dailysudoku.com

[mason]

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"?

[samgj]

[David Bryant]

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

[alanr555]

[samgj]

[Victor]

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.

[samgj]

[alanr555]

[Victor]

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 we’re 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 SudokuSan’s Assistant doesn’t check for triples in a box – apologies.

However, I’m SURE that Draw doesn’t like quite all ‘normal’ (sub X-wings) constructions. I think I’m right in saying that it doesn’t check for naked quadruples, but that’s not the only missing bit. Here’s 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 can’t go in positions 1,2,3 or 8. A computer (if it’s 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 can’t solve this Sudoku. (Why’s it a curio? – because you can solve it in a completely different way, using X-wings.) I’ll 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:-
“If you put a puzzle into Draw and it’s 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 can’t do the puzzle, that means merely that it’s probably not solvable by sub X-wings techniques.”

Please don’t take this as criticism: I’d 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 ‘collector’ 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 ‘ordinary’ 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 haven’t put in the same amount of effort.
But it’s 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 “Is this puzzle solvable by logic (as most of us interpret the term)?” – 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 Scanraid’s Sudoku Solver or no doubt others. Speaking personally, I find SudokuSan useful if I’m 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 I’m too lazy to bother working them out myself.

Here’s 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 can’t 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 here’s another Sunday Times that Draw doesn’t 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 can’t 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) I’d have to find a quad that DID’NT fit into three squares – harder for me.

[David Bryant]

[Victor]

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.)

[AZ Matt]

[David Bryant]

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