Looking for some very very very hard sudoku

Everything about Sudoku that doesn't fit in one of the other sections

Postby RW » Tue Mar 21, 2006 6:31 pm

tso wrote:I think it would be *very* welcomed if you would solve a few puzzles that are considered difficult... Pick one or two from a previous threads that have been solved by other more complex methods -- or this one from earlier in this thread:
Code: Select all
. . . | 7 . . | . 3 .
. . . | . . 4 | . 9 2
. . 4 | . 2 . | . . 7
------+-------+------
7 . . | . . 8 | 3 5 .
. . . | . 1 . | . . .
. 2 5 | 4 . . | . . 8
------+-------+------
9 . . | . 7 . | 6 . .
2 8 . | 1 . . | . . .
. 5 . | . . 9 | . . .


Ok, I admit, that one is devilish. Definitely the hardest I've ever done, 2 1/2 hours, six 30+ step trails, plus a lot of shorter ones. I've never before had to do more than two long trails in one puzzle. Sure I could start a thread on solving without pencilmarks, but I don't think this is the best example as the required effort might be quite discouraging. I'll find some other examples that don't need quite as much memorizing.

RW
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Postby gfroyle » Thu Mar 23, 2006 6:01 am

How is this one for difficulty?

Code: Select all
... ... 2..
.8. ..7 .9.
6.2 ... 5..

.7. .6. ...
... 9.1 ...
... .2. .4.

..5 ... 6.3
.9. 4.. .7.
..6 ... ...


Cheers

Gordon
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Postby ravel » Thu Mar 23, 2006 2:30 pm

gfroyle wrote:How is this one for difficulty?

Looks as hard as some monsters here. I can solve it with one step, showing that r5c2<>5, but need a monster chain with multiple inferences. Lets see, with what the experts come up for this.
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Postby Carcul » Thu Mar 23, 2006 7:54 pm

Hi Gfroyle and Ravel.

Gfroyle wrote:How is this one for difficulty?


This is a very nice puzzle, not only because I find it beautifully simmetric, but also because of the logic that can be used to solve it. Gfroyle, did you generate it yourself?

Ravel wrote:Looks as hard as some monsters here.


However, I certainly do not agree with this statement because the puzzle can be easily solved with some simple nice loops, contrary to the Norwegian monsters around here.

Ravel wrote:I can solve it with one step, showing that r5c2<>5, but need a monster chain with multiple inferences.


Very good. Just one question: how did you find that chain, and why did you considered the cell r5c2?

Ravel wrote:Lets see, with what the experts come up for this.


As far as I am concern, I did't try yet to solve the puzzle in one step, but in the meantime I found the following simple steps:

Code: Select all
 *-----------------------------------------------------------------------------*
 | 9       1345    7       | 6       13458   3458    | 2       138     148     |
 | 1345    8       134     | 2       1345    7       | 134     9       6       |
 | 6       134     2       | 138     13489   3489    | 5       138     7       |
 |-------------------------+-------------------------+-------------------------|
 | 123458  7       13489   | 358     6       3458    | 1389    12358   12589   |
 | 23458   2345    348     | 9       34578   1       | 378     6       258     |
 | 1358    6       1389    | 3578    2       358     | 13789   4       1589    |
 |-------------------------+-------------------------+-------------------------|
 | 12478   124     5       | 178     1789    289     | 6       128     3       |
 | 1238    9       138     | 4       1358    6       | 18      7       1258    |
 | 12378   123     6       | 13578   13578   2358    | 49      1258    49      |
 *-----------------------------------------------------------------------------*

1. [r2c1]=5=[r2c5]-5-[r8c5]=5=[r8c9]=2=[r8c1]-2-[r7c2|r9c2]=2=[r5c2]=5=[r1c2]-5-[r2c1],

which implies: r1c5,r5c5,r9c5<>5; r8c9<>1,8; r7c1,r9c1<>2; r5c2<>3,4.

2. [r4c1]-2-[r8c1]=2=[r8c9]-2-[r5c9]=2=[r5c1|r5c2]-2-[r4c1], => r4c1<>2.

