
--------------+--------------+------------
6   47   1    | 2   47   9   | 8   3   5 
9   3478 3478 | 5   3478 6   | 2   1   47
2   3478 5    | 1   3478 378 | 6   79  479
--------------+--------------+------------
1   6    38   | 49  378  378 | 5   49  2 
4   5    2    | 89  6    1   | 379 789 379
378 9    378  | 348 2    5   | 1   48  6 


r1c7=3 --> r1c4=8 --> r9c4=3 +
r1c7=7 --> r3c79<>7 --> r3c1=7 --> r9c3=7

Ergo r9c3<>3

Then coloring 3's forces r1c3<>3. This leaves us with:
Code: Select all

5   3478 478  | 38  9    2   | 37  6   1 
38  2    6    | 7   1    348 | 349 5   389
378 1    9    | 6   5    348 | 347 2   378
--------------+--------------+------------
6   47   1    | 2   47   9   | 8   3   5 
9   3478 3478 | 5   3478 6   | 2   1   47
2   3478 5    | 1   3478 378 | 6   79  479
--------------+--------------+------------
1   6    38   | 49  378  378 | 5   49  2 
4   5    2    | 89  6    1   | 379 789 379
378 9    78   | 348 2    5   | 1   48  6 

Finally:

r2c1=3 --> r9c1<>3 --> r7c3=3 --> r9c4=3 +
r2c1=8 --> r1c23<>8 --> r1c4=8

Ergo r9c4<>8 & r1c4<>3. Puzzle reduces to singles.
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Postby daj95376 » Thu Mar 20, 2008 8:51 pm

Draco, thanks for solutions to the other puzzles.

Puzzle #6550: Doesn't qualify as contrary

Solution: Singles, Locked Candidates (1), Naked Triple, f/s X-Wing, f/s Swordfish
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Postby daj95376 » Thu Mar 20, 2008 8:54 pm

These "17" puzzles have some interesting variations in there final solution steps. It will be interesting to see the variation as the number of remaining cells increase.

Code: Select all
18 cells remaining: #46556                   (done)
19   "       "    : #12481, #42341           (done)
20   "       "    : #11258, #20425, #26572   (done)

21   "       "    : #28972, #35933           (next)
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Postby daj95376 » Thu Mar 20, 2008 9:01 pm

Puzzle #28972:

Code: Select all
3.....7.....1..4.....2.........5.61..82...........6....1.....287...3...........3.
3416857922.81974.3.7.2438.1.3785261.682.1.3751..37628..1376..2872..381468...21.37

Code: Select all
 *-----------------------------------------------------------*
 | 3     4     1     | 6     8     5     | 7     9     2     |
 | 2     56    8     | 1     9     7     | 4     56    3     |
 | 59    7     569   | 2     4     3     | 8     56    1     |
 |-------------------+-------------------+-------------------|
 | 49    3     7     | 8     5     2     | 6     1     49    |
 | 6     8     2     | 49    1     49    | 3     7     5     |
 | 1     59    459   | 3     7     6     | 2     8     49    |
 |-------------------+-------------------+-------------------|
 | 459   1     3     | 7     6     49    | 59    2     8     |
 | 7     2     59    | 59    3     8     | 1     4     6     |
 | 8     569   4569  | 459   2     1     | 59    3     7     |
 *-----------------------------------------------------------*
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Postby daj95376 » Thu Mar 20, 2008 9:03 pm

Puzzle #35933:

Code: Select all
64.7............53.......1.7.86........4.9...5.........6....4......5.2......1....
6457319.....94.653...56.714738625149..64895375941738...6..9.4.5....5.2.1.5..1.3..

Code: Select all
  c6    -  28    Naked  Pair
r3      -  28    Naked  Pair
r2c2    <> 28    Unique Rectangle Type 1

Code: Select all
 *--------------------------------------------------*
 | 6    4    5    | 7    3    1    | 9    2    8    |
 | 128  17   127  | 9    4    28   | 6    5    3    |
 | 39   28   39   | 5    6    28   | 7    1    4    |
 |----------------+----------------+----------------|
 | 7    3    8    | 6    2    5    | 1    4    9    |
 | 12   12   6    | 4    8    9    | 5    3    7    |
 | 5    9    4    | 1    7    3    | 8    6    2    |
 |----------------+----------------+----------------|
 | 123  6    123  | 23   9    7    | 4    8    5    |
 | 4    78   379  | 38   5    6    | 2    79   1    |
 | 289  5    279  | 28   1    4    | 3    79   6    |
 *--------------------------------------------------*
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Postby Draco » Thu Mar 20, 2008 9:06 pm

Daj --

To me, finned and mutant fish are contrary:) . I can't spot the suckers. One afternoon I will sit down and re-reread Tarek's Ulitmate Fish guide and see if they sink in better.
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Postby Draco » Thu Mar 20, 2008 9:17 pm

Puzzle #35933:

From Daj's PM's:

r2c2=1 --> r2c3=7 +
r2c2=7 --> r5c2=1 --> r3c2=2 & r5c1=1

Ergo: r2c1<>1 & r2c3<>2. From here, X-wing on 2's and pair of XY-Wings in 3rd row of boxes reduce the puzzle to singles.

