The New Sudoku Players' Forum

[Viggo]

This is a proposed solution to dukuso puzzle no. 89 from top1465, which was found by Ravel recently to be a "hard one" - thank you!

The solution contains 25 steps of Nice Loops or error nets (documentet brute force eliminations). Some steps do also include simpler deductions. Actually there was a lot funn work for me in this puzzle.

For each step I have tried about five different error nets and normally I choose the simplest of them. The first solution, I made was in 35 steps. Then I looked at all the steps again to find the esentially needed steps of the 35 and came out with 25 of them and the steps was also rearranged.

I include NLN notation for each step, as I understand the notation proposed by Carcul here. Furthermore I supply some graphics for each step made manually using the into sudoku program. There may easily be some errors, and I shall be glad to know about them or any comments. I'am not so experienced in solving and spotting Unique Rectangless or Almost Locked Sets. So I hope to see smarter or different solutions to the puzzle.

The puzzle starts as this:

...3..5...5..1..3...7..4..12.....4...6..9......1..6..28..7..2...9..8..5...5..9..7

or

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 . . . | 3 . . | 5 . .
 . 5 . | . 1 . | . 3 .
 . . 7 | . . 4 | . . 1
-------+-------+------
 2 . . | . . . | 4 . .
 . 6 . | . 9 . | . . .
 . . 1 | . . 6 | . . 2
-------+-------+------
 8 . . | 7 . . | 2 . .
 . 9 . | . 8 . | . 5 .
 . . 5 | . . 9 | . . 7

First you find one single, "7" in r8c1 and then a Swordfish with the candidate "2" in r258c346 eliminating candidates in r1c3, r1c6, r3c4 and r9c4. After this short "intro" the puzzle gets hard.

Here is the graphics of the Swordfish:



I normaly start such a hard puzzle by identifying the strong links and bivalue cells like this:



I happen to often to find something interesting with the few diagonal links its also the case here:

1a. [r4c9]-9-[r4c3]=9=[r6c1]=5=[r5c1]-5-[r5c9]=5=[r4c9] => r4c9<>9

and the very similar simple discountinuous Nice Loop:

1b. [r4c8]-9-[r4c3]=9=[r6c1]=5=[r5c1]-5-[r5c9]=5=[r4c9]=6=[r4c8] => r4c8<>9

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2. [r1c2](-8-[r1c3])
         (-8-[r2c3])
         (-8-[r3c2])
         {-8-[r1c6](-7-[r2c6])
                   (-7-[r5c6])
                   -7-[r1c8]=7=[r2c7]-7-[r5c7]=7=[r5c8]-7-[r6c8]}
         =1=[r1c1]=9=[r1c89]-9-[r3c7]=9=[r6c7]-9-[r6c8](-8-[r3c8])
                                                       -8-[r9c8]=8=[r9c7]-8-[r3c7]
               =8=[r3c4](-8-[r2c6])
                        =9=[r2c4]-9-[Naked Pair: r2c1|r1c3]-46-[r2c3]-2-[r2c6]
   => empty cell r2c6 => r1c2<>8

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3. [r2c7](-9-[r2c4]=9=[r3c4]-9-[r3c1])
         (=7=[r1c8]=2=[r2c8]-2-[r3c2])
         (-9-[r2c1]=9=[r1c1]=1=[r1c2]=2=[r2c3]-2-[r2c4])
         =7=[r1c8]-7-[r1c6](-8-[r2c4]-6-[r2c1]-4-[r56c1])
                           -8-[r1c3]=8=[r3c2]=3=[r3c1](-3-[r6c1])
                                                      -3-[r5c1]-5-[r6c1]
   => empty cell r6c1 => r2c7<>9

