The New Sudoku Players' Forum

by **udosuk** » Thu Apr 24, 2008 9:38 am

Everytime I open a new JSudoku window, it automatically generates a new vanilla puzzle (by default I didn't set any variant/killer options). Sometimes I play around a bit on those. This one attracted my attention because it's taken an extraordinary long time for me to kill off. In fact it takes the program no fewer than 18 advanced moves (e.g. fishes, chains) to solve it. I wonder can the experts here crack it with one or two elegant moves?

Code: Select all: 2...157.9 ......... 5.9.2...4 7.......2 6.289.3.1 ..1.6.... 9..14.6.. ......... 8.4.762.3

I did solve it, so post it in here instead of the "Help" section.

by **daj95376** » Thu Apr 24, 2008 6:04 pm

While you're waiting to hear from the experts, I found an amusing solution.

Code: Select all: +-----------------------+ | 2 . . | . 1 5 | 7 . 9 | | . . . | . . . | . . . | | 5 . 9 | . 2 . | . . 4 | |-------+-------+-------| | 7 . . | . . . | . . 2 | | 6 . 2 | 8 9 . | 3 . 1 | | . . 1 | . 6 . | . . . | |-------+-------+-------| | 9 . . | 1 4 . | 6 . . | | . . . | . . . | . . . | | 8 . 4 | . 7 6 | 2 . 3 | +-----------------------+ b9 Naked Triple <> 578 [r8c78],[r9c8] r3 b3 Locked Candidate 1 <> 1 [r3c2] c16 X-Wing f/s <> 4 [r6c4] Franken Swordfish ... take your pick 3-Fish c35b9\r478 F 021\300 <> 5 [r4c24],[r7c2],[r8c24] 3-Fish r569\c24b6 F 300\021 <> 5 [r4c24],[r7c2],[r8c24]

Code: Select all: *--------------------------------------------------------------------* | 2 3468 368 | 346 1 5 | 7 38 9 | | 134 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | |----------------------+----------------------+----------------------| | 7 3489 358 | 34 35 1 | 489 6 2 | | 6 *45 2 | 8 9 47 | 3 457 1 | |*34 34589 1 | 2357 6 2347 | 489 45789 578 | |----------------------+----------------------+----------------------| | 9 237 357 | 1 4 238 | 6 578 578 | |*13 12367 3567 | 239 358 2389 | 149 149 578 | | 8 *15 4 | 59 7 6 | 2 19 3 | *--------------------------------------------------------------------* XY-Chains using four (*) cells -- probably a continuous loop w/eliminations r4c2 <> 4 XY-Chain on [r5c2] r6c2 <> 4 XY-Chain on [r5c2] r6c2 <> 5 XY-Chain on [r5c2] r2c1 <> 3 XY-Chain on [r6c1] r4c2 <> 4 XY-Chain on [r6c1] r6c2 <> 4 XY-Chain on [r6c1] r8c2 <> 1 XY-Chain on [r8c1] r2c1 <> 3 XY-Chain on [r8c1] r8c2 <> 1 XY-Chain on [r9c2] r8c2 <> 1 XY-Chain on [r9c2] r6c2 <> 5 XY-Chain on [r9c2] r6c2 <> 5 XY-Chain on [r9c2]

Code: Select all: Empty Rectangle 2-Fish c1b8\r68 fF 011\200 <> 3 [r6c6] finned Franken Swordfish ... take your pick 3-Fish c16b4\r256 AF 021\300 <> 4 [r6c78] 3-Fish r14b4\c24b6 fF 201\021 <> 4 [r6c78]

Code: Select all: +-----------------------------------------------------------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | |-----------------------+-----------------------+-----------------------| | 7 389 358 | 34 35 1 | 489 6 2 | | 6 45 2 | 8 9 47 | 3 457 1 | | 34 389 1 | 2357 6 247 | 89 5789 578 | |-----------------------+-----------------------+-----------------------| | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 239 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +-----------------------------------------------------------------------+

followed by a short chain that leads to two contradictions.

