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is it worth the trouble?

 
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mason
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PostPosted: Sat Nov 19, 2005 11:27 pm    Post subject: is it worth the trouble? Reply with quote

Sometimes I use the sudoku "drawer" feature from this site to check the validity of puzzles from our newspaper.If the "drawer" advises that the" puzzle may not be solvable etc etc" should I just stop trying.By the way what is "look ahead logic"?
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samgj
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Joined: 17 Jul 2005
Posts: 106
Location: Cambridge

PostPosted: Sun Nov 20, 2005 12:17 am    Post subject: Re: is it worth the trouble? Reply with quote

mason wrote:
Sometimes I use the sudoku "drawer" feature from this site to check the validity of puzzles from our newspaper.If the "drawer" advises that the" puzzle may not be solvable etc etc" should I just stop trying.By the way what is "look ahead logic"?


No -- this doesn't necessarily mean you should give up. To my shame, the drawer still doesn't understand some advanced tactics: swordfish, xy wing etc, aswell as forcing chains type logic, which is what I probably mean by "look-ahead logic". You can read more about this in this thread.

Sam
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Sun Nov 20, 2005 12:20 am    Post subject: Keep on trying! Reply with quote

Hi, Mason!

The "draw" program on this site is very helpful. However, there are a few tricks (swordfish, coloring, nishio, forcing chains) that are not in its repertoire. So the question of whether you should keep trying, or not, is largely up to you. If you don't care to master the "advanced techniques," then don't try. But since the advanced techniques can be a lot of fun, I'd advise you to persevere!

The term "look-ahead logic" is usually applied to some species of trial and error. In other words, if you can't figure out where to put the next number, just pick out a cell that has only two possibilities (or maybe a digit that can only fit in two squares in a particular row or column) and make a guess. If your guess is right, you'll probably solve the puzzle. If you guess incorrectly, you will sooner or later reach a contradiction, proving that the other value (or cell) is the right one.

Limited forms of "look-ahead logic" can be mastered by a human player who can concentrate hard enough to trace out the consequences of a particular choice five or six moves ahead. Some people can do even better than that. The guy who can "look ahead" for as many as 20 or 30 moves is extremely rare -- for all I know, he doesn't exist. So I'm uncertain where to draw the dividing line between "seeing" what the consequences of a particular choice are and outright guessing (which will always work, if you don't mind all the backtracking). dcb
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sun Nov 20, 2005 2:49 am    Post subject: Re: Keep on trying! Reply with quote

Code:

> The term "look-ahead logic" is usually applied to some species
> of trial and error. In other words, if you can't figure out where
> to put the next number, just pick out a cell that has only two
> possibilities (or maybe a digit that can only fit in two squares in
> a particular row or column) and make a guess.

I agree with this definition of 'trial and error' BUT with the limitation
that one RECORDS the derived values and allows the possibility of
having to backtrack to the "guess" point.

SamGJ expressed it well in this July 18th article. I believe that he set
there the rules for THIS site - whilst acknowledging that other rules
will apply for other sites.

--------------------------------------------------------------------------------
From SamGJ:
The choice then is whether a puzzle can be completed in its entirety without resorting to "trial and error" or bifurcation.  I take the need for "trial and error" to mean that at some point in the solving of the
puzzle it is not possible to say with absolute certainty that a particular number must go in a particular cell without testing one of several
options, following a path until the puzzle either completes or fails, and
backing up to try another option.

Daily Sudoku puzzles can always be solved in a forward direction, with no bifurcation or trial and error. I like to know that there is always a logic
step to find.  If I can't guarantee this, then when I get stuck, it is too tempting to resort to the "trial and error" approach, which to me is time-consuming, but not especially intellectually challenging.
--------------------------------------------------------------------------------
From DavidCB:
Limited forms of "look-ahead logic" can be mastered by a human player who can concentrate hard enough to trace out the consequences of a particular choice five or six or even more moves ahead.

I am uncertain where to draw the dividing line between "seeing" what
the consequences of a particular choice are and outright guessing -
which will always work, if you don't mind all the backtracking.
--------------------------------------------------------------------------------

Thus for our Colorado friend it all comes down to the question of the
'look ahead' limit whereas for me (and possibly SamGJ per the above
extract from his July posting) the notion of the possibility of having to
do some "backtracking" is what makes the difference.

