The New Sudoku Players' Forum

by **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

by **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.

by **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

by **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)

by **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 | *-----------------------------------------------------------*

by **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 | *--------------------------------------------------*

by **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.

by **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).

by **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 ...

by **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

by **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 | +-----------------------------------------------------------------------------+

by **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.

by **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 | +-----------------------------------------------------------------------------+

by **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

by **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.

The New Sudoku Players' Forum

Contrary "17" Puzzles

Puzzle #12481

Puzzle #40_2