3. [r5c9]-5-[r5c2]=5=[r1c2]-5-[r2c1]=5=[r2c5]-5-[r8c5]=5=[r8c9]-5-[r5c9], => r5c9<>5.

4. [r7c5]-1-[r1c5]=1=[r1c2]=5=[r5c2]=2=[r5c1]-2-[r8c1]=2=[r8c9]=5=[r9c8]=1=[r7c8]-1-[r7c5], => r7c5<>1.

5. [r7c6]=2=[r7c8]=1=[r9c8]-1-[r9c5]=(Almost Unique Rectangle: r7c1/r9c1/r7c5/r9c5)=1|9=[r7c5]-9-[r7c6],

which implies r7c6<>9 and that solve the puzzle.

Regards, Carcul
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Postby gfroyle » Fri Mar 24, 2006 5:23 am

Carcul wrote:. Gfroyle, did you generate it yourself?


Yes, I generated this myself..

Also this one, which seems to be extremely hard...

Code: Select all
6.. ... ..3
.7. .8. .9.
..2 ... 5..

... 3.. ...
.8. .1. .7.
... ..2 ...

..5 ... 1..
.9. .4. .8.
3.. ... ..2


Enjoy...

Gordon
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Postby ravel » Fri Mar 24, 2006 9:29 am

Carcul wrote:how did you find that chain, and why did you considered the cell r5c2?

Oh, my stupid program gave me that hint:)
gfroyle wrote:
Code: Select all
6.. ... ..3
.7. .8. .9.
..2 ... 5..

... 3.. ...
.8. .1. .7.
... ..2 ...

..5 ... 1..
.9. .4. .8.
3.. ... ..2


Wow, this beauty is the first puzzle i saw, that after basic steps (up to naked pairs) has no cell with 2 candidates.
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Postby ravel » Wed Apr 26, 2006 2:44 pm

Though normally i dont try to solve ultra hard puzzles, i could not resist this beautiful beast.
Using the hints of my program i came to the following solution, which i know is not very elegant with this monster chains, but AFAIK it is the only one so far.

[Edit: corrections, thanks to RW]

1. swordfish 2 in r147c258: r1c4,r4c17,r7c14<>2

2. swordfish 3 in r258c367: r6c37,r3c6,r7c6<>3

3. r5c7<>2:
r5c7=2 r8c7=3 r7c5=3 r1c5=2, no 2 in box 3

4. r7c8<>4:

r7c8=4 r7c5=3 r2c6=3 r1c8=1 r3c8=6 r9c8=5 r2c9=4 r2c4=6 r2c1=5 r1c2=4 r9c3=4 r1c3=8 r1c7=7 r2c3=1 r8c6=5 r8c1=1 r9c2=6 r1c6=9 r3c5=7 r9c5=9
r9c7 is empty

For the following two chains i both use this implication A:
r8c9=7 r1c7=7 r3c9=8 r3c1=9 r7c1=8 r9c3=7 r7c9=4 r9c7=9, i.e.
r8c9=7 => r3c1=9 and r9c7=9 => r39c5<>9

5. r4c5<>5:

r4c5=5 r5c9=5 r8c6=5 r7c5=3 r7c8=6 r8c9=7 <A> r6c5=9 r8c7=3 r5c3=3,
no 9 in r5

6. xwing in 5 r69c58: r6c1249,r9c46<>5
and 2 strong links in 5 r4c1-r2c1,r1c2-r4c2: r4c69<>5

7. r5c3<>3:
r5c3=3 r8c8=3 r7c5=3 r9c8=5 r6c5=5 r5c9=5 r6c8=3 r7c8=6 r8c9=7 <A> r4c5=9,
no 9 in r5

8. xy-chain
1-r3c2-4-r9c2-6-r9c8-4-r1c8-1 => r1c2<>1,r3c8<>1

9. r9c2<>6
r9c2=6 r7c1=4 r3c1=8 r1c3=9 r3c9=7 r7c9=9 r5c9=6 r5c3=4 [pair 59 in r5c46] r46c5<>9,
no 9 in c5
Last edited by ravel on Thu Apr 27, 2006 3:34 am, edited 1 time in total.
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Postby RW » Wed Apr 26, 2006 7:16 pm

Nice work ravel. Suprising that you could find such a short first reduction that let you solve several numbers. Some small misses in the notation:


ravel wrote:3. r5c7<>2:
r5c7=2 r8c3=3...


