Looking for some very very very hard sudoku

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Looking for some very very very hard sudoku

Postby p0486 » Sat Mar 18, 2006 1:36 pm

please post some very very very hard sudoku here!
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Postby coloin » Sat Mar 18, 2006 1:55 pm

Try this site
http://magictour.free.fr/topn234
more at
http://magictour.free.fr/sudoku.htm

Are you sure you are ready for them ?

C
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Postby vidarino » Sat Mar 18, 2006 1:56 pm

The top1465-list should give you something to do for a while.:)

Also, I'd like to shamelessly plug my "monsters", particularly these two;

Code: Select all
Vidar's Monster #3
+-------+-------+-------+
| 5 . . | 8 . . | 4 . . |
| . 8 . | . 9 . | . 5 . |
| . . 7 | . . 6 | . . 2 |
+-------+-------+-------+
| . . 4 | . . 3 | . . 6 |
| . 3 . | . . . | . . . |
| 9 . . | 1 . . | . . . |
+-------+-------+-------+
| . . . | 7 . . | 8 . . |
| . 4 . | . 5 . | . 1 . |
| . . 2 | . . 1 | . . 4 |
+-------+-------+-------+


and

Code: Select all
Vidar's Monster #4
+-------+-------+-------+
| 1 . . | . . 6 | . . . |
| . 6 . | 9 . . | . . 8 |
| 8 . . | . . 4 | 3 6 . |
+-------+-------+-------+
| . . 8 | . . . | 4 . . |
| . . 6 | . 4 3 | 9 . 5 |
| . 4 . | 5 . . | . . . |
+-------+-------+-------+
| . 2 . | . . . | . 7 . |
| 4 . 1 | . 7 . | . . . |
| . . 3 | . 1 . | 2 . . |
+-------+-------+-------+
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Postby tso » Sat Mar 18, 2006 3:02 pm

If SOLO's Unreasonable level puzzles are too hard for you -- and they will be -- try the Extremes.

Direct link
Last edited by tso on Sun Mar 19, 2006 1:44 pm, edited 1 time in total.
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Postby kjellfp » Sat Mar 18, 2006 9:15 pm

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|
+---+---+---+

I'd like to see it again. Can anybody help?
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Postby RW » Sun Mar 19, 2006 12:40 pm

tso wrote:If SOLO's Unreasonable level puzzles are too hard for you -- and they will be -- try the Extremes.


This felt like a nice challenge, but I was disappointed. Using my normal technique, without pencilmarks, only entering certain numbers, the unreasonable took me about 15 minutes. I then checked in simple sudoku why it was supposed to be so hard. SS got stuck two times, first one I had got around by a very obvious uniqueness-reduction, second one could be solved with a very short trailing pattern (don't know if there's a name for it, never studied techniques, just do what seems obvious to me).

I'll have a look at your monsters vidarino, I believe they can be more challenging.

RW
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Postby gfroyle » Sun Mar 19, 2006 2:09 pm

kjellfp wrote: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|
+---+---+---+

I'd like to see it again. Can anybody help?


My page has a number of these X-shape ones that I think are mostly pretty hard, though they were not constructed for difficulty so there may be easy ones among them..

But the ones that I checked seemed difficult..

http://www.csse.uwa.edu.au/~gordon/sudokupat.php

Just click "Download them all" if you want them all as a text file..

Cheers

Gordon
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Postby tarek » Sun Mar 19, 2006 2:58 pm

kjellfp wrote: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|
+---+---+---+

I'd like to see it again. Can anybody help?

The puzzle's configuration is Universally symmetrical around all axes & rotationally around centre......

These configurations usually follow -IN BROAD TERMS- the shape of an X (your example mostly) or a Diamond (A combination is possible).....

this type of symmetry is harder to construct, but it doesn't reflect how difficult the are........

Tarek
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Hardest Sudoku grid yet

Postby SudokuKing » Sun Mar 19, 2006 3:33 pm

I solved 2 of the daily challenges on this site, I am now looking at the weekly challenge, definately the hardest 9x9 Sudoku I have seen so far. It is quite twisted check it out:

http://www.psycho-sudoku.com/1.html
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Re: Hardest Sudoku grid yet

Postby vidarino » Sun Mar 19, 2006 3:49 pm

SudokuKing wrote:I solved 2 of the daily challenges on this site, I am now looking at the weekly challenge, definately the hardest 9x9 Sudoku I have seen so far. It is quite twisted check it out:

http://www.psycho-sudoku.com/1.html


Not only is it twisted, it also has too many solutions to count (I stopped my program after several minutes listing the different solutions), so calling it a Sudoku at all is equally twisted.
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Postby tso » Sun Mar 19, 2006 5:53 pm

RW wrote:
tso wrote:If SOLO's Unreasonable level puzzles are too hard for you -- and they will be -- try the Extremes.


