Sudoku rules question
7cl...@gmail.com
call them classifications. First, there are those which you can march
through mechanically, and the solution just falls into place. Second,
there seem to be those in which you eventually reach a dead end. You
might know that a cell has to be either a 4 or a 5, but there seems to
be no way to determine which, without trying one or the other (please
correct me if I am wrong). A number of things can happen at that
point, but what I am interested in is this: what is the normal
practice for Sudoku in newspapers? (I worked one that seemed to be of
that type in a newspaper, shown in the address below) Is there any
kind of general agreement that - in newspapers, at least - they should
not be of this type? Is that just a misconception on my part? Or is
that merely the line of demarcation between those classified as Easy
and those classified as Difficult? (I can see how they could be
somewhat time-consuming if the first trial described above leads to
another dead end, etc.)
The puzzle in question is here: http://rapidshare.com/files/147149351/091908.gif
Thank you.
Stephan Bird
385e6d80-9190-4df5...@y21g2000hsf.googlegroups.com,
7cl...@gmail.com wrote:
I guess the terms Easy / Difficult / Fiendish etc are rather subjective
and what one person finds easy, another may find difficult. How far do
you get in this puzzle before you have to make this decision? I have just
worked through it without having to make a decision of the sort you
describe, so I'd be interested to see the sorts of things you have tried.
Here's the puzzle in ASCII
*-----------*
|9..|...|...|
|...|.59|6..|
|.3.|68.|1..|
|---+---+---|
|.6.|...|..7|
|79.|.1.|.53|
|2..|...|.1.|
|---+---+---|
|..4|.37|.8.|
|..5|29.|...|
|...|...|..1|
*-----------*
Stephan
--
Stephan Bird MChem(Hons) AMRSC
stephan...@mad.scientist.com
Currently in Macclesfield, Cheshire
[Mr.] Lynn Kurtz
I lost what little interest I had in Soduku when a friend, who works
them all the time, was having trouble with one. I had a little time to
kill so I tried to solve it too. The only problem was, we came up with
different answers, both of which I carefully checked to be correct. At
that point, I quit.
--Lynn
Willem
) The puzzle in question is here: http://rapidshare.com/files/147149351/091908.gif
That puzzle can be solved with just basic deduction, so I guess you simply
missed an obvious clue somewhere.
Also, to answer your question: there are a lot more techniques to deduce
squares without having to resort to guessing, but usually none of those
are needed to solve newspaper sudokus.
There are sudokus of various difficulties on Kevin's site:
http://www.brainbashers.com/sudoku.asp
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
Mensanator
> On 21 Sep 2008 18:34:21 GMT, Stephan Bird <sjb2...@yahoo.com> wrote:
>
>
>
>
>
> >On Sun, 21 Sep 2008 11:09:26 -0700 in
I think "proper" puzzles are supposed to
have unique solutions. But who knows what
the quality is with a given source?
I did a few from a newspaper and my answers
always matched the published answers. I got
tired of them as the solutions depended on
ever trickier moves. It became no more fun
than solving a Rubik's cube, so I quit also.
>
> --Lynn- Hide quoted text -
>
> - Show quoted text -
Kevin Stone
> but there seems to
> be no way to determine which, without trying one or the other (please
> correct me if I am wrong)
You're wrong! As seen in another post, BrainBashers Sudoku are guaranteed to
be just what they say they are.
--
Kev
www.brainbashers.com/sudoku
Kevin Stone
> but there seems to
> be no way to determine which, without trying one or the other (please
> correct me if I am wrong)
You're wrong!
:)
As seen in another post, BrainBashers Sudoku are guaranteed to be just what
they say they are. The sudoku you quoted can now be found here:
http://www.brainbashers.com/sudokuload4388
And only requires the most basic of techniques.
Kevin Stone
> to be just what they say they are.
Mmmm - posted a fraction too early!
--
Kev
7cl...@gmail.com
> Currently in Macclesfield, Cheshire
I'll be interested in where I missed something. The file below shows
where I got hung up. At that point I tried a 5 in cell A3, and it
solved.
Thanks!
7cl...@gmail.com
> Currently in Macclesfield, Cheshire
I see it now. Cell I8 has to be a 4. Sorry!
spudnik
have gotten most of the basic techniques
from moments of excessive freetime
-- I don't know if I've gotten all of them,
becase I haven't looked at any sites/books on it.
one can easily see, for instance,
that most newspapers use a program
-- see, the symmetry, most have? --
to generate sudokus with presumably unique solutions;
guessing without a pencil & eraser is counter-
productive!
Mike Terry
CBFalconer
>
... snip ...
>
> I lost what little interest I had in Soduku when a friend, who
> works them all the time, was having trouble with one. I had a
> little time to kill so I tried to solve it too. The only problem
> was, we came up with different answers, both of which I
> carefully checked to be correct. At that point, I quit.
Then the puzzle was generated by an amateur. No Sudoku puzzle can
have any different answers - if it does it is not a Sudoku.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
7cl...@gmail.com
Just to make sure I completely understand what you're saying... The
sudoku on your site, including the most difficult ones, do not require
any "trials". In other words, if you get to a point where you seem not
to be able to proceed, there is in fact no need to resort to making an
assumption and trying it out. You have simply missed something,
correct?
