The New Sudoku Players' Forum

by **Draco** » Wed May 21, 2008 3:31 am

Please let me know if you find these interesting (or not); you can just PM me if you care to reply. If more find them interesting than not, I'll post continually as I find puzzles that look interesting.

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

After SSTS:

Code: Select all: 6 1 458 | 4589 2458 2459 | 348 457 37 9 458 3 | 7 458 6 | 2 145 148 2 7 458 | 1458 3 145 | 6 45 9 ----------------+------------------+------------- 34 346 124 | 349 2467 23479 | 1349 8 5 345 34568 2458 | 3459 1 23459 | 349 247 367 7 9 1245 | 3458 24568 2345 | 134 124 36 ----------------+------------------+------------- 8 45 7 | 6 9 145 | 145 3 2 1345 345 6 | 2 45 8 | 7 9 14 145 2 9 | 1345 457 13457 | 1458 6 148

Found a simple net (couldn't quite get it to a chain) that cracks this to SSTS to solve:

r1c9=3 r5c9=7 r6c9=6 [r6c5<>6] r4c5=6 r4c6=7 [r4c5<>2 + r4c6<>2] => r4c3=2 r6c3=1 ... and ...
r1c9=7 [r1c8<>7] r5c8=7 r6c8=2
So: r6c8<>1

Other solutions?

Cheers ...

- drac

by **hobiwan** » Wed May 21, 2008 9:56 am

No other solution, just a shorter net:

Code: Select all: Forcing Net Contradiction in r6 => [r6c8]<>1 [r6c8]=1=>[r5c8]=2=>[r5c9]=7=>[r6c9]=6=>[r4c5]=6=>([r4c5]<>2=>)[r4c6]=7=>[r4c3]=2=>[r6c3]=1

Without net I need a triple chain:

Code: Select all: Forcing Chain Contradiction in r4 => [r6c8]<>1 [r6c8]=1=>[r4c3]=1=>[r4c3]<>2 [r6c8]=1=>[r5c8]=2=>[r5c9]=7=>[r6c9]=6=>[r4c5]=6=>[r4c5]<>2 [r6c8]=1=>[r5c8]=2=>[r5c9]=7=>[r6c9]=6=>[r4c5]=6=>[r4c6]=7=>[r4c6]<>2

by **Draco** » Fri May 23, 2008 10:04 am

Starting with:

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

SSTS takes us to:

Code: Select all: 2 45 19 | 6 17 48 | 58 79 3 346 3456 19 | 78 1237 248 | 58 79 24 8 7 34 | 9 23 5 | 6 1 24 ------------+-------------+--------- 1 49 2 | 5 49 3 | 7 8 6 37 39 5 | 78 6 89 | 4 2 1 47 8 6 | 2 47 1 | 3 5 9 ------------+-------------+--------- 9 1 7 | 3 8 6 | 2 4 5 346 2346 8 | 14 5 29 | 19 36 7 5 2346 34 | 14 29 7 | 19 36 8

I would guess there are many ways to crack it from here; I went after r2c9:

r2c4=7 r5c4=8 r5c6=9 r8c7=9 r8c4=1 r9c4=4 [r9c3<>4] r3c3=4 r2c9=4
and r2c4=8 r5c6=8 r8c6=9 r2c6=2 ==> r2c9<>2.

SSTS to solve.

by **udosuk** » Fri May 23, 2008 1:42 pm

ALS-xz:

ALS A: r3c35={234}
ALS B: r9c457={1249}
restricted common: x=2 (r39c5)
common: z=4 (r3c3+r9c4)

=> r9c3, seeing r3c3+r9c4, can't be 4, must be 3

SSTS to solve. :idea:

by **Draco** » Sat May 24, 2008 12:49 am

ALS and Kraken/mutant fish are two techniques I have net yet learned (maybe I am spending too much time on forcing net / chain variants). Thanks udosuk.

Cheers...

- drac

by **udosuk** » Sat May 24, 2008 4:59 am

FYI the ALS is just an elegant presentation of logical deductions, and most (if not all) can be represented as a forcing chain. E.g. this move as an XY-chain:

[r9c3] - 4 - [r9c4] - 1 - [r9c7] - 9 - [r9c5] - 2 - [r3c5] - 3 - [r3c3] - 4 - [r9c3]

=> r9c3 <> 4

:idea:

by **hobiwan** » Sat May 24, 2008 7:21 am

Speaking of chain variants:

Almost Locked Set XY-Chain: A=[r3c39] - {234}, B=[r9c3] - {34}, C=[r9c4] - {14}, D=[r9c57] - {129}, RCs=1,3,4, X=2 => [r3c5]<>2
Singles (plus one XY-Wing)

Since two of the four ALS are just bivalue cells, you could probably write it as forcing chain or as nice loop.