Code: Select all: [r4c4]=3 [r4c5]=5 [r4c3]=8 [r4c2]=9 [r6c2]=3 [r6c1]=4 [r2c1]=1 [r8c1]=3 [r8c5]=8 ... [r2c5]=3 [r2c3]=7 [r7c3]=5 [r8c3]=6 [r1c3]=3 [r1c8]=8 [r3c7]=1 [r4c7]=4 ... [r8c7]=9 => ~[r9] & ~[b8] => [r4c3]<>3

by **Mage** » Fri Apr 25, 2008 10:41 am

Don't think I am really an expert, but here is my proposal, based on 3 AIC's :

After basic eliminations :

Code: Select all: +----------------------+----------------------+----------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | | 134 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +----------------------+----------------------+----------------------+ | 7 34589 358 | 345 35 1 | 489 6 2 | | 6 45 2 | 8 9 47 | 3 457 1 | | 34 34589 1 | 23457 6 2347 | 489 45789 578 | +----------------------+----------------------+----------------------+ | 9 2357 357 | 1 4 238 | 6 578 578 | | 13 123567 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +----------------------+----------------------+----------------------+

1) an AIC loop : (5=4)r5c2 - (4=3)r6c1 - (3=1)r8c1 - (1=5)r9c2

=> r2c1<>3, r46c2<>4, r4678c2<>5, r8c2<>1, wich leads to :

Code: Select all: +-------------------+-------------------+-------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 358 | 345 35 1 | 489 6 2 | | 6 45 2 | 8 9 47 | 3 457 1 | | 34 389 1 | 23457 6 2347 | 489 45789 578 | +-------------------+-------------------+-------------------+ | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +-------------------+-------------------+-------------------+

2) the second AIC : (5=4)r5c2 - (4)r1c2=(4)r1c4 - (4)r4c4=(35)r4c45

=> r4c3<>5 => r5c2=5, r6c1=4,...

Code: Select all: +----------------+----------------+----------------+ | 2 3468 368 | 46 1 5 | 7 38 9 | | 1 478 78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +----------------+----------------+----------------+ | 7 389 38 | 34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +----------------+----------------+----------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +----------------+----------------+----------------+

3) the last AIC : (8=7)r3c6 - (7=4)r5c6 - (4=3)r4c4 - (3)r4c3 = (3)r1c3 - (3=8)r1c8

=> r3c78<>8 => r3c7=1 and singles to the end.

edited Thanks to udosuk for pointing my typos.

by **udosuk** » Fri Apr 25, 2008 7:56 pm

Danny, everything was decent in your solution except the final chain - it's way too "cannibalistic".

Mage, it seems your 3rd move need to be corrected:

Mage wrote:
Code: Select all
+----------------+----------------+----------------+ | 2 3468 368 | 46 1 5 | 7 38 9 | | 1 478 78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +----------------+----------------+----------------+ | 7 389 38 | 34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +----------------+----------------+----------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +----------------+----------------+----------------+

3) the last AIC : (8=7)r3c6 - (7=4)r5c6 - (4=3)r4c4 - (3)r4c2 = (3)r1c2 - (3=8)r1c8

It should be (8=7)r3c6 - (7=4)r5c6 - (4=3)r4c4 - (3)r4c3 = (3)r1c3 - (3=8)r1c8

Great solution. I like it, but hopefully can change all those AICs into ALS-like moves later. :idea:

by **udosuk** » Sat Apr 26, 2008 2:55 pm

It seems Danny has deleted his latest post here for some reasons? :?:

Anyway:

I wrote:Great solution. I like it, but hopefully can change all those AICs into ALS-like moves later.

