The New Sudoku Players' Forum

by **Draco** » Mon Jun 16, 2008 6:10 am

Here's one that my solver rates as pretty hard, SE gives a 7.3 and both need several forcing chains (16 if I recall SE's list correctly, 20 for my solver if I let it go after short chains first, which I tend to do) to solve.

Any one able to bring some brevity to this situation, please chime in! The solution I have so no need for that (just in case submacrolize reads this thread). PMs after SSTS applied:

Code: Select all: .......91..48.1....6...534....4...89....5....29...6....872...3....6.75..62....... 378 357 235 | 37 23467 234 | 2678 9 1 379 37 4 | 8 23679 1 | 267 2567 2567 1789 6 1289 | 79 279 5 | 3 4 278 ----------------+-----------------+---------------- 137 1357 1356 | 4 237 23 | 1267 8 9 13478 1347 1368 | 1379 5 2389 | 1267 1267 2367 2 9 138 | 137 378 6 | 147 157 3457 ----------------+-----------------+---------------- 5 8 7 | 2 149 49 | 1469 3 46 1349 134 139 | 6 1389 7 | 5 12 28 6 2 139 | 5 13489 3489 | 14789 17 478

Cheers...

- drac

by **daj95376** » Mon Jun 16, 2008 8:27 am

There's probably a shorter solution, but I worked hard enough on this one that you're going to get the whole solution.

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

Code: Select all: c5b8 Locked Candidate 1 <> 1 [r4c5],[r6c5] r5 b4 Locked Candidate 1 <> 4 [r5c79] r8 b7 Locked Candidate 1 <> 4 [r8c59] r2 b3 Locked Candidate 1 <> 5 [r2c2] r6 b6 Locked Candidate 1 <> 5 [r6c3] c167 Swordfish f/s <> 8 [r1c3] -or- r368 Swordfish f/s <> 8 [r1c3] +-----------------------------------------------------------------------+ | 378 357 235 | 37 23467 234 | 2678 9 1 | | 379 37 4 | 8 23679 1 | 267 2567 2567 | | 1789 6 1289 | 79 279 5 | 3 4 278 | |-----------------------+-----------------------+-----------------------| | 137 1357 1356 | 4 237 23 | 1267 8 9 | | 13478 1347 1368 | 1379 5 2389 | 1267 1267 2367 | | 2 9 138 | 137 378 6 | 147 157 3457 | |-----------------------+-----------------------+-----------------------| | 5 8 7 | 2 149 49 | 1469 3 46 | | 1349 134 139 | 6 1389 7 | 5 12 28 | | 6 2 139 | 5 13489 3489 | 14789 17 478 | +-----------------------------------------------------------------------+ r5c6 =8= r9c6 -8- r9c7 =8= r1c7 =6= r1c5 =4= r1c6 -4- r7c6 -9- r5c6 => [r5c6]<>9 ___________________________________________________________________________________

Code: Select all: c9 Naked Pair <> 28 [r2c9],[r5c9],[r9c9] c5b2 Locked Candidate 1 <> 9 [r7c5],[r8c5],[r9c5] r8 b7 Locked Candidate 2 <> 9 [r9c3] +-----------------------------------------------------------------------+ | 78 57 25 | 3 246 24 | 2678 9 1 | | 379 37 4 | 8 269 1 | 267 2567 567 | | 189 6 1289 | 7 29 5 | 3 4 28 | |-----------------------+-----------------------+-----------------------| | 137 1357 1356 | 4 237 23 | 1267 8 9 | | 13478 1347 1368 | 9 5 238 | 1267 1267 367 | | 2 9 38 | 1 378 6 | 47 57 3457 | |-----------------------+-----------------------+-----------------------| | 5 8 7 | 2 14 49 | 1469 3 46 | | 1349 134 139 | 6 138 7 | 5 12 28 | | 6 2 13 | 5 1348 3489 | 14789 17 47 | +-----------------------------------------------------------------------+ 2- r1c6 -4- r7c6 -9- r7c8 =9= r9c7 =8= r1c7 -8- r3c9 -2 => [r3c5]<>2 _______________________________________________________________________

Code: Select all: r1 b1 Locked Candidate 1 <> 7 [r1c7] +-----------------------------------------------------------------------+ | 78 57 25 | 3 246 24 | 268 9 1 | | 9 3 4 | 8 26 1 | 267 2567 567 | | 18 6 128 | 7 9 5 | 3 4 28 | |-----------------------+-----------------------+-----------------------| | 137 157 1356 | 4 237 23 | 1267 8 9 | | 13478 147 1368 | 9 5 238 | 1267 1267 367 | | 2 9 38 | 1 378 6 | 47 57 3457 | |-----------------------+-----------------------+-----------------------| | 5 8 7 | 2 14 49 | 1469 3 46 | | 134 14 9 | 6 138 7 | 5 12 28 | | 6 2 13 | 5 1348 3489 | 14789 17 47 | +-----------------------------------------------------------------------+ r5c6 =8= r6c5 -8- r6c3 -3- r6c9 =3= r5c9 -3- r5c6 => [r5c6]<>3 _________________________________________________________________