Thanks.
Kevin Stone
> sudoku on your site, including the most difficult ones, do not require
> any "trials". In other words, if you get to a point where you seem not
> to be able to proceed, there is in fact no need to resort to making an
> assumption and trying it out. You have simply missed something,
> correct?
Correct. No BrainBashers Sudoku ever requires a guess.
--
Kev
Michael Press
<3220cc3b-cee0-45d6...@m73g2000hsh.googlegroups.com>,
Mensanator <mensa...@aol.com> wrote:
Always I first fill in all candidates, because
working a puzzle otherwise is not much fun, and
is tedious. But filling in the candidates is
tedious, so I wrote a program to do that. Still
have to type the puzzle in, so the program can
print out the candidates.
The first thing I ever did with S. was to write a
branch and bound program to `solve' it.
--
Michael Press
--CELKO--
A friend of mine, Richard Romley wrote a Soduku solver as a single SQL
statement. We then tested it with data from several websites and
published puzzles. Since SQL is a set-oriented language, it found all
the possible answers.
LOTS of them have multiple answers, some of the newspaper ones had
over a dozen.
riderofgiraffes
Is it not the case that some sudoku do require
deeper reasoning, which may at some level be
equated to trial-n-backup / branch-n-bound?
Consider the following example. I would be
interested to see the reasoning behind a non-
"try it and see" solution ...
+-------+-------+-------+
| 7 . 8 | . . . | 3 . . |
| . . . | 2 . 1 | . . . |
| 5 . . | . . . | . . . |
+-------+-------+-------+
| . 4 . | . . . | . 2 6 |
| 3 . . | . 8 . | . . . |
| . . . | 1 . . | . 9 3 |
+-------+-------+-------+
| . 9 . | 6 . . | . . 4 |
| . . . | . 7 . | 5 . . |
| . . . | . . . | . . . |
+-------+-------+-------+
Obviously viewing in fixed font will help.
If this does not fall to the simpler reasoning, and
yet every BrainBashers sudoku does, then that means
that the BrainBashers site does not produce the most
difficult examples.
Anthony Buckland
"Mensanator" <mensa...@aol.com> wrote in message
news:3220cc3b-cee0-45d6...@m73g2000hsh.googlegroups.com...
...
>I think "proper" puzzles are supposed to
>have unique solutions. But who knows what
>the quality is with a given source?
>
>I did a few from a newspaper and my answers
>always matched the published answers. I got
>tired of them as the solutions depended on
>ever trickier moves. It became no more fun
>than solving a Rubik's cube, so I quit also.
I still enjoy them, getting the most out of
newspaper Sudoku by timing myself.
Strangely, I find I make the most mistakes
at lower levels. Maybe not so strange;
there are more "givens" to miss in
breakfast-time brain fog.
I once detected ambiguity in a Reader's
Digest puzzle, wrote in about it, and found
the editor was surprised to have had low
quality supplied (RD claimed a unique
solution, the one in question had over 200!).
Since then, they've shaped up, and actually
had a diagonals-too Sudoku which had
two solutions until the diagonals were
brought in, so it's possible to have four
"dimensions" to take into account.
Simon Tatham
> A friend of mine, Richard Romley wrote a Soduku solver as a single SQL
> statement. We then tested it with data from several websites and
> published puzzles. Since SQL is a set-oriented language, it found all
> the possible answers.
>
> LOTS of them have multiple answers, some of the newspaper ones had
> over a dozen.
That sounds pretty unlikely to me. My first instinct in such a case
would be to check and double-check the purported solutions to make
sure they were actually all valid, because it would seem much more
probable that the SQL statement was erroneously returning some false
positives.
Do you have any detailed examples?
--
Simon Tatham "I'm going to pull his head off. Ear by ear."
<ana...@pobox.com> - a games teacher
spudnik
counterproductive.
apparently, the midwesterner's very definition of his game,
is that it has to be uniquely soluble (his first successful market
was in Japan).
have you seen the "greater than" sudoku,
viz www.LAcitybeat.com, which has no entires, but
is uniquely soluble?... at any rate,
all of these puzzles have the solution printed
in the next issue, that I've ever noticed.
they are so ubiquitous, one does not bother
to complete one, in which one has made an error --
one error, of the same number in a row etc.!
> > any "trials". In other words, if you get to a point where you seem not
> > to be able to proceed, there is in fact no need to resort to making an
> > assumption and trying it out. You have simply missed something,
> > correct?
thus:
yes, my only interest in doing them,
is insight to the theory, which is just "magical skwares,"
the origin of matrix theory; eh?
a professor of mine in reply, stated that
16 was the minimum number of entries for unique solution,
but I think he was BSing us; I have'nt come near
to dys/proving that.
the one in today's local "free" paper had 2 planes of mirror symmetry,
more than the usual output from the program; however,
it was only rated one star out of five:
it had 30 filled-in entries, more than I've counted, before;
the least I've seen in a 5-starrer was 21, i think.