Desperately needing closure, I applied a "generalised ALS-xyz-wing" to replace the last AIC, and added one turbot fish & one xy-wing to complete the solving route. But at least it looks elegant enough to me. Here goes:

Code: Select all: +-------------------------+-------------------------+-------------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | |-134 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +-------------------------+-------------------------+-------------------------+ | 7 -34589 358 | 345 35 1 | 489 6 2 | | 6 *45 2 | 8 9 47 | 3 457 1 | |*34 -34589 1 | 23457 6 2347 | 489 45789 578 | +-------------------------+-------------------------+-------------------------+ | 9 -2357 357 | 1 4 238 | 6 578 578 | |*13 -123567 3567 | 2359 358 2389 | 149 149 578 | | 8 *15 4 | 59 7 6 | 2 19 3 | +-------------------------+-------------------------+-------------------------+

Quad ALS-xz (xy-ring?)

ALS A: r68c1 = {134}
ALS B: r59c2 = {145}
restricted common: x = 4 (r5c2+r6c1)
common: z = 1 (r8c1+r9c2)
=> r8c2, seeing r8c1+r9c2, can't be 1

ALS A: r68c1 = {134}
ALS B: r59c2 = {145}
restricted common: x = 1 (r8c1+r9c2)
common: z = 4 (r5c2+r6c1)
=> r46c2, seeing r5c2+r6c1, can't be 4

ALS A: r5c2+r6c1 = {345}
ALS B: r8c1+r9c2 = {135}
restricted common: x = 3 (r68c1)
common: z = 5 (r59c2)
=> r4678c2, seeing r59c2, can't be 5

ALS A: r5c2+r6c1 = {345}
ALS B: r8c1+r9c2 = {135}
restricted common: x = 5 (r59c2)
common: z = 3 (r68c1)
=> r2c1, seeing r68c1, can't be 3

Code: Select all: +----------------------+----------------------+----------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +----------------------+----------------------+----------------------+ | 7 *389 *358 |#345 #35 1 | 489 6 2 | | 6 45 2 | 8 9 47 | 3 457 1 | |*34 *389 1 |-23457 6 -2347 | 489 45789 578 | +----------------------+----------------------+----------------------+ | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +----------------------+----------------------+----------------------+

ALS-xz:

ALS A: r4c23+r6c12 = {34589}
ALS B: r4c45 = {345}
restricted common: x = 5 (r4c345)
common: z = 4 (r4c4+r6c1)
=> r6c46, seeing r4c4+r6c1, can't be 4

Code: Select all: +----------------------+----------------------+----------------------+ | 2 *3468 368 |*346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 *34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +----------------------+----------------------+----------------------+ | 7 389 358 | 345 35 1 | 489 6 2 | | 6 -45 2 | 8 9 *47 | 3 457 1 | | 34 389 1 | 2357 6 237 | 489 45789 578 | +----------------------+----------------------+----------------------+ | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +----------------------+----------------------+----------------------+

Turbot fish on 4:

One of r1c24 must be 4, one of r25c6 must be 4
r1c4+r2c6 can't be both 4
=> One or both of r1c2+r5c6 must be 4
=> r5c2, seeing r1c2+r5c6, can't be 4

After singles:

Code: Select all: +-------------------+-------------------+-------------------+ | 2 *3468 -368 |*46 1 5 | 7 *38 9 | | 1 #478 #78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 @38 |@34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+

Generalised ALS-xyz-wing:

ALS A: r1c248 = {3468}
ALS B: r2c23 = {478}
ALS C: r4c34 = {348}
restricted common between A & B+C: x=y=4 (r12c2+r14c4)
common among A+B+C: z=8 (r1c28+r2c2+r4c3)
=> r1c3, seeing r1c28+r2c2+r4c3, can't be 8

Code: Select all: +-------------------+-------------------+-------------------+ | 2 3468 *36 |*46 1 5 | 7 38 9 | | 1 478 78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 -38 |*34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+

XY-wing @ r14c34:

r1c4=4|6
If r1c4=4 => r4c4=3
If r1c4=6 => r1c3=3
=> r4c3, seeing r1c3+r4c4, can't be 3

The rest are naked singles. :idea:

by **daj95376** » Sat Apr 26, 2008 7:22 pm

Withdrawn: Unable to convert my notation into NL notation.

by **Draco** » Sat Apr 26, 2008 11:58 pm

I am most certainly not an expert, but have a solution to suggest whilst awaiting word from one.