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4. [r3c7](=9=[r6c7]-9-[r6c8])
         (-8-[r5c7])
         {-8-[r9c7]=8=[r9c8](-8-[r5c8])
                            -8-[r6c8](-7-[r6c5])
                                     -7-[r6c2]=7=[r4c2](-7-[r4c5])
                                                       -7-[r4c6]=7=[r5c6]=2=[r5c4]}
         -8-[r3c2]=8=[r46c2]-8-[r5c3]=8=[r5c9]=5=[r4c9](-5-[r4c5])
                                                       =3=[r5c7]-3-[r5c13]
              =3=[r6c1](-3-[r9c1])
                       -3-[r3c1]=3=[r3c2]-3-[r9c2]=3=[r9c5]-3-[r4c5]
   => empty cell r4c5 => r3c7<>8

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5. [r2c7]{=7=[r1c8](=2=[r3c8])
                   -7-[r1c6]-8-[r1c3]}
         {-8-[r9c7]=8=[r9c8]=4=[r7c8](-4-[r7c23])
                                     =9=[r7c9]-9-[r12c9]=9=[r3c7](-9-[r3c1])
                                                                 -9-[r3c4]=9=[r2c4]
                -9-[r2c1]=9=[r1c1]=1=[r1c2](-1-[r9c2])
                                           -1-[r7c2](=1=[r9c1])
                                                    -3-[r7c3]-6-[r1c3]}
         =7=[r1c8]=2=[r1c5]-2-[r2c46]=2=[r2c3]-2-[r8c3]=2=[r9c2]=4=[r8c3]-4-[r1c3]
   => empty cell r1c3 => r2c7<>8


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6. [r2c7](-6-[r2c1])
         {=7=[r1c8](=2=[r3c8])
                   -7-[r1c6]-8-[r3c4]=8=[r3c2]=3=[r3c1]-3-[r56c1]}
         -6-[r3c7]-9-[r3c4]=9=[r2c4]-9-[r2c1](-4-[r6c1])
                                             -4-[r5c1]-5-[r6c1]
   => empty cell r6c1 => r2c7<>6 => r2c7=7

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7. [r2c9](-9-[r7c9]=9=[r7c8])
         {-9-[r2c4]=9=[r3c4](-9-[r3c1])
                            =5=[r3c5]-5-[r7c5]=5=[r7c6]}
         -9-[r2c1]=9=[r1c1]=1=[r1c2]-1-[r7c2]
   => no candidates of 1 in row 7 => r2c9<>9

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8. [r2c4](-2-[r5c4]=2=[r5c6]-2-[r8c6])
         (=9=[r2c1])
         {=9=[r3c4]-9-[r3c7](-6-[r2c9])
                            (-6-[r3c4])
                            (-6-[r3c5]=6=[r1c5]-6-[r1c1])
                            -6-[r3c1]=6=[r9c1]-6-[r9c4]=6=[r8c4]-6-[r8c79]}
         -2-[r2c6]-8-[r2c9]-4-[r8c9](-3-[r8c7])
                                    -3-[r8c6]-1-[r8c7]
   => empty cell r8c7 => r2c4<>2

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9. [r7c2](-3-[r46c2])
         (-3-[r9c12])
         -3-[r3c2]=3=[r3c1]-3-[r56c1]=3=[r5c3](-3-[r5c679])
                                              =8=[r46c2]
               -8-[r3c2](-2-[r3c8]=2=[r1c8])
                        -2-[r9c2](=2=[r8c3])
                                 =2=[r9c5](-2-[r13c5]=2=[r2c6]-2-[r5c6]=2=[r5c4])
                                          =3=[r9c7]-3-[r6c7]=3=[r4c9]-3-[r4c56]
               =3=[r6c5]=4=[r6c4](-4-[r89c4]=4=[r7c5]-4-[r7c38])
                                 -4-[r6c12]=4=[r5c1]-4-[r9c1]=4=[r9c2]-4-[r9c8]