This felt like a nice challenge, but I was disappointed. Using my normal technique, without pencilmarks, only entering certain numbers, the unreasonable took me about 15 minutes. I then checked in simple sudoku why it was supposed to be so hard. SS got stuck two times, first one I had got around by a very obvious uniqueness-reduction, second one could be solved with a very short trailing pattern (don't know if there's a name for it, never studied techniques, just do what seems obvious to me).

I'll have a look at your monsters vidarino, I believe they can be more challenging.

RW


The monsters are substantially more challenging. However, SOLO is an unlimited source. The Unreasonable level puzzles generally -- but do not always -- require comprehensive forcing chains, Nishio or similar level tactics -- and are unlikely to be solved without pencilmarks by humans in a logical fashion. You used a uniqueness-reduction without pencil marks? A very short "trailing pattern" without a candidate grid? Really? Maybe you could describe your technique and maybe post these puzzles you found so easy?

Here's a few SOLO Unreasonables chosen at random for the rest to judge if they're so easy:

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 | . . .


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


Code: Select all
. . . | 4 . . | . 2 .
. . . | . . . | . 4 8
. . 8 | . 3 . | 6 . 5
------+-------+------
. 8 . | . 9 . | 2 . .
9 . . | 7 . 2 | . . 1
. . 2 | . 4 . | . 5 .
------+-------+------
3 . 5 | . 1 . | 4 . .
7 2 . | . . . | . . .
. 6 . | . . 3 | . . .
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Postby RW » Sun Mar 19, 2006 7:21 pm

tso wrote:Maybe you could describe your technique and maybe post these puzzles you found so easy?


The original grid:

Code: Select all
*-----------*
|61.|..8|.7.|
|8..|.5.|12.|
|...|...|...|
|-----------|
|...|3.6|.85|
|.68|...|29.|
|52.|8.9|...|
|-----------|
|...|...|...|
|.37|.9.|..4|
|.8.|2..|.17|
*-----------*


The very basic techniques get us to this point, where Simple Sudoku had no more solvable:
Code: Select all
*-----------*
|612|..8|57.|
|8..|.5.|12.|
|...|..2|..8|
|-----------|
|...|326|.85|
|.68|...|29.|
|52.|8.9|...|
|-----------|
|...|.8.|..2|
|237|.9.|8.4|
|.8.|2..|.17|
*-----------*

I've developed quite an eye for uniqueness patterns, and in this case my attention fell upon number 5 in r2c5 that forces number 5 in row 5 into either column 4 or 6. My next thought in these cases is "what would turn this into a double solution situation?" Then I quickly spotted that placing number 1 in r3c5 would give us number 6 in r9c5 and two 1-5 pairs in r5c4, r5c6, r8c4 and r8c6 =>double solution => only space left for 1 in row 3 is in column 4. Situations like these, where a very short 2 or 3 step trail leads to a double solution, are very common. I use this technique in almost every puzzle.

The first time I really got stuck was in the same situation as SS got stuck the second time:
Code: Select all
*--------------------------------------------*
| 6    1    2  | 49   34   8  | 5    7    39 |
| 8    4    3  | 69   5    7  | 1    2    69 |
| 79   759  59 | 1    36   2  | 36   4    8  |
|--------------------------------------------|
| 179  79   19 | 3    2    6  | 4    8    5  |
| 3    6    8  | 45   7    45 | 2    9    1  |
| 5    2    4  | 8    1    9  | 7    36   36 |
|--------------------------------------------|
| 149  59  1569| 7    8    345| 369  35   2  |
| 2    3    7  | 56   9    1  | 8    56   4  |
| 49   8    569| 2    46   453| 369  1    7  |
*--------------------------------------------*

Copied the candidates from simple sudoku to make it easier for you to follow. The big problem was actually to spot the swordfish in r2c4, r2c9, r6c8, r6c9, r8c4 and r8c8. I admit that this is a pattern that I often miss. Fortunately, it's quite obvious there this time so I eventually saw it and could remove candidate 6 from r7c8 (already removed in the diagram). After this I did what I always do when I can't get anything in one step. I start picking numbers and mentally read a few steps ahead, if a contradiction or forcing chain would appear. Fortunately, my first pick was number 9 in r9c1. Here's what I saw: If r9c1=9 then r7c2=5 and r9c3=6. Now we've reached the contradiction as both r7c8 and r9c7 in box three would have to hold number 3. Rest of the puzzle is easy.