Because I realize it may be unclear, let me make it clear that I am using a solver to do this!:) One that doesn't handle many fish variants (as I haven't learned them well enough to code them up yet).
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Postby eleven » Fri Mar 21, 2008 6:30 pm

Puzzle #42341.
Code: Select all
 +-----------------------------------------------------+
 |  7    3    1    |  5    2    6    |  9    8    4    |
 |  5   #48  #468  |  9    17   148  |  67   3    2    |
 |  4-68 9    2    |  3    47   48   |  67   1    5    |
 |-----------------+-----------------+-----------------|
 | #468 #48   3    |  1    456  45   |  2    7    9    |
 |  9    5    7    |  2    8    3    |  4    6    1    |
 |  1    2    4-6  |  7    46   9    |  8    5    3    |
 |-----------------+-----------------+-----------------|
 |  2    7    9    |  8    15   15   |  3    4    6    |
 |  3    6    5    |  4    9    7    |  1    2    8    |
 | #48   1   #48   |  6    3    2    |  5    9    7    |
 +-----------------------------------------------------+
Nice uniqueness pattern 48 solves it directly. One of r2c3 and r4c1 must be 6.

Puzzle #28972:
Code:
Code: Select all
 *-----------------------------------------------------------*
 | 3     4     1     | 6     8     5     | 7     9     2     |
 | 2     56    8     | 1     9     7     | 4     56    3     |
 | 59    7     569   | 2     4     3     | 8     56    1     |
 |-------------------+-------------------+-------------------|
 | 49    3     7     | 8     5     2     | 6     1     49    |
 | 6     8     2     | 49    1     49    | 3     7     5     |
 | 1     59    459   | 3     7     6     | 2     8     49    |
 |-------------------+-------------------+-------------------|
 |*459   1     3     | 7     6     49    |*59    2     8     |
 | 7     2    #59    | 59    3     8     | 1     4     6     |
 | 8     56-9  456-9 | 459   2     1     |#59    3     7     |
 *-----------------------------------------------------------*

w-wing solves also here. Should not be contrary ...
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Postby hobiwan » Fri Mar 21, 2008 8:35 pm

Puzzle #35933:

ALS-XZ: A=[r8c238] - {3789}, B=[r257c1] - {1238}, X=3, Z=8 => [r3c2],[r9c1]<>8
Puzzle solved

Alternative:
Discontinuous Nice Loop: [r9c4]-2-[r7c4]-3-[r7c1]=3=[r3c1]=9=[r9c1]=8=[r9c4] => [r9c4]<>2
Puzzle solved
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Postby daj95376 » Fri Mar 21, 2008 10:36 pm

Okay. Now that everyone is warmed up. Let's see if more unsolved cells is more challenging.

Note: I've dropped listing the original puzzle and intermediate steps. Let me know if this presents a problem.

Code: Select all
Puzzle #40_2:

+-----------------------------------------------------------------------------+
|  389     359     359    |  1       389     4      |  2       6       7      |
|  68      1       7      |  28      2568    258    |  4       3       9      |
|  369     4       2      |  379     369     379    |  8       5       1      |
|-------------------------+-------------------------+-------------------------|
|  39      23569   3569   |  239     7       1      |  359     8       4      |
|  1       359     4      |  6       3589    3589   |  3579    279     23     |
|  7       2359    8      |  4       2359    2359   |  359     1       6      |
|-------------------------+-------------------------+-------------------------|
|  2       3679    369    |  5       39      379    |  1       4       8      |
|  4       379     39     |  23789   1       23789  |  6       279     5      |
|  5       8       1      |  279     4       6      |  379     279     23     |
+-----------------------------------------------------------------------------+
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Puzzle #40_2

Postby Draco » Fri Mar 21, 2008 11:25 pm

Well my solver kicks out so many long chains that it would take me a couple of hours to transcribe all of them. It gets there but in too many steps to be worth publishing.

On the other hand coloring the puzzle on 6's and trying the paths off the 6's in box #1 leads me quickly to a puzzle that reduces to singles.