"nine-valued logic" ha-ha not even wrong.
> ps : sudoku = 9 - valued logic ;)
thus:
perhaps the "bending glass tubes" were just
a form of slow elasticity, not plasticity or
liquidity. it is easy to see that the artisans
would orient the stained glass, so as not
to create local concetrations of weight;
is lead illiquid, and "currents
in the mantle?..."
Young's experiment was actually two pinholes,
giving a lovely moire' pattern, meanwhile effectively
bursting the corpuscles of Newton and Descartes;
any linear path would give the pattern of the slits, or
a skware or trigonal grating will reestablish the moire';
the light was sunlight through another pinhole,
effectively coherent white light....
the whole wave/particle duality is mathematical,
not really very important, shown by Dirac,
usally preferable to choose one or the other
for doing the math ... leaving that to others,
for the moment-being!
> They don't. The fringes get closer together.
thus:
did you ever consider that, if a.i.g.etaladvomitorium stopped
using the Black-Sholes formula for valuations,
you might be wiped-out?...
well, not at one fell swoop, obviously, since
you are by definition bi-versified.
thus:
in how many ways iff the googolplex a solopsists daymare?...
you neglect the mere fact that the USA is a republic,
whose constitution is explicitly a)
without separation of church & state,
the doctrine of Hugo Black's dissent, and b)
dysestablishmentarian, contra No Child Left Behind
come the Rapture....
did anyone see the report of the new (House?) law,
No Child Left sonething?
> 4. Hindus/Babylonians/Egyptians/Greeks/etc are +3, believing in
--USA out of Darfur Cruizade!
http://larouchepub.com/other/2008/3537willl_zardari_survive.html
--ROTC, your summer vacation in the Sahara Desert ( S u d a n ) ;
presage the Draft for your middleschool class of '12 --
brought to you by Allstate (tm) and Oxford U. Press!
http://larouchepub.com/pr/2008/080813moloch_brown.html
http://wlym.com
Phil B
"Simon Tatham" <ana...@pobox.com> wrote in message
news:Fji*KZ...@news.chiark.greenend.org.uk...
Yes, any Sudoku which has 2 or more digits not represented for a start.
This trivial one very obviously has lots of solutions:
1????????
?????????.
?????????.
?????????.
?????????.
?????????.
?????????.
?????????.
?????????.
Phil
lui...@yahoo.com
> "[Mr.] Lynn Kurtz" wrote:
>
> Then the puzzle was generated by an amateur. No Sudoku puzzle can
> have any different answers - if it does it is not a Sudoku.
>
There is not algorithm to decide if a Sudoku have two or more
solutions
without trying all the possible combinations. But that is not an
algorithm.
Ludovicus
A N Niel
<phil.remove.brady@hotmail> wrote:
Simon means Sudokus published in newspapers, since they are supposed to
have unique solution. Richard claims lots of newspapers have failed
to meet this requirement. Simon says that seems unlikely.
--CELKO--
You can check the code fro yourself at:
http://www.celko.com/sudoku.txt
It is in SQL Server T-SQL dialect, but easy to translate. This is a
single query Sudoku solver by Richard Romley in SQL Server dialect. If
you are a long time fan, you will know that name from my columns in
RDBMS and DATABASE PROGRAMMING & DESIGN magazines. Richard is now
retired from Smith-Barney Solomon but when he was working on Wall
Street, he was the "go to" SQL guy. On a regular basis, he cooked my
SQL puzzles (note: 'to cook" is a verb in recreational mathematics
that means to post a better solution than the person who posted the
puzzle).
The purpose of this query is to take a 9x9 Sudoku grid as input and
return ALL -- repeat ALL -- possible solution grids. I bet you thought
that a puzzle always had a single solution. Nope. In fact, Richard
found one published puzzle with over 35 answers.
The number of essentially different solutions, when symmetries such as
rotation, reflection and re-labeling are taken into account, was shown
by Ed Russell and Frazer Jarvis to be just 5,472,730,538 which is
still a large result set.
There is an article on Sodoku solving from IEEE SPECTRUM on-line about
how it is NP-complete. There is a proof that if you have 26 known
cells at the start, then you have one and only one answer. Less than
that, you cannot predict the size of the answer set. If you want to do
something very dumb with this code, then type in the digits one to
nine in a single row or column. You can then bitch that it failed to
return hundreds of millions of answer girds in less than a second!
Yes, someone actually did this!
The real purpose of the procedure is to demonstrate that:
1) A long parameter list is not harmful. So instead of writing a
parser in a proprietary 3GL language, XML or whatever, you can depend
on the compiler to do all that checking and validation. Considering
that most proprietary solutions do not bother with all that checking
and validation of input like a compiler, it is not a fair comparison.
If the answer does not have to be right, the answer is always 42.
2) A huge multi-table self-join (i.e. 81 correlations) is not harmful
when the tables are small. Avoiding self-joins was a heuristic a few
years ago, but the optimizers are smarter, primary storage is bigger
and it just might be time to re-think things.