Don't worry, I don't blame solo for having easy puzzles, I did two more and they took me nearly an hour each. I average around 15min on vanhegan extremes, so these can be considered a lot harder. I'm not sure yet if I want to try vidar's monsters, as they would probably be the first puzzles ever that force me to give up or start making notes...

RW
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Postby tso » Mon Mar 20, 2006 2:18 am

RW wrote:I've developed quite an eye for uniqueness patterns ... Situations like these, where a very short 2 or 3 step trail leads to a double solution, are very common. I use this technique in almost every puzzle.


Yep, that certainly works. Impressive technique to use where I would surely have broken down and filled in at least some of the candidates. I'm going to have to try to see if I can find these without candidates myself.

Code: Select all
+-------+---------+-------+
| 6 1 2 | .  .  8 | 5 7 . |
| 8 . . | .  5  . | 1 2 . |
| . . . | . (1) 2 | . . 8 |
+-------+---------+-------+
| . . . | 3  2  6 | . 8 5 |
| . 6 8 |(15).(15)| 2 9 . |
| 5 2 . | 8  .  9 | . . . |
+-------+---------+-------+
| . . . | .  8  . | . . 2 |
| 2 3 7 |(15)9(15)| 8 . 4 |
| . 8 . | 2 (6) . | . 1 7 |
+-------+---------+-------+


r3c5=1 -> r9c5=6 -> r8c46=[15][15]
r3c5=1 -> r45c5=[47][47] -> r5c46=[15][15]
This gives a dual solution, therefore r3c5<>1 and r3c4=1



RW wrote:The first time I really got stuck was in the same situation as SS got stuck the second time:
Code: Select all
*--------------------------------------------*
| 6    1    2  | 49   34   8  | 5    7    39 |
| 8    4    3  | 69   5    7  | 1    2    69 |
| 79   759  59 | 1    36   2  | 36   4    8  |
|--------------------------------------------|
| 179  79   19 | 3    2    6  | 4    8    5  |
| 3    6    8  | 45   7    45 | 2    9    1  |
| 5    2    4  | 8    1    9  | 7    36   36 |
|--------------------------------------------|
| 149  59  1569| 7    8    345| 369  35   2  |
| 2    3    7  | 56   9    1  | 8    56   4  |
| 49   8    569| 2    46   453| 369  1    7  |
*--------------------------------------------*




Uh, but you said (bolds are mine):
RW wrote:
Using my normal technique, without pencilmarks, only entering certain numbers, the unreasonable took me about 15 minutes.



You reached this position without pencilmarks? In what sense -- since you point out that you excluded '6' from r7c8 by Swordfish -- maybe you could *see* this swordfish without pencilmarks, but what exactly does it mean to exclude the '6' from a cell without the candidates enumerated? If the reason that you don't use candidates is simply that you have a photograhic memory and/or are able to see many, many, steps forward -- that doesn't mean the puzzle isn't difficult, only that you are exceptionaly talented.

RW wrote:Copied the candidates from simple sudoku to make it easier for you to follow.

Easier for *me* to follow? Are you implying that finished off the puzzle, finding the deductions you describe from the following grid, without entering candidates?

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


Your description of these final two deductions implies that you *did* use a candidate grid, and in fact, there are many candidate eliminations that simply cannot be made without a grid to eliminate them from.

RW wrote:The big problem was actually to spot the swordfish in r2c4, r2c9, r6c8, r6c9, r8c4 and r8c8. I admit that this is a pattern that I often miss. Fortunately, it's quite obvious there this time so I eventually saw it and could remove candidate 6 from r7c8 (already removed in the diagram).