   => no candidates of 4 in column 8 => r7c2<>3

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10. [r9c7](-6-[r9c4])
          -6-[r3c7](-9-[r6c7]=9=[r6c8]-9-[r7c8]=9=[r7c9]-9-[r1c9])
                   (-9-[r3c1])
                   -9-[r3c4]=9=[r2c4]-9-[r2c1]=9=[r1c1]
                      =1=[r1c2](-1-[r9c2])
                               -1-[r7c2]{=1=[r9c1]-1-[r9c4](-4-[r9c58])
                                                            -4-[r8c4]}
                                        (-4-[r7c5]=4=[r6c5]-4-[r6c12])
                                        -4-[r7c8]=4=[r8c9]-4-[r12c9]=4=[r1c8]=2=[r3c8]
               -2-[r3c2]=2=[r2c3](-2-[r2c6]-8-[r2c9])
                                 =4=[r2c1]-4-[r5c1]=4=[r5c3]=8=[r1c3]-8-[r1c9]-6-[r2c9]
    => empty cell r2c9 => r9c7<>6

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11. [r2c4](=9=[r2c1])
          (-8-[r2c9])
          (-8-[r2c6]-2-[r8c6])
          =9=[r3c4]-9-[r3c7](-6-[r2c9]-4-[r8c9])
                            (-6-[r3c5]=6=[r1c5]-6-[r1c1])
                            -6-[r3c1]=6=[r9c1]-6-[r9c4]=6=[r8c4](-6-[r8c7])
                                                                -6-[r8c9](-3-[r8c7])
                                                                         -3-[r8c6]-1-[r8c7]
    => empty cell r8c7 => r2c4<>8

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12. [r3c1](=3=[r3c2]-3-[r9c2])
          -6-[r3c7](=6=[r8c7]-6-[r8c39])
                   (-9-[r1c9])
                   -9-[r3c4]=9=[r2c4]-9-[r2c1]=9=[r1c1]
      =1=[r1c2]{-1-[r79c2]=1=[r9c1](=6=[r7c3])
                                   =3=[r8c3]-3-[r8c9]}
               =2=[r2c3](-2-[r2c6]-8-[r2c9])
                        =8=[r1c3](-8-[r1c9])
                                 =4=[r2c1]-4-[r2c9]-6-[r1c9]-4-[r8c9]
    => empty cell r8c9 => r3c1<>6

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13. [r7c9](-3-[r7c3])
          (-3-[r45c9])
          (-3-[r8c9])
          =9=[r7c8]-9-[r6c8]=9=[r6c7]=3=[r5c7]-3-[r5c3]=3=[r8c3]=2=[r9c2]-2-[r13c2]=2=[r2c3]
              -2-[r2c6](-8-[r2c9])
                       -8-[r1c6]-7-[r5c6]=7=[r5c8]=1=[r4c8]=6=[r4c9](-6-[r2c9])
                                                                    -6-[r8c9]-4-[r2c9]
    => empty cell r2c9 => r7c9<>3

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14. [r2c4](-6-[r1c5])
          =9=[r3c4]{=5=[r3c5](-5-[r4c5])
                             -5-[r7c5]=5=[r7c6]
                     (Nice Loop: [r9c2]=2=[r9c5]=6=[r7c5]=3=[r7c3]-3-[r9c2])-3-[r9c3]}
                   (-9-[r3c7]=9=[r6c7])
                   -9-[r3c1](-3-[r56c1]-4-[r5c3])
                            -3-[r9c1]=3=[r78c3]-3-[r5c3](-8-[r4c2])
                                                        -8-[r5c7]=8=[r9c7]
       =3=[r9c5](-3-[r4c5])
                -3-[r6c5]=3=[r6c2]-3-[r4c2]-7-[r4c5]

    => empty cell r4c5 => r2c4<>6 => r2c4=9

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15. [r2c9](-6-[r2c1]-4-[r56c1])
          -6-[r3c7]-9-[r3c1](-3-[r6c1])
                            -3-[r5c1]-5-[r6c1]

    => empty cell r6c1 => r2c9<>6
    => Box line reduction in row 1,3  r1c1,r1c3<>6

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16. [r1c8](=2=[r3c8]-2-[r3c2]=2=[r2c3]-2-[r8c3])
          (-6-[r4c8]=6=[r4c9]=5=[r5c9]=3=[r8c9]-3-[r8c3])
          -6-[r3c7](=6=[r8c7]-6-[r8c3]-4-[r7c2])
                   -9-[r3c1]=9=[r1c1]=1=[r1c2]-1-[r7c2]