Anthony Buckland
<lui...@yahoo.com> wrote in message
news:b5adeae4-60c7-41dd...@e53g2000hsa.googlegroups.com...
...
>There is not algorithm to decide if a Sudoku have two or more
>solutions
>without trying all the possible combinations. But that is not an
>algorithm.
>Ludovicus
With respect, a standard dictionary definition of
algorithm is "a set of rules for solving a problem
in a finite number of steps" so trying all of the
(finite) number of possibilties is still an algorithm.
To find whether or not a Sudoku has multiple
solutions:
1) apply all known rules until
a) the Sudoku is solved or
b) an impasse is reached
In case b), successively choose all possibilities
in one square with the minimum number of
choices; for each possibility, repeat from 1).
Iterate to whatever (finite) depth is required.
Eventually finding all solutions with no case-b
choices left is guaranteed. A neglible amount
of time will be spent on actual choice-making,
and all other solving time will be spent usefully
in arriving at solutions.
Then, 2) count the solutions.
Mensanator
> >> Do you have any detailed examples? <<
>
> You can check the code fro yourself at:
>
> http://www.celko.com/sudoku.txt
>
> It is in SQL Server T-SQL dialect, but easy to translate.
Easier than sollving the Soduku itself?
Simon Tatham
> >> Do you have any detailed examples? <<
>
> You can check the code fro yourself at:
> The purpose of this query is to take a 9x9 Sudoku grid as input and
> return ALL -- repeat ALL -- possible solution grids. I bet you thought
> that a puzzle always had a single solution. Nope. In fact, Richard
> found one published puzzle with over 35 answers.
What I meant by "detailed example" was: can you _exhibit_ a
published puzzle with a large number of answers, and at least two of
those answers? I was intending to independently verify the _output_
of the code, not to debug it.
> There is an article on Sodoku solving from IEEE SPECTRUM on-line about
> how it is NP-complete. There is a proof that if you have 26 known
> cells at the start, then you have one and only one answer.
You've posted that statement in this newsgroup before, and it is
still false. Last time, I exhibited the following counterexample:
. . 9 | 7 5 . | . . .
1 4 . | . . 6 | 2 . .
6 . . | . 2 4 | . 9 .
------+-------+------
. . 6 | . . . | . . .
5 9 . | . . 2 | . . .
3 . . | 6 9 1 | . . .
------+-------+------
. . . | . . 7 | . 3 .
4 5 . | . 6 9 | 7 . .
. . 2 | 4 . . | . . .
which has 28 known cells and still has multiple answers.
--
Simon Tatham "infinite loop _see_ loop, infinite"
<ana...@pobox.com> - Index, Borland Pascal Language Guide
spudnik
unless it's in the archives of whole issues. anyway,
it's very simple:
the borders of the smallest boxes are decorated with >,
in all four directions (up or down or left or right,
on all four sides of the box); so,
just make an arbitrarily filled-in sudoku,
install the "greater than (or lesser than)" symbols,
then erase the numbers & try it the next day.
perhaps, though, it must be proven,
that there is only one solution thereby;
anyone?
also, you can send to the producer of these,
various format sudokus, psycho...@hotmail.com.
thus:
spacetime is a misnomer, enunciated by an otherwise great
mathematician,
Minkowski, alas then died young. it's just phase-space,
whereby the "curvature" part becomes quite nonsequiter:
did you not see the ellipses that Kepler hath found?
> Wrong. It is space-time curvature. The planets follow geodesics
> in space-time, not in space. Please learn some GR.
thus:
Newton was not really a scientist; a biblical chronologer,
alchemist & likely freemason, yes -- if you want to count
*that* latter as a social skill.
Newton is the secular church of England,
as adumbrated through the Harry Potter PSes,
in their ongoing trashing of Leibniz.
there was a recent novelization of Newton,
as a "genius" *and* a spy, that is probably nearer
to the truth; otherwise,
it is abundantly clear in between the lines
of the "major biographers" -- or, at least,
in that recent biography.
well, again, only larouchiax seem to be aware
of this!
> Newton's social skills? That's a good one! Are you pulling our legs?
spudnik
I don't care if you tell me the number, as long
as you don't tell me how to solve it!
Patrick Hamlyn
In fact, if we reqard as equal any two Sudokus which have the same pattern but
with digits transposed, you just described *all* Sudokus.
--
Patrick Hamlyn posting from Perth, Western Australia
Windsurfing capital of the Southern Hemisphere
Moderator: polyforms group (polyforms...@egroups.com)
Patrick Hamlyn
>If you want to do
>something very dumb with this code, then type in the digits one to
>nine in a single row or column.
Clearly such an arrangement has the maximum number of solutions (up to summetry,
relabelling etc).
Is there any arrangement with more digits specified which also fails to
eliminate *any* solutions?
7cl...@gmail.com
I worked the first "super difficult" Sudoku on your site. Not
surprisingly I reached a dead end. I could solve it, but only by
postulating. If there is a logical next step (see link below), I don't
see it. Please educate me. Thanks
Derek Holt
7clo...@gmail.com wrote:
I have not looked at the puzzle you mention, but the more advanced
forms of reasoning to solve Sudokus, such as "XY wing" and "simple
colouring" generally involve the following types of argument.
