tough sudoku problem
DanInPhilly
next step:
. 4 3 . 6 . 7 2 .
7 1 . . . . 3 5 .
9 . . . . 3 4 8 .
3 8 5 . 4 . 2 1 7
4 . . 3 . 1 5 9 8
1 . 9 . 5 . 6 4 3
. . 1 2 3 . 9 . 4
. 9 . . . . . 3 2
2 3 4 . 9 . . . 5
TIA,
Dan
Marc Dashevsky
> . 4 3 . 6 . 7 2 .
> 7 1 . . . . 3 5 .
> 9 . . . . 3 4 8 .
> 3 8 5 . 4 . 2 1 7
> 4 . . 3 . 1 5 9 8
> 1 . 9 . 5 . 6 4 3
> . . 1 2 3 . 9 . 4
> . 9 . . . . . 3 2
> 2 3 4 . 9 . . . 5
I'm not a Sudoku expert, but when I encounter a puzzle where my
rules allow me to go no further, I make a copy of the semicompleted
puzzle. I then choose a cell that has only two possible values and
assume that one of those values is correct. I next fill in as much
of the puzzle as I can based on that assumption until (1) I complete
the puzzle correctly [rarely], (2) I end up with two of the same value
in the same column, row or nonad, thereby revealing that the cell I
started with contains the wrong value, or (3) I hit another dead end.
In this last case I just pick another two-value cell.
In the case of your puzzle, I was very lucky: I assigned 8 to the
7th cell in the bottom row. I ran into another dead end quickly
and assigned 6 to the 6th cell in the bottom row. This led to a
complete solution.
--
Go to http://MarcDashevsky.com to send me e-mail.
DanInPhilly
then I posted it here, and a smarter person showed me how to figure it out
logically, without making any assumptions. I'm hoping that the latter is
possible in this case.
"Marc Dashevsky" <use...@MarcDashevsky.com> wrote in message
news:MPG.256beb908...@news.supernews.com...
Zurab57
1-st move: there should be 8 in first left column and 8-th row, so we
wright "8" in the cell at the crossing of this lines.
Zurab57
sorry, it is not right.
Sylvia Else
It's not necessarily possible to solve a partially completed sudoku
unless one knows which of the digits were provided, and which were
inserted by the solver. You need to provide the original as well as the
point you've reached.
Sylvia.
Nick
> . 4 3 . 6 . 7 2 .
> 7 1 . . . . 3 5 .
> 9 . . . . 3 4 8 .
> 3 8 5 . 4 . 2 1 7
> 4 . . 3 . 1 5 9 8
> 1 . 9 . 5 . 6 4 3
> . . 1 2 3 . 9 . 4
> . 9 . . . . . 3 2
> 2 3 4 . 9 . . . 5
There's an X-wing on 8s (rows 2 and 8, columns 3 and 5). That
immediately resolves the 18s in the bottom right square and it all falls
apart from there on.
--
Online waterways route planner: http://canalplan.org.uk
development version: http://canalplan.eu
Sylvia Else
Actually, I think I'll take that back. It would still be nice to see the
starting point, though.
Sylvia.
Nick
It helps if the solver has made a mistake along the way! But I was
intrigued by the concept of a Sudoku where it's easier to solve if you
remove some of the digits!
Sylvia Else
I was thinking that since the soduku has to have a unique solution, one
can eliminate certain digits if they would result in pairs of digits
that could be reversed to get an alternate solution. Knowing whether a
pair of digits can be reversed would depend on whether either of them
was provided.
However, if a digit was not provided, but was instead inserted by the
solver, either it is correct, in which case it cannot be reversed, or it
is incorrect, in which case a contradiction should be found.
So much for thinking.
Sylvia.
Marc Dashevsky
says...
> "DanInPhilly" <dj...@aol2.com> writes:
>
> > . 4 3 . 6 . 7 2 .
> > 7 1 . . . . 3 5 .
> > 9 . . . . 3 4 8 .
> > 3 8 5 . 4 . 2 1 7
> > 4 . . 3 . 1 5 9 8
> > 1 . 9 . 5 . 6 4 3
> > . . 1 2 3 . 9 . 4
> > . 9 . . . . . 3 2
> > 2 3 4 . 9 . . . 5
>
> There's an X-wing on 8s (rows 2 and 8, columns 3 and 5). That
> immediately resolves the 18s in the bottom right square and it all falls
> apart from there on.
Would you explain what an X-wing is?
Willem
) In article <87iqd9v...@temporary-address.org.uk>, 3-no...@temporary-address.org.uk
) says...
)> "DanInPhilly" <dj...@aol2.com> writes:
)>
)> > . 4 3 . 6 . 7 2 .
)> > 7 1 . . . . 3 5 .
)> > 9 . . . . 3 4 8 .
)> > 3 8 5 . 4 . 2 1 7
)> > 4 . . 3 . 1 5 9 8
)> > 1 . 9 . 5 . 6 4 3
)> > . . 1 2 3 . 9 . 4
)> > . 9 . . . . . 3 2
)> > 2 3 4 . 9 . . . 5
)>
)> There's an X-wing on 8s (rows 2 and 8, columns 3 and 5). That
)> immediately resolves the 18s in the bottom right square and it all falls
)> apart from there on.