Code: Select all: c36 X-Wing f/s <> 3 [r4c1] c1 Naked Triple <> 178 [r5c1],[r8c1] c3b4 Locked Candidate 1 <> 8 [r3c3] XYZ-Wing [r4c2]/[r1c2]+[r4c1] <> 7 [r5c2] XYZ-Wing [r5c2]/[r4c1]+[r8c2] <> 1 [r4c2] r4 b4 Locked Candidate 1 <> 7 [r4c57] r4 b5 Naked Pair <> 23 [r4c37] 3-Fish c28b7\r589 AF 021\300 <> 1 [r8c5] +--------------------------------------------------------------+ | 78 57 25 | 3 246 24 | 268 9 1 | | 9 3 4 | 8 26 1 | 267 267 5 | | 18 6 12 | 7 9 5 | 3 4 28 | |--------------------+--------------------+--------------------| | 17 57 156 | 4 23 23 | 16 8 9 | | 34 14 136 | 9 5 8 | 1267 1267 67 | | 2 9 8 | 1 7 6 | 4 5 3 | |--------------------+--------------------+--------------------| | 5 8 7 | 2 14 49 | 169 3 46 | | 34 14 9 | 6 38 7 | 5 12 28 | | 6 2 13 | 5 1348 349 | 1789 17 47 | +--------------------------------------------------------------+ r9c6 =9= r9c7 =8= r8c9 -8- r8c5 -3- r9c6 => [r9c6]<>3 ________________________________________________________

The 1st, 3rd, and 4th chains are forcing chains w/o the obvious companion statement.

by **Draco** » Tue Jun 17, 2008 1:52 am

Danny,

Hard work indeed; thanks for taking the time to detail it!

Cheers...

- drac

by **daj95376** » Fri Jun 20, 2008 7:17 am

Since Draco started the thread, I hope it's okay to add to it.

I've added some logic to my chains routine to (hopefully) help me decide which chains are more productive than others. However, I often run into a wall where multiple chains are needed and none stand out. For example:

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

Code: Select all: +-----------------------------------------------------------------------+ | 2 4 5 | 178 368 1678 | 1369 139 169 | | 13 9 8 | 5 2 16 | 136 4 7 | | 6 7 13 | 19 39 4 | 5 8 2 | |-----------------------+-----------------------+-----------------------| | 37 5 39 | 68 1 89 | 679 2 4 | | 17 6 19 | 2 4 5 | 8 79 3 | | 4 8 2 | 69 7 3 | 169 5 169 | |-----------------------+-----------------------+-----------------------| | 589 3 4 | 1789 5689 16789 | 2 179 189 | | 589 1 7 | 3 589 2 | 4 6 89 | | 89 2 6 | 4 89 17 | 137 137 5 | +-----------------------------------------------------------------------+

Code: Select all: { 1} -8r4c4 8r4c6 9r7c6 8r9c5 [chain__5] <> 8 [r7c4] { 5} -3r2c7 3r2c1 7r4c1 7r9c7 3r9c8 [chain__5] <> 3 [r1c8],[r9c7] { 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] { 1} -9r3c4 1r3c4 1r5c3 9r4c3 9r7c6 [chain__5] <> 9 [r7c4] { 1} -9r4c6 9r6c4 1r3c4 1r5c3 9r5c8 [chain__5] <> 9 [r4c7] { 1} -6r7c5 6r1c5 6r6c9 9r6c4 9r3c5 -9r7c5 [chain__2] <> 9 [r7c5] { 1} -3r9c8 3r1c8 3r2c1 1r5c1 7r5c8 -7r9c8 [chain__2] <> 7 [r9c8] { 1} -6r1c9 6r6c9 9r6c4 9r7c6 9r8c9 -9r1c9 [chain__2] <> 9 [r1c9] { 15} -1r3c4 1r3c3 1r5c1 7r4c1 7r9c7 1r9c6 [chain__5] <> 1 [r12c6],[r7c4] { 10} -6r2c6 6r2c7 6r4c4 8r4c6 9r7c6 6r7c5 [chain__5] <> 6 [r1c5],[r7c6] { 2} 1r9c8 7r9c6 7r4c7 3r4c1 3r2c7 3r9c8 [chain__9] <> 1 [r9c8] { 1} 8r7c5 9r9c5 9r3c4 6r6c4 6r1c9 6r7c5 [chain__9] <> 8 [r7c5] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6] { 1} -5r8c5 5r7c5 6r1c5 6r6c9 9r6c4 9r3c5 -9r8c5 [chain__2] <> 9 [r8c5] { 1} -5r7c1 5r7c5 6r1c5 6r6c9 9r6c4 9r7c6 -9r7c1 [chain__2] <> 9 [r7c1] { 1} 6r1c7 6r4c4 9r6c4 1r3c4 1r5c3 9r5c8 9r1c7 [chain__9] <> 6 [r1c7] { 1} 8r8c5 9r9c5 9r3c4 6r6c4 6r1c9 6r7c5 5r8c5 [chain__9] <> 8 [r8c5] _____________________________________________________________________________________