    => empty cell r7c2 => r1c8<>6

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17. [r5c6](-7-[r5c8])
          -7-[r1c6]=7=[r1c5]=6=[r1c9](-6-[r3c7])
                                     -6-[r4c9]=6=[r4c8]=7=[r6c8]=9=[r6c7]-9-[r3c7]
    => empty cell r3c7 => r5c6<>7

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18. [r9c7](-1-[r9c1]=1=[r1c1]=9=[r3c1]=3=[r3c2])
          {=8=[r9c8]-8-[r3c8]=8=[r3c4]-8-[r2c6](-2-[r8c6])
                                               -2-[r5c6]=2=[r5c4]}
          -1-[r79c8]=1=[r4c8]-[r4c46]=1=[r5c6]-1-[r8c6]-3-[r8c79]

    => no candidates of 3 in box 9 => r9c7<>1
    => XYZ-wing r69c78, r5c7<>8

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19. [r7c6]{-1-[r8c46]=1=[r8c7]-1-[r5c7](-3-[r45c9])
                                       =1=[r4c8]-1-[r4c46]}
          -1-[r5c6]=1=[r5c4]=2=[r5c6]-2-[r8c6]-3-[r8c9]

    => no candidates of 3 in column 9 => r7c6<>1
    => Empty Rechtangle in box 8, r5c4<>1

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20. [r2c9]-8-[r6c8](-9-[r13c8])
                   -9-[r7c8]=9=[r7c9]-9-[r1c9]=9=[r3c7]-3-[r3c1]=9=[r1c1]=1=[r1c2]
       -1-[r7c2]-4-[r7c89]=4=[r8c9]-4-[r12c9]=4=[r1c8]=2=[r3c8]-2-[r3c2]=2=[r2c3]
       -2-[r2c6]-8-[r2c9]

    => Empty cell r2c9 => r9c8<>8
    => r9c7=8
    => Pointing pair in row 8, r8c3,r8c6<>3

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21. [r6c2](-4-[r56c1])
          =7=[r4c2]=8=[r5c3]-8-[r12c3]=8=[r3c2]=3=[r3c1](-3-[r6c1])
                                                        -3-[r5c1]-5-[r6c1]
    => Empty cell r6c1 => r6c2<>4

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22. [r1c2](-4-[r1c9])
          (-4-[r1c3]-8-[r1c89])
          =1=[r1c1]=9=[r3c1](=3=[r3c2]=2=[r2c3]-2-[r2c6]-8-[r2c9]=8=[r3c8]-8-[r6c8])
                            -9-[r3c7]-6-[r1c9]-9-[r6c9]=9=[r7c8]-9-[r6c8]

    => Empty cell r6c8 => r1c2<>4
    => Box-line reduction column 1,3 r7c3,r8c3,r9c1<>4

23. [r8c4]-1-[r8c6]-2-[r2c6]-8-[r2c9]-4-[r8c9]=4=[r8c4] => r8c4<>1

=> X-wing r58c67 r4c6<>1




24. [r8c7]-1-[r8c6]-2-[r8c3]=2=[r9c2]=4=[r7c2]=1=[r7c8]-1-[r8c7] => r8c7<>1

=> Singles r8c6=1, r4c1=1, r5c7=1



25. [r2c6]-8-[r2c9]-4-[r8c9]=4=[r8c4]=2=[r5c4]-2-[r5c6]=2=[r2c6] => r2c6<>8

=> One pointing pair and singles solves the rest of the puzzle



This puzzle is harder than "Emilys Friend". Probably it is at the level of dukuso no. 77.

/Viggo

[ravel]

Hi Viggo,

what a surprise to see your solution yesterday, when i posted the ultrahard list

I went through your steps now roughly with a solver, some steps are unclear for me (maybe i missed something, i cannot load your pictures here to compare the candidates):
In step 2 before the naked pair i missed r3c1=9 or r4c3=9,
in step 9 i cannot see, why r4c3<>38 to get r5c3=3 and r46c2=8,
in step 14 i cannot see, why r5c3<>4 (-3-[r56c1]-4-[r5c3]),
in step 22, why r3c1=9 (not r1c3=9 and r6c1=9).