Should be r5c3=3 I suppose

ravel wrote:4. r7c8<>4:

r7c8=4 r7c5=3 r2c6=3 r1c5=2 r1c8=1 r3c8=6 r9c8=5 r2c9=4 r2c4=6 r2c1=5 r1c2=4 r9c3=4 r1c3=8 r1c7=7 r2c3=1 r8c1=1...


Missing step (?), is r8c6=5 supposed to be in there?

ravel wrote:5. r4c5<>5:

r4c5=5 r5c9=5 r8c6=5 r7c5=3 r7c8=6 r8c9=7 <A> r6c5=9,
no 9 in r5


Am I missing something:?: isn't there a 9 in r5c3... could be easily excluded by adding r8c7=3 r6c8=3 r5c3=3...

All can be fixed, so nothing to worry about. Still a few more ultrahard puzzles to solve in your list, maybe I'll try some of them if the coming summer is extremely rainy...

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Postby ravel » Wed Apr 26, 2006 10:36 pm

Hi RW,

many thanks for reading it so carefully, i knew, i should not post it in the moment, when i thought, its ok ...

RW wrote:
ravel wrote:3. r5c7<>2:
r5c7=2 r8c3=3...

Should be r5c3=3 I suppose

i meant r8c7=3
RW wrote:
ravel wrote:r7c8=4 r7c5=3 r2c6=3 r1c5=2 r1c8=1 r3c8=6 r9c8=5 r2c9=4 r2c4=6 r2c1=5 r1c2=4 r9c3=4 r1c3=8 r1c7=7 r2c3=1 r8c1=1...

Missing step (?), is r8c6=5 supposed to be in there?

Yes. exactly
RW wrote:
ravel wrote:r4c5=5 r5c9=5 r8c6=5 r7c5=3 r7c8=6 r8c9=7 <A> r6c5=9,
no 9 in r5

Am I missing something:?: isn't there a 9 in r5c3... could be easily excluded by adding r8c7=3 r6c8=3 r5c3=3...

You did not miss anything, r8c7=3 and r5c3=3 were missing.
RW wrote:Still a few more ultrahard puzzles to solve in your list, maybe I'll try some of them if the coming summer is extremely rainy...

I am looking forward to a rainy summer (in Finland):)
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Postby bobob » Thu May 04, 2006 11:51 am

How about this one:

Code: Select all
... .2. .6.
... 4.8 ...
.2. .1. 58.

9.. ... 3..
24. ... .97
..1 ... ..4

.56 .8. .4.
... 9.1 ...
.8. .3. ...


Found it here http://sudokupro.com/sudoku/show/1252
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Postby ravel » Thu May 04, 2006 12:31 pm

bobob wrote:How about this one ...

Maybe something for the SUPERIOR thread with many pairs and triples, but not really tough.
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Postby Havard » Thu May 04, 2006 12:32 pm

[edit: claimed that puzzle had multiple solutions...shame shame...]
Last edited by Havard on Thu May 04, 2006 8:51 am, edited 1 time in total.
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Postby ravel » Thu May 04, 2006 12:49 pm

Havard wrote:This sudoku belongs in the sudoku-of-shame section... It has multiple solutions...

Hm, i got only one solution (?)
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Postby Havard » Thu May 04, 2006 12:50 pm

whops, my bad... Sorry about that!:)
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Postby claudiarabia » Mon May 15, 2006 3:32 pm

[quote="kjellfp"]I seem to remember that there's one very hard with the pattern
Code: Select all
+---+---+---+
|X..|...|..X|
|.X.|.x.|.X.|
|..X|...|X..|
+---+---+---+
|x..|X.X|..x|
|.x.|.X.|.x.|
|x..|X.X|..x|
+---+---+---+
|..X|...|X..|
|.X.|.x.|.X.|
|X..|...|..X|
+---+---+---+


once I tried to make such a sudoku. I produced the pattern to be seen above with even more clues than kjell had, but apparently the structure of the whole 9x9-matrix isn't for having a one-solutional Sudoku with this pattern.
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