Note: the chain__5 chains are really forcing chains, but of the most basic format where one implication stream is trivial. Otherwise, I'm not using forcing chains to resolve the puzzle.

What's the smallest number of chains from this list that will render the puzzle solvable through Singles?

[Edit: added specific chains and added/reworded last paragraphs.]

by **eleven** » Fri Jun 20, 2008 8:07 am

I dont know, but you should not miss the MUG 589 in r789c15, so r7c5 must be 6.

by **hobiwan** » Fri Jun 20, 2008 1:32 pm

daj95376 wrote:What's the smallest number of chains in this PM that, when their eliminations are combined, will render the puzzle solvable through Singles?

If the chains can be done sequentially I am down to two:

Code: Select all: Forcing Chain Contradiction in b8 r9c6=1 r6c4=9 r3c4=1 r7c4<>1 / r9c6<>1 r9c6=7 r4c7=7 r4c4=6 \ r4c6=8 r7c6=9 r7c6<>1 Discontinuous Nice Loop r4c7 -7- r4c1 -3- r2c1 =3= r2c7 -3- r9c7 -7- r4c7 => r4c7<>7 Singles

If all chains have to come from the original pm I'll have to look again.

by **daj95376** » Fri Jun 20, 2008 5:04 pm

eleven wrote:I dont know, but you should not miss the MUG 589 in r789c15, so r7c5 must be 6.

Thanks for the feedback!

I don't understand MUGs, but the recent messages on the topic caused that pattern of 589 to jump out at me. I didn't know (for sure) what to do with it, but I guessed and tested [r7c5]=6 ... and Simple Sudoku allowed it!

by **daj95376** » Fri Jun 20, 2008 5:08 pm

hobiwan wrote:If all chains have to come from the original pm I'll have to look again.

Nice solution hobiwan!

I'm sorry for not providing enough information. I've updated my original message and hope that my goal is now more specific. I know that the combined effect of my chains reduces the PM to Singles. What I'm having a difficult time doing is finding a (descent) subset of them that'll do the same thing.

by **hobiwan** » Mon Jun 23, 2008 5:38 pm

I don't know whether you are still interested, but this is the best I could find:

Code: Select all: { 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] 1 XY-Chain, 1 W-Wing, 1 Finned X-Wing { 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6] 1 W-Wing, 1 Finned X-Wing { 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6] { 5} -3r2c7 3r2c1 7r4c1 7r9c7 3r9c8 [chain__5] <> 3 [r1c8],[r9c7] 1 Skyscraper { 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6] { 5} -3r2c7 3r2c1 7r4c1 7r9c7 3r9c8 [chain__5] <> 3 [r1c8],[r9c7] { 15} -1r3c4 1r3c3 1r5c1 7r4c1 7r9c7 1r9c6 [chain__5] <> 1 [r12c6],[r7c4] Singles

[Edit: copied wrong chain in last example, thanks daj95376]

by **Draco** » Mon Jun 23, 2008 7:16 pm

Danny,

Always enjoy more puzzles... glad you "hijacked" this.

I don't have chains for your PM's to crack to singles, but I do have a single contradiction net. Perhaps someone else can reduce this to a nice loop or two:

r4c6=8 r6c4=9 r3c4=1 r3c5=9 r1c5=3
r4c6=8 r7c6=9 r9c5=8
r4c6=8 [r1c6<>8] + r9c5=8 [r1c5<>8] = r1c4=8 r7c4=7 r9c6=1
r3c5=9 r4c1=3 r4c7=7
r3c5=9 r2c7=3 [r9c7<>3] r9c8=3
[r9c6<>7 + r9c8<>7] = r9c7=7

r4c6<>8

Singles to solve.

Cheers...

- drac

by **daj95376** » Mon Jun 23, 2008 11:56 pm

hobiwan wrote:I don't know whether you are still interested, but this is the best I could find:
Code: Select all
{ 13} -6r1c9 6r6c9 9r6c4 1r3c4 6r2c6 [chain__5] <> 6 [r1c56],[r2c7] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6] { 5} -3r2c7 3r2c1 7r4c1 7r9c7 3r9c8 [chain__5] <> 3 [r1c8],[r9c7] { 1} -6r7c5 6r1c5 6r6c9 9r6c4 9r3c5 -9r7c5 [chain__2] <> 9 [r7c5] _____________________________________________________________________________________

Nice try hobiwan. Yes, I'm still interested. However, don't you still need ...