I do not know about anyone else but I do not have the facility to STORE
the position after each move (so as to enable backtracking). For me
the backtrack is a re-print of the initial puzzle!

Perhaps we all need to support SamGJ by acknowledging that this site
does not endorse bifurcation and that we will attempt to find methods
that do not require any form of bifurcation to reach a unique solution.

Alan Rayner BS23 2QT

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samgj
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Joined: 17 Jul 2005
Posts: 106
Location: Cambridge

PostPosted: Sun Nov 20, 2005 11:45 am    Post subject: Re: Keep on trying! Reply with quote

alanr555 wrote:

Perhaps we all need to support SamGJ by acknowledging that this site
does not endorse bifurcation and that we will attempt to find methods
that do not require any form of bifurcation to reach a unique solution.


Hi Alan and co

I greatly appreciate all your support for the site, but actually I wouldn't go this far. Some people like to solve puzzles by looking ahead, and this is in itself an interesting intellectual (and perhaps more memory oriented) test. So although my puzzles don't REQUIRE look ahead, people should use whatever methods they enjoy! It seems likely that trial and error can often be quite a fast method to get past a choke point.

Sam
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Fri Nov 25, 2005 11:20 pm    Post subject: Re: Is it worth the trouble? Reply with quote

Sam G-J's Draw doesn't include X-wings of course, but there are 1 or 2 other 'simpler' tests that aren't included: Draw doesn't seem to look for quadruples (chains of length 4 as some people call them). And I think that it probably doesn't like a technique I've seen in the Sunday Times, where a row/column contains, say, the triple (346, 36, 34), with the two 6s in the same box, which rules out other 6s in this box if you think about it.

SudokuSan, the only other site that I like, does do X-wings and does have an easy-to-use Assistant. But they don't do quadruples either, and also don't recognise non-linear triples in a box. (By the way, if you haven't yet tried a SudokuSan with X-wings, do have a go - satisfying if you can manage without writing out all candidate numbers! - routinely part of their hardest daily puzzle). http://www.sudokusan.com/

A little less easy to use, but more comprehensive is http://www.sudokusolver.co.uk/index.html
which includes all multiples & all X-wing extensions.

None of these include Forcing Chains, Nishio, or other methods that many of us consider forms of trial & error.
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samgj
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Location: Cambridge

PostPosted: Sat Nov 26, 2005 5:43 pm    Post subject: Re: Is it worth the trouble? Reply with quote

Victor wrote:
Draw doesn't seem to look for quadruples (chains of length 4 as some people call them).


Unless I misundestand you, it should deal with these. Can you send me or post an example of what you mean and I'll take a look?

Quote:
And I think that it probably doesn't like a technique I've seen in the Sunday Times, where a row/column contains, say, the triple (346, 36, 34), with the two 6s in the same box, which rules out other 6s in this box if you think about it.


I think you're right about this. The draw thing is long overdue a rewrite, but it keeps getting bumped off the top of the todo list by other fanciful ideas :)

Sam
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alanr555



Joined: 01 Aug 2005
Posts: 194
Location: Bideford Devon EX39

PostPosted: Sun Nov 27, 2005 7:09 pm    Post subject: Re: Is it worth the trouble? Reply with quote

Code:

> I think that it probably doesn't like a technique I've seen in the Sunday
> Times, where a row/column contains, say, the triple (346, 36, 34), with
> the two 6s in the same box, which rules out other 6s in this box if you
> think about it.

This is nothing to do with triples.

There is a general rule which says that if the only occurences of a
particular digit in a line (row/col) are within one region then that digit
CANNOT occur in either of the two parallel lines whilst within that region.
The related rule states
If the only occurences of a particular digit within a region are in
one line (row/col) then that digit CANNOT occur in either of the
other two regions on the same line.