You know that some cell can be either 1 or 2. In either case, a short
and simple chain of deductions reveals that some other cell must be 3,
or maybe cannot be a 3.
It seems to me that this type of reasoning is just disguised
guesswork. It is essentially guessing but with only a single level of
branching allowed. All of the super difficult/fiendish puzzles that I
have seen in newspapers could be solved moderately easily with a
single level of branching, once you have found the best square to
branch from.
Incidentally, some another forms of reasoning advocated on websites,
such as "unique rectangles" makes the assumption that the solution is
unique i.e. the reasoning goes, if this cell were a 1, then there
could not possibly be a unique solution, so it cannot be 1.
I don't like that, because I would expect a valid solution to a Sudoku
to tacitly include a uniqueness proof as part of the solution.
Derek Holt.
7cl...@gmail.com
Thanks - I utilized all the obvious "by elimination" reasoning, which
is why I got as far as I did, so the next step is very non-obvious, to
me at least. See the diagrams in the link in my preceding post.
Phil Carmody
> --CELKO-- <jcel...@earthlink.net> wrote:
>> There is an article on Sodoku solving from IEEE SPECTRUM on-line about
>> how it is NP-complete. There is a proof that if you have 26 known
>> cells at the start, then you have one and only one answer.
>
> You've posted that statement in this newsgroup before, and it is
> still false. Last time, I exhibited the following counterexample:
>
> . . 9 | 7 5 . | . . .
> 1 4 . | . . 6 | 2 . .
> 6 . . | . 2 4 | . 9 .
> ------+-------+------
> . . 6 | . . . | . . .
> 5 9 . | . . 2 | . . .
> 3 . . | 6 9 1 | . . .
> ------+-------+------
> . . . | . . 7 | . 3 .
> 4 5 . | . 6 9 | 7 . .
> . . 2 | 4 . . | . . .
>
> which has 28 known cells and still has multiple answers.
Isn't there a grid with 77 known cells that has multiple answers?
Phil
--
The fact that a believer is happier than a sceptic is no more to the
point than the fact that a drunken man is happier than a sober one.
The happiness of credulity is a cheap and dangerous quality.
-- George Bernard Shaw (1856-1950), Preface to Androcles and the Lion
Richard Heathfield
<snip>
>
> Isn't there a grid with 77 known cells that has multiple answers?
There are many such grids. Here's an example, with just the relevant row
given:
123 | 458 | 679
45 | 93 | 128
89 | 12 | 345
(The other two rows, not shown here, are fully populated, giving the other
54 known cells.)
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
amy666
how does one create such a ' real ' ( unique solvable ) sudoku then ?
regards
tommy1729
amy666
how to make a sudoku that has only got a single unique solution ??
if that is hard to answer , it easy to imagine the newspapers published S with several solutions ...
amy666
seems reasonable , but how do you know that so surely ?
also , how does one then design a sudoku that has a unique solution ?
Simon Tatham
> Isn't there a grid with 77 known cells that has multiple answers?
Oh yes. But the other useful property of the 28-cell grid I
exhibited is that no cell can be deduced from the other 27. So if
the "proof" was incompletely stated and intended to say that once
you have 26 _non-redundant_ clues then the solution must be unique,
my grid provides a counterexample to that too.
--
Simon Tatham "What a caterpillar calls the end of the
<ana...@pobox.com> world, a human calls a butterfly."
Willem
) Incidentally, some another forms of reasoning advocated on websites,
) such as "unique rectangles" makes the assumption that the solution is
) unique i.e. the reasoning goes, if this cell were a 1, then there
) could not possibly be a unique solution, so it cannot be 1.
I have once seen a sudoku that had gave unique solution if you used
these 'unique rectangle' methods, but in fact it turned out to be
flawed and have several solutions. I lost it, unfortunately.
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
> surprisingly I reached a dead end
At which point you should have checked how the answer was deduced using the
"Show Answer".
I find it a little odd that someone who doesn't know Sudoku that well, to
try my hardest, and then wonder why they reach a dead end?
The puzzle in question requires X-Wings, Swordfish and XY-Wings to complete.
Not at all easy, indeed some might say 'Super Hard'. Which, funnily enough,
is the level you chose!
--
Kev
Duncan Booth
> I worked the first "super difficult" Sudoku on your site. Not
> surprisingly I reached a dead end. I could solve it, but only by
> postulating. If there is a logical next step (see link below), I don't
> see it. Please educate me. Thanks
>
> http://rapidshare.com/files/147870853/Super.gif
>
Yuck, what a horrible download site.
Anyway, once I've downloaded it, cells B5, F5 are the only two places for a
2 on row 5. B3, F3 are the only two places for a 2 on row 3. Together these
tell you that the 2 in column F must be row 3 or 5, so you can eliminate
the 2 from F1 and place 8 in F1.