A "normal" chain for another cell:

Forcing Chain Contradiction in r9 => [r9c7]=1
[r9c7]<>1=>[r9c7]=9=>[r4c5]=9=>[r4c2]=4=>[r9c2]<>4
[r9c7]<>1=>[r9c7]=9=>[r9c5]=2=>[r3c5]=3=>[r3c3]=4=>[r9c3]<>4
[r9c7]<>1=>[r9c4]=1=>[r9c4]<>4
Singles

by **Draco** » Tue May 27, 2008 1:49 am

udosuk wrote:FYI the ALS is just an elegant presentation of logical deductions, and most (if not all) can be represented as a forcing chain. E.g. this move as an XY-chain:

[r9c3] - 4 - [r9c4] - 1 - [r9c7] - 9 - [r9c5] - 2 - [r3c5] - 3 - [r3c3] - 4 - [r9c3] => r9c3 <> 4

I had not thought of that; thanks! Now I'll be looking for chains on ALS's that I see. For instance, a nice short one giving the same results (the same bi-value as my first chain for its start):

r2c4=7 r6c5=7 r4c5=4 r8c7=9 r8c4=1 r9c4=4 +
r2c4=8 r5c6=8 r8c6=9 r2c6=2 r3c5=3 r3c3=4 => r9c3<>4

No doubt there are even more ways through this particular door. Thanks again for the explanation!

Cheers...

- drac

by **Draco** » Wed Jun 04, 2008 10:45 pm

Here's a freshly generated puzzle with one path through -- others?

Code: Select all: ......2.7.....914..5.2.....62.......4..576..1.......89.....4.5..846.....2.6...... 1389 4 139 | 138 6 5 | 2 39 7 378 6 2 | 378 38 9 | 1 4 5 1379 5 1379 | 2 4 137 | 89 6 38 --------------+-----------------+---------- 6 2 13 | 1389 1389 138 | 5 7 4 4 9 8 | 5 7 6 | 3 2 1 137 137 5 | 4 13 2 | 6 8 9 --------------+-----------------+---------- 1379 137 1379 | 138 2 4 | 78 5 6 5 8 4 | 6 139 137 | 79 139 2 2 137 6 | 13789 5 1378 | 4 139 38

Contradiction Net:
r2c5=3 r6c5=1
r2c5=3 r4c5=8 r8c5=9 r8c7=7 r3c7=9 r3c9=8 r9c9=3
r4c5=8 r4c4=9
[r6c5<>3 + r4c5<>3 + r4c4<>3] = r4c6=3
[r8c5<>3] + r4c6=3 [r8c6<>3] = r8c8=3
Cannot have two 3’s in box 9, ergo: r2c5<>3

Clear a couple of singles, then:
r3c7=8 r7c4=8 + r3c7=9 r1c3=9 r1c4=1 => r7c4<>1

SSTS to solve

Cheers...

- drac

by **daj95376** » Thu Jun 05, 2008 1:46 am

Code: Select all: ......2.7.....914..5.2.....62.......4..576..1.......89.....4.5..846.....2.6...... r3 b3 Locked Candidate 1 <> 8 [r3c16] r7 b7 Locked Candidate 1 <> 9 [r7c47] c36 X-Wing f/s <> 7 [r7c4] +-----------------------------------------------------------------------+ | 1389 4 139 | 138 6 5 | 2 39 7 | | 378 6 2 | 378 38 9 | 1 4 5 | | 1379 5 1379 | 2 4 137 | 89 6 38 | |-----------------------+-----------------------+-----------------------| | 6 2 13 | 1389 1389 138 | 5 7 4 | | 4 9 8 | 5 7 6 | 3 2 1 | | 137 137 5 | 4 13 2 | 6 8 9 | |-----------------------+-----------------------+-----------------------| | 1379 137 1379 | 138 2 4 | 78 5 6 | | 5 8 4 | 6 139 137 | 79 139 2 | | 2 137 6 | 13789 5 1378 | 4 139 38 | +-----------------------------------------------------------------------+

It can be solved with: chains, XYZ-Wings, and an XY-Chain; -or-

Contradiction Network: (sans side-effect eliminations)

Code: Select all: r1c8=3 r89c8=19 r8c7=7 r7c8=8 r7c4,r8c6=13 r8c5=9 r8c8=1 r8c6=3 r7c4=1 ... r2c5=3 / \ r1c4=8 contradiction! => [r1c8]<>3 \ / r9c4=7 r2c4=3

Singles to complete.

by **Draco** » Thu Jun 05, 2008 1:59 am

Nice network Danny; your new algorithm is really cranking 'em out!

Cheers...

- drac

by **daj95376** » Thu Jun 05, 2008 5:05 am

Draco wrote:Nice network Danny; your new algorithm is really cranking 'em out!

Actually, it's not from my new algorithm. In fact, it's from egg on my face in my previous solver. I implemented chains wrong in it and ended up with a great network generator. Unfortunately, it doesn't record the steps, so I have to manually recreate them if I want to use them.

The new algorithm doesn' have n-tuples and locked candidates capability, yet. However, it records the steps!!!

Cheers

by **hobiwan** » Thu Jun 05, 2008 10:17 am

Draco wrote:Here's a freshly generated puzzle with one path through -- others?

I tried to come up with an ALS-solution, but I still need one chain:

Almost Locked Set XZ-Rule: A=[r7c123] - {1379}, B=[r7c7],[r9c9] - {378}, X=7, Z=3 => [r9c2]<>3
Locked Candidates Type 1 (Pointing): 3 in b7 => [r7c4]<>3
Discontinuous Nice Loop r2c4 =7= r2c1 -7- r3c3 =7= r7c3 -7- r7c7 -8- r7c4 -1- r1c4 =1= r3c6 =7= r2c4 => r2c4<>3, r2c4<>8
Naked Single: [r2c4]=7
Almost Locked Set XY-Wing: A=[r3c679] - {1389}, B=[r7c47] - {178}, C=[r8c7] - {79}, Y,Z=7,9, X=1 => [r1c4],[r89c6]<>1
SSTS

The New Sudoku Players' Forum

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