The situation in the quote above is just an example of the first of the
two rules just given.
eg a triplet (346,36,34) in r1c4,r1c5,r1c8
would imply that all the '6's in line 1 are in region 2.
This means that the single ACTUAL 6 for that region must be in
one of the two cells (r1c4 and r1c5) - in row 1 anyway! - and so
a '6' CANNOT occur in rows 2 or 3 in that region. If there are any
'6' candidates in r2c4, r2c5,r2c6,r3c4,r3c5,r3c6 they may be eliminated.

NB: In this scenario the presence of the 34 in r1c8 is irrelevant.
The constraint is NOT the triple, just the number of '6's and the fact
that they are all in row 1 of region 2. The values could just as easily
have been 67, 68,69 in r1c4,r1c5,r1c6. The conclusion is the same so
long as r1c1 to r1c3 and r1c7 to r1c9 do NOT contain any '6's.

+++
I would be VERY surprised if the DRAW facility did not include these
general rules. The original querent seems just to have muddied the
water by referring to the triple when such is irrelevant.

Alan Rayner  BS23 2QT
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Tue Dec 06, 2005 5:18 pm    Post subject: Re: Is it worth the trouble? - curio Reply with quote

This is a reply to Alan, who replied to a post of mine, sounding a bit outraged on behalf of Sam G-F. Having thought about it, I believe that weíre each (only) partly right.

Alan is certainly right to say that my waffles about a particular kind of triple are nonsense: thanks for pointing it out. The case I mentioned is merely another (slightly unusual) way of arriving at the familiar situation of knowing that a certain number must be in a particular row/column in just one box. And I made another mistake, saying incorrectly that SudokuSanís Assistant doesnít check for triples in a box Ė apologies.

However, Iím SURE that Draw doesnít like quite all Ďnormalí (sub X-wings) constructions. I think Iím right in saying that it doesnít check for naked quadruples, but thatís not the only missing bit. Hereís an example that can be solved using quadruples, the whole puzzle something of a curio:-
000 000 000
017 300 890
049 800 720

000 000 256
000 405 000
573 000 000

062 003 580
051 009 470
000 000 000

If you look at column 1, you can see that the quad 1479 canít go in positions 1,2,3 or 8. A computer (if itís been programmed to search for them) will see the naked quad 2368 in those positions, or the hidden quad 1479 in the other four. The rest of the puzzle is quite easy. Try it if you want: Draw canít solve this Sudoku. (Whyís it a curio? Ė because you can solve it in a completely different way, using X-wings.) Iíll put another example or two at the end of this post, though I only need one to justify this definitive answer to the original query:-
ďIf you put a puzzle into Draw and itís happy, i.e. by giving it a difficulty rating, then you can be sure that the puzzle IS solvable using ordinary techniques. BUT if Draw canít do the puzzle, that means merely that itís probably not solvable by sub X-wings techniques.Ē

Please donít take this as criticism: Iíd strongly defend Daily Sudoku and its creator. A couple of months ago, when I was convalescing, I spent some time web-surfing in search of Sudoku stuff. I found several good Ďcollectorí sites with examples of swordfishes, etc., and a couple of good logic solvers, and one good site offering puzzles up to and including forcing chains (which feel too much like trial & error for me) and one excellent site offering puzzles up to and including X-wings, mentioned in my previous post. And I found dozens of sites offering Ďordinaryí puzzles. For my money, none of these is as good as Daily Sudoku. In fact, I feel mildly irritated on behalf of Sam G-F, the Times Pappocom, and one or two others, that so many printed Sudokus (inc. those in most papers) are poorly done: it seems obvious that the programmers havenít put in the same amount of effort.
But itís a completely different pecking order when it comes to solvers. Draw is fine for printing out a puzzle in the format you like, or giving a Hint to a beginner. But if you want a hint, SudokuSan will do at least as well as Draw, AND explain why. If you want a definitive answer to the question ďIs this puzzle solvable by logic (as most of us interpret the term)?Ē Ė then the Sudoku Solver By Logic will tell you. And if you give up and want to see how the whole puzzle is done, you can use the latter program, or Scanraidís Sudoku Solver or no doubt others. Speaking personally, I find SudokuSan useful if Iím stuck: I can work for a moment or two on screen perhaps and then from a printout that includes all the candidate numbers, which I like because Iím too lazy to bother working them out myself.