After STSS (2 color chain exclusions, no fish to get here):

Code: Select all: 2 3468 368 | 346 1 5 | 7 38 9 134 13478 378 | 3479 38 34789 | 5 2 6 5 3678 9 | 367 2 378 | 18 138 4 ----------------+----------------+-------------- 7 3489 358 | 345 35 1 | 489 6 2 6 45 2 | 8 9 47 | 3 457 1 34 34589 1 | 2357 6 2347 | 489 45789 578 ----------------+----------------+-------------- 9 2357 357 | 1 4 238 | 6 578 578 13 123567 3567 | 2359 358 2389 | 149 149 578 8 15 4 | 59 7 6 | 2 19 3

Mike or Danny - pls tell me if I inferred incorrectly, but I think the use of ~ means both squares contain the value? That is how I am using it in the first chain:

Chain 1: r9c2=5=r9c4 and r9c2~5~r4c3 ==> r4c4<>5
Chain 2: r1c2-4-r5c2 and r1c4-4-r4c4-3-r4c5 ==> r4c3<>5
STSS (singles + 1 locked set)
Chain 3: r1c8-3-r1c3=3=r4c3-3-r1c4 and r1c8=3=r3c8=1=r3c7-1-r8c7 ==> r4c7<>4
Singles to Solve

by **daj95376** » Sun Apr 27, 2008 1:00 am

Draco, (an example)

Code: Select all: [r4c3]~2~[r4c8]

means that [r4c3] needs to be 2, but isn't because [r4c8]=2 occurred earlier and prevented it. Therefore, [r4c8]<>2 must follow. Most users would probably write [r4c3]-2-[r4c8].

===== ===== ===== ===== ===== =====

Side Note: Would someone please remind me how you express the following implication chain in NL notation. That's what forced me to withdraw my post a couple of messages back.

Code: Select all: [r8c4]=3 => [r8c4]<>2 => [r6c4]=2 => [r6c4]<>5 => [r9c4]=5

TIA!!!

by **udosuk** » Sun Apr 27, 2008 1:11 pm

daj95376 wrote:Side Note: Would someone please remind me how you express the following implication chain in NL notation. That's what forced me to withdraw my post a couple of messages back.

Code: Select all
[r8c4]=3 => [r8c4]<>2 => [r6c4]=2 => [r6c4]<>5 => [r9c4]=5

I'm no expert in Nice-Loop notation. Had a look in the Sudopedia page:

http://www.sudopedia.org/wiki/Nice_Loop

Could be something like this?

Code: Select all: [r8c4]=2=[r6c4]=5=[r9c4]

Not sure what you can deduce from this though. :?:

Heck the more I dwell on this puzzle the more I feel about the inadequacy of ALS-xz.

From this position:

Code: Select all: +-------------------+-------------------+-------------------+ | 2 3468 *368 |@46 1 5 | 7 38 9 | | 1 478 -78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 *38 |@34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+

It's so simple that:

r2c3=8 => r14c3=[63] => r14c4=[44] => contradiciton

But even this little elimination involving 5 cells can't be described as an ALS-xz deduction.

I keep on looking for a simple ALS-xz move to advance from that position, but it's so frustrating.

I guess I have to settle for the "generalised ALS-xyz-wing" above. Like someone recently said in this forum, life is too short for these.

Draco wrote:Chain 3: r1c8-3-r1c3=3=r4c3-3-r1c4 and r1c8=3=r3c8=1=r3c7-1-r8c7 ==> r4c7<>4

Don't understand what you mean by this. :?:

Care to elaborate in plain logic?

by **hobiwan** » Sun Apr 27, 2008 5:32 pm

udosuk wrote:But even this little elimination involving 5 cells can't be described as an ALS-xz deduction.