That one is pretty straightforward, but the next two steps look kind of
vicious. I used Brian Eppstein's solver (and converted his coordinates to
yours) as it gives good explanations of each step. The full output from
your starting position was:
C:\eppstein>\python25\python Sudoku.py -v
431 ..5 .7.
2.. 9.4 ..1
5.9 .13 2.4
614 8.7 .2.
3.5 14. 6..
89. 3.6 41.
1.6 43. 7..
74. 5.1 ..2
95. ... 14.
^Z
Beginning solver iteration 1.
Preventing 8 from being placed in R8C5 or R9C5. These placements would
conflict with R1C5 and R2C5, which are the only cells in square 2 that can
contain that digit.
Ending solver iteration 1 after successful application of the align rule.
Beginning solver iteration 2.
Preventing 6 from being placed in R2C8. In square 3, digits 3 and 5 may
only be placed in R2C7 and R2C8. To leave enough room for those digits, no
other digits may be placed in those cells.
Preventing 8 from being placed in R2C7 or R2C8. In square 3, digits 3 and
5 may only be placed in R2C7 and R2C8. To leave enough room for those
digits, no other digits may be placed in those cells.
Ending solver iteration 2 after successful application of the pair rule.
Beginning solver iteration 3.
Preventing 2 from being placed in R9C6. In row 5 and row 7, digit 2 can
only be placed in column 2 or column 6. Placing 2 in R9C6 would leave too
few columns for 2 to be placed in all of these rows.
Ending solver iteration 3 after successful application of the digit rule.
Beginning solver iteration 4.
Placing 8 in R9C6. No other digit may be placed in that cell.
Ending solver iteration 4 after successful application of the eliminate
rule.
Beginning solver iteration 5.
Preventing 8 from being placed in R1C9, R2C2, or R8C8. In row 3, row 5,
and row 7, digit 8 can only be placed in column 2, column 8, or column 9.
Placing 8 in R1C9, R2C2, or R8C8 would leave too few columns for 8 to be
placed in all of these rows.
Ending solver iteration 5 after successful application of the digit rule.
Beginning solver iteration 6.
Placing 9 in R1C9. In the cyclic sequence of cells R1C9-R3C8-R5C8-R5C6-
R5C2-R6C3-R9C3-R9C9-R1C9, each cell has two possible digits, each of which
may also be placed at one of the cell's two neighbors in the sequence,
except that R1C9 shares 6 as a possible value with both of its neighbors.
Placing 6 in R1C9 would make it impossible to fill the cycle's remaining 7
cells with the remaining 6 digits, so only 9 can be placed in R1C9.
Ending solver iteration 6 after successful application of the repeat rule.
Beginning solver iteration 7.
Placing 6 in R3C8. It is the only cell in square 3 in which 6 can be
placed.
Placing 6 in R9C9. It is the only cell in square 9 in which 6 can be
placed.
Placing 6 in R8C5. It is the only cell in row 8 in which 6 can be placed.
Placing 6 in R1C4. It is the only cell in column 4 in which 6 can be
placed.
Placing 6 in R2C2. It is the only cell in column 2 in which 6 can be
placed.
Placing 8 in R1C7. It is the only cell in square 3 in which 8 can be
placed.
Placing 8 in R8C3. It is the only cell in row 8 in which 8 can be placed.
Placing 8 in R3C2. It is the only cell in row 3 in which 8 can be placed.
Placing 8 in R2C5. It is the only cell in column 5 in which 8 can be
placed.
Placing 9 in R7C6. It is the only cell in square 8 in which 9 can be
placed.
Placing 9 in R5C8. It is the only cell in row 5 in which 9 can be placed.
Placing 9 in R8C7. It is the only cell in row 8 in which 9 can be placed.
Placing 9 in R4C5. It is the only cell in column 5 in which 9 can be
placed.
Ending solver iteration 7 after successful application of the locate rule.
Beginning solver iteration 8.
Placing 2 in R1C5. It is the only cell in square 2 in which 2 can be
placed.
Placing 2 in R5C6. It is the only cell in square 5 in which 2 can be
placed.
Placing 2 in R9C4. It is the only cell in square 8 in which 2 can be
placed.
Placing 2 in R7C2. It is the only cell in row 7 in which 2 can be placed.
Placing 2 in R6C3. It is the only cell in row 6 in which 2 can be placed.
Placing 3 in R9C3. It is the only cell in square 7 in which 3 can be
placed.
Placing 3 in R8C8. It is the only cell in square 9 in which 3 can be
placed.
Placing 3 in R2C7. It is the only cell in row 2 in which 3 can be placed.
Placing 3 in R4C9. It is the only cell in column 9 in which 3 can be
placed.
Placing 5 in R6C5. It is the only cell in square 5 in which 5 can be
placed.
Placing 5 in R2C8. It is the only cell in square 3 in which 5 can be
placed.
Placing 5 in R4C7. It is the only cell in square 6 in which 5 can be
placed.
Placing 5 in R7C9. It is the only cell in square 9 in which 5 can be
placed.
Placing 7 in R2C3. It is the only cell in square 1 in which 7 can be
placed.