After this I did what I always do when I can't get anything in one step. I start picking numbers and mentally read a few steps ahead, if a contradiction or forcing chain would appear. Fortunately, my first pick was number 9 in r9c1. Here's what I saw: If r9c1=9 then r7c2=5 and r9c3=6. Now we've reached the contradiction as both r7c8 and r9c7 in box three would have to hold number 3. Rest of the puzzle is easy.


r9c1=9 -> r7c2=5 -> r7c8=3;
(r9c1=9 AND r7c2=5) -> r9c3=6;
(r9c1=9 AND r9c3=6) -> r9c7=3

Contradiction, therefore r9c1=4.
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Postby RW » Mon Mar 20, 2006 12:13 pm

tso wrote:You reached this position without pencilmarks? In what sense -- since you point out that you excluded '6' from r7c8 by Swordfish -- maybe you could *see* this swordfish without pencilmarks, but what exactly does it mean to exclude the '6' from a cell without the candidates enumerated? If the reason that you don't use candidates is simply that you have a photograhic memory and/or are able to see many, many, steps forward -- that doesn't mean the puzzle isn't difficult, only that you are exceptionaly talented.

The fact is that I have never entered a single pencilmark into any grid I've been working on. By working like this right from the start I've improved my short-term memory significantly. In the beginning I could read at most 3 or 4 steps ahead, by now my record is to mentally solve the last 48 numbers of a puzzle, then write them down one row at a time starting from the upper left corner.

In the swordfish case I noticed the swordfish and saw that r7c8 couldn't be 6. As this didn't help me I started to look for another solution. I picked the 9 and my trail of thought was something like this: "r9c1=9 -> r7c2=5 -> r9c3=6 -> r9c7=3 r7c8=6;-> r6c8=3 => r6c9=6... wait a minute, there was a swordfish pattern around here, doesn't that make this impossible?" Then I rechecked my trail against the swordfish and saw that there was a contradiction.

So to "exclude a candidate" from a grid without pencilmarks means to memorize that the candidate can't be there. That's why I simply can't work with a pencilmark grid. A pencilmark grid shows which numbers can be in each cell, my way of solving is to memorize which candidates can't be in each cell. There was actually a point where I changed my technique from solving based on possible candidates to solving based on not-possible candidates, and this improved my solving times significantly. In this specific case this meant that I did not try to remember the possible numbers 3 and 5 in r7c8, but the impossible number 6 (the other impossibles can be seen from the box and column, so I don't need to remember them). Only half amount of data to remember, which does make a huge difference when memorizing stuff all over the grid. If there is anybody else out there solving without pencilmarks I can really recommend this techinque, at least it works well for me.

RW
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Postby tso » Mon Mar 20, 2006 7:11 pm

RW wrote:The fact is that I have never entered a single pencilmark into any grid I've been working on.


In other words, you are exceptionally skilled and/or have mastered a very effective technique. Once a person has mastered juggling 5 clubs, it is as easy as walking. That doesn't change the fact that the juggling 5 clubs is an incredibly difficult skill that few will ever master -- and not without a great deal of practice.


RW wrote:... by now my record is to mentally solve the last 48 numbers of a puzzle, then write them down one row at a time starting from the upper left corner.


Ok, 7 clubs.


The asterisks exclude the 6 at r7c8 while the trail leading from (9)(5)(6)(3) force a 6 at r7c8. So r9c1 must be 4.
Code: Select all
+-------+-------+-------+
| 6 1 2 | . . 8 | 5 7 . |
| 8 4 3 | * 5 7 | 1 2 * |
| . . . | 1 . 2 | . 4 8 |
+-------+-------+-------+
| . . . | 3 2 6 | 4 8 5 |
| 3 6 8 | . 7 . | 2 9 1 |
| 5 2 4 | 8 1 9 | 7 * * |
+-------+-------+-------+
| .(5). | 7 8 . | .[6]2 |
| 2 3 7 | * 9 1 | 8 * 4 |
|(9)8(6)| 2 . . |(3)1 7 |
+-------+-------+-------+



Those less talented could use your method and still use pencilmarks, entering marks to indicate not-possibles. I've used this tactic on [what I would consider] easier puzzles.


I think it would be *very* welcomed if you would solve a few puzzles that are considered difficult (but it doesn't have to be a 'monster') by most of us using your method and give the play-by-play in a new thread in the advanced solving techniques forum. 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 | . . .


Some of us started as no-pencilmark solvers back when the hardest puzzles available weren't much harder than the easiest and would be glad to increase the chance reaching a solution in pen.
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