I cant find a move for [r2c8]<>8 too, but if you really want to use ALS-XZ you can use the following:

Almost Locked Set XZ-Rule: A=[r2478c3] - {35678}, B=[r14c4] - {346}, X=3, Z=6 => [r1c3]<>6
Singles
Naked Pair: 3,8 in [r1c38] => [r1c2]<>3, [r1c2]<>8
W-Wing: 8/7 in [r3c6],[r7c8] verbunden durch 7 in [r5c68] => [r3c8]<>8
Finned Swordfish: 8 r236 c267 f[r6c9] => [r4c7]<>8
Locked Candidates Type 1 (Pointing): 8 in b6 => [r6c2]<>8
W-Wing: 7/8 in [r3c6],[r6c9] verbunden durch 8 in [r36c7] => [r6c6]<>7
Singles
Almost Locked Set XZ-Rule: A=[r3c78] - {138}, B=[r6c27] - {389}, X=8, Z=3 => [r3c2]<>3
Puzzle solved

Not the easiest path, I know...

by **Mage** » Sun Apr 27, 2008 7:12 pm

hobiwan wrote:
udosuk wrote:From this position:
Code: Select all
+-------------------+-------------------+-------------------+ | 2 3468 *368 |@46 1 5 | 7 38 9 | | 1 478 -78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 *38 |@34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+
It's so simple that:

r2c3=8 => r14c3=[63] => r14c4=[44] => contradiciton

But even this little elimination involving 5 cells can't be described as an ALS-xz deduction.

I cant find a move for [r2c2]<>8 too, but if you really want to use ALS-XZ you can use the following:

Almost Locked Set XZ-Rule: A=[r2478c3] - {35678}, B=[r14c4] - {346}, X=3, Z=6 => [r1c3]<>6...

Her is as small AIC+ALS that does the job :
(8=3)r4c3 - (3=4)r4c4 - (4=6)r1c4 - (6)r1c3=(38)r14c3 => r2c3<>8

It should be possible to translate that in NL/ALS form...

by **daj95376** » Sun Apr 27, 2008 7:17 pm

udosuk wrote:From this position:
Code: Select all
+-------------------+-------------------+-------------------+ | 2 3468 *368 |@46 1 5 | 7 38 9 | | 1 478 -78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 *38 |@34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 57 | 1 4 3 | 6 578 578 | | 3 67 567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+

I don't know ALS-anything, but you might consider attacking it from:

Code: Select all: [r1c3]=6 => [r4c3]=3 => [r14c4]=4 contradiction!

[r1c3]<>6 will advance the PM through several SSTS moves.

by **udosuk** » Mon Apr 28, 2008 2:25 am

Thanks guys & gals!

hobiwan's nice move on r1c3 cracks it, which is echoed by Danny's (daj95376) observation. Mage, although your AIC+ALS isn't exactly what I'm looking for, your previous contributions laid down the ground work for this solution. All in all a great collaborative effort. I can leave this little firecracker in peace now.

Here is the complete walkthrough, one quad-ALS-xz + three ALS-xz's + one turbot fish + basic moves:

The complete walkthrough I wrote:Original puzzle:
Code: Select all
+---+---+---+ |2..|.15|7.9| |...|...|...| |5.9|.2.|..4| +---+---+---+ |7..|...|..2| |6.2|89.|3.1| |..1|.6.|...| +---+---+---+ |9..|14.|6..| |...|...|...| |8.4|.76|2.3| +---+---+---+

After basic moves (singles, subsets, locked candidates):
Code: Select all
+------------------------+------------------------+------------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | |-134 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +------------------------+------------------------+------------------------+ | 7 -34589 358 | 345 35 1 | 489 6 2 | | 6 *45 2 | 8 9 47 | 3 457 1 | |*34 -34589 1 | 23457 6 2347 | 489 45789 578 | +------------------------+------------------------+------------------------+ | 9 -2357 357 | 1 4 238 | 6 578 578 | |*13 -123567 3567 | 2359 358 2389 | 149 149 578 | | 8 *15 4 | 59 7 6 | 2 19 3 | +------------------------+------------------------+------------------------+