Placing 7 in R5C2. It is the only cell in square 4 in which 7 can be
placed.
Placing 7 in R3C4. It is the only cell in square 2 in which 7 can be
placed.
Placing 7 in R9C5. It is the only cell in square 8 in which 7 can be
placed.
Placing 7 in R6C9. It is the only cell in square 6 in which 7 can be
placed.
Placing 8 in R5C9. It is the only cell in square 6 in which 8 can be
placed.
Placing 8 in R7C8. It is the only cell in square 9 in which 8 can be
placed.
Ending solver iteration 8 after successful application of the locate rule.
-----------------------------------
| 4 3 1 | 6 2 5 | 8 7 9 |
| | | |
| 2 6 7 | 9 8 4 | 3 5 1 |
| | | |
| 5 8 9 | 7 1 3 | 2 6 4 |
|-----------------------------------|
| 6 1 4 | 8 9 7 | 5 2 3 |
| | | |
| 3 7 5 | 1 4 2 | 6 9 8 |
| | | |
| 8 9 2 | 3 5 6 | 4 1 7 |
|-----------------------------------|
| 1 2 6 | 4 3 9 | 7 8 5 |
| | | |
| 7 4 8 | 5 6 1 | 9 3 2 |
| | | |
| 9 5 3 | 2 7 8 | 1 4 6 |
-----------------------------------
Rules used: locate, eliminate, align, pair, digit, repeat
Level: fiendish
time 0.52999997139
Kevin Stone
Which seems to use guessing?
Which isn't required for this puzzle (as per my other reply).
--
Kev
Kevin Stone
Kevin Stone
I've imported this as:
http://www.brainbashers.com/sudokuload4395
Which makes it a little easier to work with.
--
Kev
Duncan Booth
>
>>> http://rapidshare.com/files/147870853/Super.gif
>>>
>> Yuck, what a horrible download site.
>>
>> I used Brian Eppstein's solver
>
> Which seems to use guessing?
>
It can when that's the only way it knows to proceed, but I don't see any
guesses in what I posted, just application of a fixed set of rules.
Kevin Stone
>>
>> Which seems to use guessing?
>>
> It can when that's the only way it knows to proceed, but I don't see any
> guesses in what I posted, just application of a fixed set of rules.
What about this section:
<start>
Beginning solver iteration 6.
Placing 9 in R1C9. In the cyclic sequence of cells R1C9-R3C8-R5C8-R5C6-
R5C2-R6C3-R9C3-R9C9-R1C9, each cell has two possible digits, each of which
may also be placed at one of the cell's two neighbors in the sequence,
except that R1C9 shares 6 as a possible value with both of its neighbors.
Placing 6 in R1C9 would make it impossible to fill the cycle's remaining 7
cells with the remaining 6 digits, so only 9 can be placed in R1C9
<end>
Isn't this is a guess first, that leads to a contradiction?
--
Kev
Duncan Booth
No. It is an application of the following rule:
repeat:
Look for cycles of bilocated or bivalued vertices with one
repetition. We use the same graphs described for the bilocal and
bivalue rules; if there exists a cycle in which some two adjacent
edges are labeled by the same digit, and all other adjacent pairs of
cycle edges have differing digits, then the repeated digit must be
placed at the cell where the two same-labeled edges meet (in the
case of the bilocal graph) or can be eliminated from that cell (in
the case of the bivalue graph).
Kevin Stone
>>
>> Beginning solver iteration 6.
>> Isn't this is a guess first, that leads to a contradiction?
>>
> No. It is an application of the following rule:
>
> repeat:
> Look for cycles of bilocated or bivalued vertices
It doesn't appear to be a strategy that can be implemented using normal
human abilities though.
--
Kev
Phil Carmody
I think it can be, as long as you permit the human to go "and if ... then ...".
7cl...@gmail.com
> 7clo...@gmail.com wrote:
> > I worked the first "super difficult" Sudoku on your site. Not
> > surprisingly I reached a dead end. I could solve it, but only by
> > postulating. If there is a logical next step (see link below), I don't
> > see it. Please educate me. Thanks
>
> >http://rapidshare.com/files/147870853/Super.gif
>
> Yuck, what a horrible download site.
I agree, but if you have a better one, please let me know.
> Anyway, once I've downloaded it, cells B5, F5 are the only two places for a
> 2 on row 5. B3, F3 are the only two places for a 2 on row 3. Together these
> tell you that the 2 in column F must be row 3 or 5, so you can eliminate
> the 2 from F1 and place 8 in F1.
How about:
B3 = 2
F3 = 8
F5 = 9
B5 = 7
F1 = 2
It would be another matter if there weren't 3 possibilities for F3.
Duncan Booth
>> Yuck, what a horrible download site.
>
> I agree, but if you have a better one, please let me know.
Google docs?
>
>> Anyway, once I've downloaded it, cells B5, F5 are the only two places
>> for
> a
>> 2 on row 5. B3, F3 are the only two places for a 2 on row 3. Together
>> the
> se
>> tell you that the 2 in column F must be row 3 or 5, so you can
>> eliminate the 2 from F1 and place 8 in F1.