)
) Would you explain what an X-wing is?
In column 3, the 8 can only be in row 2 or row 8.
In column 5, the 8 can only be in row 2 or row 8.
That means that the 8s are either in (3,2) and (5,8) or in (3,8) and (5,2).
And that in turn means that there can't be an 8 in any of the other columns
of rows 2 and 8. So you can eliminate those.
This is quite a visual pattern to spot, and it's a lot easier if you
highlight all squares that can contain an 8.
SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
Kevin Stone
>> There's an X-wing on 8s (rows 2 and 8, columns 3 and 5). That
>> immediately resolves the 18s in the bottom right square and it all falls
>> apart from there on.
>
> Would you explain what an X-wing is?
See http://www.brainbashers.com/sudokuxwing
--
Kev
Nick
> Go to http://MarcDashevsky.com to send me e-mail.
http://lmgtfy.com/?q=sudoku+x+wing
DanInPhilly
Now if you'll all bear with me:
AAAAAAAAARRRRRRRRRRRRRGGGGGGGHHHHHH!!!!!!!!!!!
"Nick" wrote in message ...
Marc Dashevsky
Thanks to all who answered. I'll have to search to see if I can
find other solution techniques that I have not yet discovered.
--CELKO--
Many of the published puzzles have multiple answers. Sorry.
Her is the code for an SQL statement that will find all the answers,
or blow up trying.
Sylvia Else
>>> I was thinking that since the soduku has to have a unique solution, .. <<
>
> Many of the published puzzles have multiple answers. Sorry.
As I understand it, if there are multiple answers, then they are not, by
definition, Sodukus.
While I don't doubt that it is possible to construct Sudoku-like puzzles
that have multiple solutions, I haven't come across any.
Sylvia.
Barry
Although it has been a few years....
Kevin has great explanations of methods of solving sodukos.
I haven't looked lately to see if he added the really complex ones.
I wrote a program based on Kevin's methods. It's ugly because
I implemented each step at a time.
Willem wrote one using a method (of which I haven't studied
because I was bored with sudo) which outperformed just about
everything.
barry
Nick
Here you go:
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
... ... ...
Sylvia Else
> Sylvia Else <syl...@not.at.this.address> writes:
>
>> --CELKO-- wrote:
>>>>> I was thinking that since the soduku has to have a unique solution, .. <<
>>> Many of the published puzzles have multiple answers. Sorry.
>> As I understand it, if there are multiple answers, then they are not,
>> by definition, Sodukus.
>>
>> While I don't doubt that it is possible to construct Sudoku-like
>> puzzles that have multiple solutions, I haven't come across any.
>
> Here you go:
>
> ... ... ...
> ... ... ...
> ... ... ...
>
> ... ... ...
> ... ... ...
> ... ... ...
>
> ... ... ...
> ... ... ...
> ... ... ...
Ok, now I've come across one.
Sylvia.
Richard Heathfield
<snip>
> As I understand it, if there are multiple answers, then they are
> not, by definition, Sodukus.
On the contrary, that's exactly what they are!
They are not, however, Sudokus. :-)
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
"Usenet is a strange place" - dmr 29 July 1999
Sig line vacant - apply within
Matthew Russotto
Sylvia Else <syl...@not.at.this.address> wrote:
>It's not necessarily possible to solve a partially completed sudoku
>unless one knows which of the digits were provided, and which were
>inserted by the solver. You need to provide the original as well as the
>point you've reached.
Unless the solver made an error, why would it make a difference?
--
The problem with socialism is there's always
someone with less ability and more need.
Willem
) In article <007e24ee$0$23455$c3e...@news.astraweb.com>,
) Sylvia Else <syl...@not.at.this.address> wrote:
)
)>It's not necessarily possible to solve a partially completed sudoku
)>unless one knows which of the digits were provided, and which were
)>inserted by the solver. You need to provide the original as well as the
)>point you've reached.
)
) Unless the solver made an error, why would it make a difference?
There are techniques that become inappliccable if some squares are filled
in with their values. In that case, it becomes possible that the sudoku
can not be solved anymore by any known logic technique. However, solving
by trial-and-error always remains possible; the solution remains unique.
Nick
> Matthew Russotto wrote:
> ) In article <007e24ee$0$23455$c3e...@news.astraweb.com>,
> ) Sylvia Else <syl...@not.at.this.address> wrote:
> )
> )>It's not necessarily possible to solve a partially completed sudoku
> )>unless one knows which of the digits were provided, and which were
> )>inserted by the solver. You need to provide the original as well as the
> )>point you've reached.
> )
> ) Unless the solver made an error, why would it make a difference?
>
> There are techniques that become inappliccable if some squares are filled
> in with their values. In that case, it becomes possible that the sudoku
> can not be solved anymore by any known logic technique. However, solving
> by trial-and-error always remains possible; the solution remains unique.
I know of cases where removing some possibles prevents better
deductions, but I've never come across a case where actually fixing a
square removes a technique without enabling an easier one. I'd love to
see it - do you have an example?