Quad ALS-xz (xy-ring)

ALS A: r68c1 = {134}
ALS B: r59c2 = {145}
restricted common: x = 4 (r5c2+r6c1)
common: z = 1 (r8c1+r9c2)
=> r8c2, seeing r8c1+r9c2, can't be 1

ALS A: r68c1 = {134}
ALS B: r59c2 = {145}
restricted common: x = 1 (r8c1+r9c2)
common: z = 4 (r5c2+r6c1)
=> r46c2, seeing r5c2+r6c1, can't be 4

ALS A: r5c2+r6c1 = {345}
ALS B: r8c1+r9c2 = {135}
restricted common: x = 3 (r68c1)
common: z = 5 (r59c2)
=> r4678c2, seeing r59c2, can't be 5

ALS A: r5c2+r6c1 = {345}
ALS B: r8c1+r9c2 = {135}
restricted common: x = 5 (r59c2)
common: z = 3 (r68c1)
=> r2c1, seeing r68c1, can't be 3
Code: Select all
+----------------------+----------------------+----------------------+ | 2 3468 368 | 346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +----------------------+----------------------+----------------------+ | 7 *389 *358 |#345 #35 1 | 489 6 2 | | 6 45 2 | 8 9 47 | 3 457 1 | |*34 *389 1 |-23457 6 -2347 | 489 45789 578 | +----------------------+----------------------+----------------------+ | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +----------------------+----------------------+----------------------+

ALS-xz:

ALS A: r4c23+r6c12 = {34589}
ALS B: r4c45 = {345}
restricted common: x = 5 (r4c345)
common: z = 4 (r4c4+r6c1)
=> r6c46, seeing r4c4+r6c1, can't be 4
Code: Select all
+----------------------+----------------------+----------------------+ | 2 *3468 368 |*346 1 5 | 7 38 9 | | 14 13478 378 | 3479 38 *34789 | 5 2 6 | | 5 3678 9 | 367 2 378 | 18 138 4 | +----------------------+----------------------+----------------------+ | 7 389 358 | 345 35 1 | 489 6 2 | | 6 -45 2 | 8 9 *47 | 3 457 1 | | 34 389 1 | 2357 6 237 | 489 45789 578 | +----------------------+----------------------+----------------------+ | 9 237 357 | 1 4 238 | 6 578 578 | | 13 2367 3567 | 2359 358 2389 | 149 149 578 | | 8 15 4 | 59 7 6 | 2 19 3 | +----------------------+----------------------+----------------------+

Turbot fish on 4:

One of r1c24 must be 4, one of r25c6 must be 4
r1c4+r2c6 can't be both 4
=> One or both of r1c2+r5c6 must be 4
=> r5c2, seeing r1c2+r5c6, can't be 4

After singles:
Code: Select all
+-------------------+-------------------+-------------------+ | 2 3468 -368 |*46 1 5 | 7 38 9 | | 1 478 #78 | 479 3 4789 | 5 2 6 | | 5 3678 9 | 67 2 78 | 18 138 4 | +-------------------+-------------------+-------------------+ | 7 389 #38 |*34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 578 578 | +-------------------+-------------------+-------------------+ | 9 2 #57 | 1 4 3 | 6 578 578 | | 3 67 #567 | 29 8 29 | 14 14 57 | | 8 1 4 | 5 7 6 | 2 9 3 | +-------------------+-------------------+-------------------+

ALS-xz:

ALS A: r14c4 = {346}
ALS B: r2478c3 = {35678}
restricted common: x = 3 (r4c34)
common: z = 6 (r1c4+r8c3)
=> r1c3, seeing r1c4+r8c3, can't be 6