>
> How about:
>
> B3 = 2
> F3 = 8
> F5 = 9
> B5 = 7
> F1 = 2
>
> It would be another matter if there weren't 3 possibilities for F3.
But "cells B5, F5 are the only two places for a 2 on row 5" so if you fill
those cells in with 9 and 7 you won't be able to put a 2 anywhere on that
row.
--
Duncan Booth http://kupuguy.blogspot.com
Matthew Russotto
Isn't that "remote pairs"?
--
It's times like these which make me glad my bank is Dial-a-Mattress
7cl...@gmail.com
Right, thanks!
spudnik
the missing entires can be either 67
76, or 76
67;
amazing. I'll have to look at th3 28-entry solution,
later.
spudnik
with 1x1x1 sudokus (duh) and
2x2x2 sudokus, which is really tractable, and
I can see the simple patterns, but
I still didn't get it. of course,
I guess, these are "five halves Dimensional,"
like the original sudoku.
thus:
Thomas Young showed that quantum mechanics is strictly classsical,
quite anti-Newtonian, a long time ago.
there's a recent book on him, quite interesting,
that already makes these categorical errors
in the first two pages!
thus:
I had understood that virtually all of ZPE was crankiness,
except for Dirac's original dyscovery, and Alfven's work
in the lab. most especially Casimir force, since
there are probably many complications,
when 2 "massive flat plates" get so close....
what phenomena requires that space -- outer space,
in the solar system, intragalactic or
between galaxies or clusters of galalxies --
be filled with positrons?...
is it a nonsequiter?...
monsieur Bernier holds back, but
what can honestly be said to such a fountain
of paralinguism?...
oops; I said, I wouldn'twaste any more
of your time; sorry!
thus quoth:
That development of scientific calculating machines, which led into
the Twentieth-Century development of the general purpose electronic
computer, began with the development, first, of such a machine built
by Johannes Kepler, one crafted by him to assist his calculations for
astronomy. Secondly, a copy of what Kepler described as his machine,
was crafted by Blaise Pascal. Thirdly, Pascal's work was the starting-
point of reference for the then revolutionary technological
development of the early general-purpose scientific calculator, by
Gottfried Leibniz. Fourth, the development of the design for the
mechanical forerunner of the modern digital computer, was chiefly a
reflection of the influence of Gottfried Leibniz on Babbage's
invention of the mechanical model for the modern electronic computer.
Full circle, back to Kepler's astronomy: on his own account, Babbage's
discovery was prompted by his continuing close personal association
with Britain's leading astronomer of that time, Sir John Herschel, and
also with the followers of Kepler and Leibniz among those broader
European circles of Babbage's personal acquaintance, as typified by
the scientist Alexander von Humboldt, the latter both in Germany and
the Monge-Carnot Ecole Polytechnique program in France.
http://www.larouchepub.com/lar/2006/3329_signs.html
> even a vague idea what science is.
>
> If Newton was not a scientist, then I fully expect
thus:
"why were you a LaRouchiac?" in seven words or so. well,
I've seen mention of the RTC as sort of a model
for some or all of this, but
only larouchiax seem to know that it was used to liquidate,
not only the insolvent S&Ls -- those were primarily
for home-loans, of course -- but so were the ones that
hadn't gone out on the limb,
sold for a dime on the dollar to BoA, City etc. ad vomitorium.,
to leverage their hedgie-wedgies.
this could be turned into a positive thing, since
McCain was involved in the underlaying fiasco. now, if
he would just dump Dick Cheeny, and if
Obama would dump George Soros,
they could have a substantive race -- or,
one without the albatrosses.
I could go on, but I'm not so much of a larouchiac, these days,
nor is Lyn running, this year -- what a surprize!
now, that big insurance company should be called,
IAG; dig it, if the number of the beast begins with a 5?
the true nature was also partially revealed, when
the RTC was used to launch the Fourth investigation
into Whitewater (one L. Jean Lewis sent a note
to the Solicitor General).
> This is worse than a bad deal - this isn't a deal at all. This is a
blank check to some of the richest companies in the world.
thus:
Newton was not really a scientist; a biblical chronologer,
alchemist & likely freemason, yes -- if
you want to count *that* latter as a social skill....
Newton is the secular church of England,
as adumbrated through the Harry Potter PSes,
in their ongoing trashing of Leibniz....
there was a recent novelization of Newton,
as a "genius" *and* a spy, that is probably nearer
to the truth; otherwise,
it is abundantly clear in between the lines
of the "major biographers" -- or, at least,
in that recent biography....
well, again, only larouchiax seem to be aware
of this!
> Newton's social skills? That's a good one! Are you pulling our
legs?
--USA out of Darfur Cruizade!
http://larouchepub.com/other/2008/3537willl_zardari_survive.html
--ROTC, your summer vacation in the Sahara Desert ( S u d a n ) ;
presage the Draft for your middleschool class of '12 --
brought to you by Allstate (tm) and Oxford U.Press!
http://larouchepub.com/pr/2008/080813moloch_brown.html
http://wlym.com