Code: Select all: *-----------------------------------------------------------* | 2 4 5 | 178 38 178 | 1369 19 169 | | 13 9 8 | 5 2 6 | 13 4 7 | | 6 7 13 | 19 39 4 | 5 8 2 | |-------------------+-------------------+-------------------| | 37 5 39 | 68 1 89 | 679 2 4 | | 17 6 19 | 2 4 5 | 8 79 3 | | 4 8 2 | 69 7 3 | 169 5 169 | |-------------------+-------------------+-------------------| | 5 3 4 | 1789 6 789 | 2 179 189 | | 89 1 7 | 3 5 2 | 4 6 89 | | 89 2 6 | 4 89 17 | 17 3 5 | *-----------------------------------------------------------* { 15} -1r3c4 1r3c3 1r5c1 7r4c1 7r9c7 1r9c6 [chain__5] <> 1 [r12c6],[r7c4]

I hate to admit this

, but your missing chain led to ...

Code: Select all: { 5} -3r2c7 3r2c1 7r4c1 7r9c7 3r9c8 [chain__5] <> 3 [r1c8],[r9c7] { 15} -1r3c4 1r3c3 1r5c1 7r4c1 7r9c7 1r9c6 [chain__5] <> 1 [r12c6],[r7c4] { 1} -9r7c6 9r4c6 3r4c3 7r4c1 7r9c7 1r9c6 -1r7c6 [chain__2] <> 1 [r7c6]

by **Steve K** » Tue Jun 24, 2008 3:29 pm

Here is what I found: (after ss) - the first puzzle, i suppose
1) (8)r1c7=(8-9)r9c7=(9)r7c7-(9=4)r7c6-(4)r1c6=(4-6)r1c5=(6)r1c7 loop =>
r9c7<>147, r7c5<>9, r9c6<>4, r1c5<>237, r1c7<>27

2) (8)r5c6=(8)r9c6-(8=9)r9c7-(9)r7c7=(9)r7c6 => r5c6<>9 some singles

3) (6)r4c7=(6-5)r4c3=(5-2)r4c1=(2-4)r1c6=(4-6)r1c5=(6)r1c7 loop => r4c3<>13, r247c7<>6 one single
4) (7)r1c12 => r2c12<>7 some singles
5) fxw(3) r8c5=r8c1-r4c1=r4c56 => r6c5<>3
6) pair 28 r38c9 => r9c9<>8, r25c9<>2
7) (2)r4c5=(2-6)r2c5=(6)r1c5-(6)r1c7=(6)r4c7 => r4c7<>2 ss from here

by **hobiwan** » Tue Jun 24, 2008 5:58 pm

daj95376 wrote:Nice try hobiwan. Yes, I'm still interested. However, don't you still need ...

Yes I do, I copied the wrong chain (edited my original post). Still, your last solution is shorter than mine.

by **Draco** » Tue Jun 24, 2008 8:02 pm

Steve K wrote:Here is what I found: (after ss) - the first puzzle, i suppose
1) (8)r1c7=(8-9)r9c7=(9)r7c7-(9=4)r7c6-(4)r1c6=(4-6)r1c5=(6)r1c7 loop =>
r9c7<>147, r7c5<>9, r9c6<>4, r1c5<>237, r1c7<>27

2) (8)r5c6=(8)r9c6-(8=9)r9c7-(9)r7c7=(9)r7c6 => r5c6<>9 some singles

3) (6)r4c7=(6-5)r4c3=(5-2)r4c1=(2-4)r1c6=(4-6)r1c5=(6)r1c7 loop => r4c3<>13, r247c7<>6 one single
4) (7)r1c12 => r2c12<>7 some singles
5) fxw(3) r8c5=r8c1-r4c1=r4c56 => r6c5<>3
6) pair 28 r38c9 => r9c9<>8, r25c9<>2
7) (2)r4c5=(2-6)r2c5=(6)r1c5-(6)r1c7=(6)r4c7 => r4c7<>2 ss from here

Nice loops! Your loops and finned X-Wing used less than half the number of steps I needed with forcing chains/nets.

Danny still seems to have the shortest solution so far.

Cheers...

- drac

by **daj95376** » Tue Jun 24, 2008 9:39 pm

hobiwan wrote:I copied the wrong chain (edited my original post). Still, your last solution is shorter than mine.

You discovered the importance of [r7c6]<>1. Let's call it a joint effort on reducing the solution to three chains. Thanks!!!

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