After singles and naked pair r1c38={38} @ r1:
Code: Select all
+----------------+----------------+----------------+ | 2 *46 *38 |#46 1 5 | 7 38 9 | | 1 *48 7 | 49 3 489 | 5 2 6 | | 5 368 9 | 67 2 78 | 18 138 4 | +----------------+----------------+----------------+ | 7 389 -38 |#34 5 1 | 489 6 2 | | 6 5 2 | 8 9 47 | 3 47 1 | | 4 389 1 | 237 6 27 | 89 5 78 | +----------------+----------------+----------------+ | 9 2 5 | 1 4 3 | 6 78 78 | | 3 7 6 | 29 8 29 | 14 14 5 | | 8 1 4 | 5 7 6 | 2 9 3 | +----------------+----------------+----------------+

ALS-xz:

ALS A: r1c23+r2c2={3468}
ALS B: r14c4={346}
restricted common: x = 6 (r1c24)
common: z = 3 (r1c3+r4c4)
=> r4c3, seeing r1c3+r4c4, can't be 3

The rest are naked singles.

by **Draco** » Mon Apr 28, 2008 7:38 am

udosuk wrote:
Draco wrote:Chain 3: r1c8-3-r1c3=3=r4c3-3-r1c4 and r1c8=3=r3c8=1=r3c7-1-r8c7 ==> r4c7<>4

Don't understand what you mean by this. Care to elaborate in plain logic?

Whoops, sorry. There was a typo in that. Should've been Chain 3: r1c8-3-r1c3=3=r4c3-3-r4c4 and r1c8=3=r3c8=1=r3c7-1-r8c7 ==> r4c7<>4.

I noticed the typo only after I reread my initial reply and found the SAME typo (sigh -- typo's left in place and BOLDED -- the 1's should be 4's. Apologies for any confusion (especially my own):

After Chain 2 & STSS the PMs are:

Code: Select all: 2 3468 368 | 46 1 5 | 7 38 9 1 478 78 | 479 3 4789 | 5 2 6 5 3678 9 | 67 2 78 | 18 138 4 -----------+------------+------------ 7 389 38 | 34 5 1 | 489 6 2 6 5 2 | 8 9 47 | 3 47 1 4 389 1 | 237 6 27 | 89 578 578 -----------+------------+------------ 9 2 57 | 1 4 3 | 6 578 578 3 67 567 | 29 8 29 | 14 14 57 8 1 4 | 5 7 6 | 2 9 3

Working from the bi-value square at r1c8, there are 2 chains. The first one (I'll stay away from NL notation in case I messed up the transcription) is:

r1c8=3 --> r1c3<>3 --> r4c3=3 --> r1c4=4

This yields the first 4 we need to show r4c7<>4. The second chain:

r1c8=8 --> r3c8=3 --> r3c7=1 -->r8c7=4

This yields the second 4 intersecting with r4c7, so we can state that r4c7<>4 and the puzzle is reduced to singles.

Was my use of r1c8-3-r1c3=3=r4c3-3-r1c4 a misuse of NL notation (I like to use NL notation even though I focus on forcing chains)?

Cheers...

- drac

[edit : added notes on repeated typo's]

by **udosuk** » Mon Apr 28, 2008 8:16 am

Okay, thanks Draco, I understand your move now. The typos (r1c4 should be r4c4 instead) were the culprits.

Draco wrote:The second chain:

r1c8=8 --> r3c8=3 --> r3c7=1 -->r8c7=4

This yields the second 4 intersecting with r4c7, so we can state that r4c7<>4 and the puzzle is reduced to singles.

Isn't it more direct that r1c8=8 immediately force r3c7=1? The strong link placement on r3c8 isn't really required here.

So, to cap off your 2 "chains" in Nice-Loop notation ("chains" in quotes because I ain't expert for these and not sure if they're legitimate nice-loops), here I try to write them out myself:

Chain 3a: [r1c8]-3-[r1c3]=3=[r4c3]-3|4=[r4c4]
Chain 3b: [r1c8]-8|1=[r3c7]-1|4=[r8c7]
=> one or both of r4c4+r8c7 must be 4 => r4c7 can't be 4

Any corrector please?

The New Sudoku Players' Forum

A very hard puzzle produced from JSudoku

A very hard puzzle produced from JSudoku