I know... doesn't count.:)
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Postby daj95376 » Sat Mar 22, 2008 2:25 am

I don't know if Puzzle #40_2 has a single-step solution. On the assumption that it'll take several elimination steps, I'll take the easy ones. (If I knew ALS, I bet this would be even easier!)

Code: Select all
[r5c5]=3 => [r7c5]=9 => contradiction in [b2]~379 => [r5c5]<>3
[r5c5]=9 => [r7c5]=3 => contradiction in [b2]~379 => [r5c5]<>9

[r6c5]=3 => [r7c5]=9 => contradiction in [b2]~379 => [r6c5]<>3
[r6c5]=9 => [r7c5]=3 => contradiction in [b2]~379 => [r6c5]<>9

Code: Select all
+-----------------------------------------------------------------------------+
|  389     359     359    |  1       389     4      |  2       6       7      |
|  68      1       7      |  28      2568    258    |  4       3       9      |
|  369     4       2      |  379     369     379    |  8       5       1      |
|-------------------------+-------------------------+-------------------------|
|  39      23569   3569   |  239     7       1      |  359     8       4      |
|  1       359     4      |  6       58-39   3589   |  3579    279     23     |
|  7       2359    8      |  4       25-39   2359   |  359     1       6      |
|-------------------------+-------------------------+-------------------------|
|  2       3679    369    |  5       39      379    |  1       4       8      |
|  4       379     39     |  23789   1       23789  |  6       279     5      |
|  5       8       1      |  279     4       6      |  379     279     23     |
+-----------------------------------------------------------------------------+
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Postby ronk » Sat Mar 22, 2008 3:14 am

An opening move for #40_2:

r2c4 -2- ALS:(r89c4,r7c56 =2|379|8= r89c4) -8- r2c4 -2- continuous loop

... implies r4c4<>2, r8c6<>379

Then after basic moves ...

finned jellyfish r1478\c1345 plus fin r1c2 implies r3c1<>3

and an xy-wing for r7c5<>9
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Postby StrmCkr » Sat Mar 22, 2008 3:43 am

puzzle40_2

ALS/ALS: [r2c4] and [r7c5|r7c6|r8c4|r9c4], 8 is restricted common, other common candidate 2 can be removed from r4c4

SINGLE: r4c2 set to 2, unique in Row
SINGLE: r4c3 set to 6, unique in Row
SINGLE: r4c7 set to 5, unique in Row
SINGLE: r7c2 set to 6, unique in Column
SINGLE: r7c6 set to 7, unique in Row
SINGLE: r8c2 set to 7, unique in Column
SINGLE: r1c3 set to 5, unique in Column
SINGLE: r3c4 set to 7, unique in Row
SINGLE: r3c4 set to 7, unique in Column

ALS/ALS: [r7c5] and [r2c4|r8c4|r9c4], 3 is restricted common, other common candidate 9 can be removed from r8c6
X-CYCLE on 9 (Grouped Discontinuous Alternating Nice Loop, length 6):
9[r1c5]-9[r7c5]=9[r8c4|r9c4]-9[r4c4]=9[r4c1]-9[r3c1]=9[r1c1|r1c2]-9[r1c5]-
- Discontinuity is two weak links joined at r1c5, 9 can be removed from that cell

POINTING PAIR: 9s at r3c5/r3c6 points to r3c1, removing 9

XY CHAIN length=4, 8 taken off r2c5, chain ends: r1c5 and r2c4
XY CHAIN length=4, 8 taken off r2c6, chain ends: r1c5 and r2c4

HIDDEN UNIQUE RECTANGLE removing 5 at r6c5 because of r26c56 and two strong links on 2

XY CHAIN length=4, 3 taken off r5c5, chain ends: r1c5 and r4c4
XY CHAIN length=4, 3 taken off r6c5, chain ends: r1c5 and r4c4
XY CHAIN length=4, 3 taken off r3c5, chain ends: r1c5 and r7c5

X-CYCLE on 3 (Discontinuous Alternating Nice Loop, length 6):
3[r5c6]-3[r3c6]=3[r3c1]-3[r4c1]=3[r4c4]-3[r5c6]-
- Discontinuity is two weak links joined at r5c6, 3 can be removed from that cell

X-CYCLE on 3 (Discontinuous Alternating Nice Loop, length 6):
3[r4c4]=3[r4c1]-3[r3c1]=3[r3c6]-3[r6c6]=3[r4c4]=
- Discontinuity is two strong links joined at r4c4, all other candidates (9) can be removed from that cell

cascade of singles at this point.
Some do, some teach, the rest look it up.
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