When i compared the eliminations of my brute force 12- and 10-step solutions, interestingly there was not one duplicate:

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r3c8<>6, r1c8<>6, r1c8<>8, r2c4<>8, r2c7<>8, r2c7<>9, r1c3<>9, r3c4<>8, r4c9<>6, r2c3<>9, r3c2<>8, r2c3<>2
r4c3<>3, r7c8<>6, r6c7<>7, r5c7<>3, r5c6<>7, r6c1<>9, r1c1<>1, r6c8<>8, r7c2<>3, r9c8<>8


And i found only 4 and 3 resp. of the eliminations in your steps. So many other solutions seem to be possible, but i think you agree, that they are hard to find

[Viggo]

Hi Ravel, thank you for your reply.

I'am suppriced to know, that you cannot load the graphics. Do anyone else have the same problem? Do you have an idea on why you cannot load these graphic files? I have no problem in loading the graphics when I look on the website. I should like to know if I can do something about that. The graphics can also be seen on this web-site: http://www.sitecenter.dk/broendegaard/scrapbog/ and they are named vbnxx.jpg. xx is the step number.

For your information, I have insvestigated your solvers great solution in the thread on the Emilys Friend puzzle. So I'am convinced, that your solvers steps will produce a simpler solution in general.

I shall try to answer your questions:

I went through your steps now roughly with a solver, some steps are unclear for me (maybe i missed something, i cannot load your pictures here to compare the candidates):

In step 2 before the naked pair i missed r3c1=9 or r4c3=9,

You have got r3c4=8 - I hope we agree to this point. Then a strong interference link exsists [r3c4]=9=[r2c4]. So the only left candidate of 9 in column 4 is in r2c4. "r2c9=9" eliminates the candidate 9 in r2c1, which "activate" the naked pair. I have just seen that this confusion may also be due to the fact that step 1 reveals r4c3=9.

in step 9 i cannot see, why r4c3<>38 to get r5c3=3 and r46c2=8,

Sorry, I have forgotten to write down after step 1, that r4c3=9 (single). I think that makes the confusion.

in step 14 i cannot see, why r5c3<>4 (-3-[r56c1]-4-[r5c3]),

When 3 is removed from r56c1, the cells becommes a Naked Pair with the candiadates 45. Therefore r5c3<>4. Maybe I should have given a comment about the Naked Pair.

in step 22, why r3c1=9 (not r1c3=9 and r6c1=9).

I think it is the same problem about r4c3=9 after step 1 that makes the confusion. When r4c3=9 then r1c3 and r6c1 cannot be 9.

I hope these answers helps. But everything would be easier explained, if you could see the graphics.

/Viggo

[ravel]

I'am suppriced to know, that you cannot load the graphics.

It would not be a problem, but my mummy there does not allow picture sites
Maybe i also should say, that i usually turn the graphics off here, when looking at the forum, otherwise it is still loading, when im looking at the last entry, and i have to go down and again and again ...

Thanks for your explanations, everything clear now. My main mistake was, that i missed, that two 9's have been eliminated in step 1.

Congratulations to your solution

[daj95376]

Viggo,

Not all of us have high-speed Internet access. This means that I can either wait a long time to load threads where you've included several graphics, or else I have to skip the threads and end up missing anything anyone else has to say of interest.

[ravel]

daj95376,

if you use firefox, under extras/settings there should be a box with something like "load graphics/only from the original site" (i dont have the english version installed). It allows me to switch loading the graphics or not.

If i remember right, there should be an equivalent method for IE.

[Viggo]

Congratulations to your solution

Thank you!

Not all of us have high-speed Internet access. This means that I can either wait a long time to load threads where you've included several graphics, or else I have to skip the threads and end up missing anything anyone else has to say of interest.

Thank you for this information. I have got the high-speed a half year ago, and I seem to have forgotten how it was... I do recommend high speed. Hopefully you are able to switch off the graphics and use the supplied text as a source of information. By the way, every puzzle graphic is about 80 kB.

/Viggo