Hereís an old Sunday Times puzzle. (a) You can solve it using ordinary techniques, the most complicated being dividing column 6 into two triples. (b) Draw canít do it. (I neither know nor care why that is.)
300 000 500
024 700 800
000 002 000

600 500 020
400 907 003
030 080 006

000 500 000
000 500 000
007 006 940
006 000 001

And hereís another Sunday Times that Draw doesnít like.
900 060 170
070 400 000
000 000 503

200 805 030
050 000 090
080 302 001

301 000 000
000 007 010
047 020 005
You can put four numbers in easily, including an 8 in R1C6. After that, you can find a couple of pairs, but I think you then have to divide column 5 into a triple & a quad. Looking at it (with the 8 pencilled in), you can see that in the triple 358 canít be in rows 3,4,5,6. A computer (or human working with candidate lists) could see the naked quad 1479 in these positions, or the hidden triple 358 in the others. Rest of the puzzle is easy.
The odd thing is that this little gap in the software makes a negligible difference to difficulty level. If it were the other way round (in dividing a 7-free-squares-in-a-region into triple & quad), then where the computer sees a naked triple (standard fare for Daily S) Iíd have to find a quad that DIDíNT fit into three squares Ė harder for me.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Tue Dec 06, 2005 7:55 pm    Post subject: This is fun, but ... Reply with quote

victor wrote:
Hereís an old Sunday Times puzzle. (a) You can solve it using ordinary techniques, the most complicated being dividing column 6 into two triples. (b) Draw canít do it. (I neither know nor care why that is.)
300 000 500
024 700 800
000 002 000

600 500 020
400 907 003
030 080 006

000 500 000
000 500 000
007 006 940
006 000 001


Well, it's no wonder Draw can't do it -- it's got ten rows! Smile

Can you repost this puzzle, Victor? I really liked the hidden quad example, and I'd like to understand this one, too, but it won't quite work as it stands. dcb
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Victor



Joined: 29 Sep 2005
Posts: 207
Location: NI

PostPosted: Tue Dec 06, 2005 10:33 pm    Post subject: Re: Is it worth the trouble? - curio Reply with quote

David Bryant spotted another example of my carelessness - sorry. (My only half-excuse is that the phone rang as I about to edit/check it, and so I just posted anyway.) Here it is again, typed properly:-

300 000 500
024 700 800
000 002 000

600 040 020
400 907 003
030 080 006

000 500 000
007 006 940
006 000 001

Thanks for the appreciation expressed for the double quad. (I can't remember where it came from.)
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA

PostPosted: Fri Dec 09, 2005 10:02 pm    Post subject: Hidden and Naked Quads Reply with quote

Quote:
000 000 000
017 300 890
049 800 720

000 000 256
000 405 000
573 000 000

062 003 580
051 009 470
000 000 000

If you look at column 1, you can see that the quad 1479 canít go in positions 1,2,3 or 8. A computer (if itís been programmed to search for them) will see the naked quad 2368 in those positions, or the hidden quad 1479 in the other four. The rest of the puzzle is quite easy.


Victor, or anybody: I must not understand the lexicon of "position" in a column. How can 2 and 8 be candidates in c1r2? I am lost. Help?
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado

PostPosted: Fri Dec 09, 2005 11:36 pm    Post subject: Understanding Victor's hint Reply with quote

Hi, Matt!

I think Victor's hint is clear enough -- he doesn't mean that every one of the values {2, 3, 6, 8} can fit in r1c1, r2c1, r3c1, & r8c1 -- he means that the candidates for those four cells cannot include any values other than {2, 3, 6, 8}. Or, to look at it another way, the cells r1c1, r2c1, r3c1, and r8c1 must contain the values {2, 3, 6, 8} in some order.

To make it more explicit, here's the candidate list for the first column:
r1c1 -- 2/3/6/8
r2c1 -- 2/3/6
r3c1 -- 3/6
r4c1 -- 1/4/9
r5c1 -- 1/9
r6c1 -- *5*
r7c1 -- 1/4/7/9
r8c1 -- 2/3/6/8
r9c1 -- 1/4/7/9

Does it make more sense now? dcb
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