When unable to solve with reasoning/logic is it ok to guess?

Advanced methods and approaches for solving Sudoku puzzles

Postby Hammerite » Tue Jul 05, 2005 9:29 pm

You find this tiresome? So do I.

[Edited by Pappocom: unnecessarily offensive tone.]
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Postby lunababy_moonchild » Tue Jul 05, 2005 9:37 pm

No, I didn't say I find it tiresome I said that it's old - which is different, in the light of being precise. It's old because it's been done before.

I'm entitled to disagree with you, and to state my disagreement, all without it affecting my intelligence (or being wrong for that matter).

If you don't want to answer my question, then it's a little difficult for me to be mathematically precise. Never mind, I'll find it out for myself.

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Postby tso » Wed Jul 06, 2005 2:30 am

lunababy_moonchild wrote:Even if it is old I don't see how "Therefore bifurcation is logic, if all branches are followed. " can be classed as logic, or perhaps I just haven't followed other, previous, arguments on the subject.

As you say : "( ( A implies B ) and ( not (B) ) ) implies ( not (A) )" So.... how does 'let's try this and see how far it goes and if it's not successful I'll try that and see how far that goes, therefore I'll get an answer eventually if I keep trying' fit in to logic?

Perhaps, if I may suggest a new slant and ask the users of this forum to stop stating that forms of logic used by other people are simply wrong and start stating things like 'IMO' (in my opinion) and 'I use this form of solving techinique' would be a better way of communicating and then we wouldn't get bogged down in the same old same old. Which seems to be turning into a chicken and egg scenario anyway.


"One last thing -- ........." Already said it was up to the individual how they played the game and I certainly didn't say that it was wrong and that solvers shouldn't do it, if that was implied in any of my posts then it was most definitely accidental .

A rose by any other name would still smell as sweet.

When solvers speak of bifurcation and trial and error in Sudoku, most often, what they really mean is "Reductio ad absurdum".

From the Wikipedia, which see (the bolds are mine):


"Reductio ad absurdum ... is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then conclude the original assumption must have been wrong, since it gave us this absurd result. This is also known as proof by contradiction. It makes use of the law of excluded middle — a statement which cannot be false, must then be true."

From Webster.com, which see (the bolds are mine):

Main Entry: re·duc·tio ad ab·sur·dum
1 : disproof of a proposition by showing an absurdity to which it leads when carried to its logical conclusion

"Trial and error" is imprecise. It can include simply filling in the grid at random, checking to see if it is the solution, if not, trying again. T&E can be, but does not HAVE to be logical. What we do is that other thing with the pretentious name.

Even brute force search is also logical. Computers are LOGIC machines -- the early ones were refered to as *logic engines". They are incapable of doing anything OTHER than logic. Put it this way -- I fancy myself as a logical person, my brother, not so much. I can solve a puzzle by brute force, he cannot. He tries this then that, than this again, then the other thing, then this a third time -- and gives up. He's a very creative, illogical person. He thinks Sudoku's are stupid.

Brute force is the typically the longest route to solution. Each new algorithm or logical tactic we add to our capabilities shortens that search. But we're still searching -- searching for the next place in the puzzle to apply each tactic in sequence.

It would be absurd for me to say "In my humble opinion, 2+2 is 4." Some things ARE fact, and I would open myself up for ridicule by chosing to use disclaimers. (Especially since I have demonstrated that I'm clearly not humble.)

Where we all mostly agree is that we want to find the *subjectively* best forms of logic to apply. We disagree somewhat on what's best or what best means in some cases. Generally, I think it means what will solve the hardest puzzles, most quickly. BUT, if a method is good enough, which puzzles are the hardest may change! Worst case scenario, some brainiac finds a way to solve any puzzle so simply, so obviously once you know the trick, that Sudoku's cease to exist. (It is unlikely or impossible for this to happen to Sudoku, but it has happened with many other puzzles and abstract games.)

We're not just fussbudgets correcting spelling errors (which is good because my spellling is atrocious). Imprecise language can have consequences. The false idea that some Sudoku's cannot be solved with logic and that some forms of logic don't count as logic is winning. New Sudoku Websites, newspapers columns and software brag that "their puzzle's can all be solved with logic without guessing", implying that other Sudoku's are otherwise. Have you ever, in your life, seen any other puzzle being promoted or described this way? The Rubik's Cube, which so many UK newspaper articles compare Sudokus to -- was far more complicated to solve than Sudoku -- there really is no comparison. Did anyone claim that it could or complain that it could not be solved by logic?

Speaking of Rubik's cube, can you imagine if Mr. Rubik thought that the puzzle was too hard for humans to solve, so instead of releasing it as is, he used only three colors instead of six, so that the puzzle would be vastly easier? Yet one after the other, Sudoku puzzle makers follow Wayne's lead and choose NOT to make the hardest possible puzzles -- and even denounce those who do. By this time in the Rubik's cube's life, people were clammoring for a 4x4x4 cube and eventually a 5x5x5, then a dodecahedron (Megaminx -- now *that* was hard), etc. But we insist that we are sensible logical people. If we cannot solve a puzzle, it is therefore not logical. It must not exist. And that is what is happening.


I just noticed today a website that clearly is copying Pappocom as much as possible -- for only a few dollars more. There, they make this claim:

"All of the puzzles generated by Su-doku quest are "true" su-doku puzzles, that is they have only 1 solution which can be reached through logical reasoning and deduction, there's no need for guessing. "

We use only the finest digits from the decimal system, unlike some other people.
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Postby lunababy_moonchild » Wed Jul 06, 2005 10:29 am


Thank you for your reply.

I'd like to make myself perfectly clear on this - pedantic although it may be. I have never said that T&E is not a form of logic nor have I said that it should never be used. I did say that I didn't see how it could be logic because to me it is guessing, which is a lack of knowledge on my part since I'm not overly familiar with the finer points of logic.

"He tries this then that, than this again, then the other thing, then this a third time -- and gives up." this is what I understand T&E to be.

However, if I understand you correctly, you could say that T&E is akin to the If...then...else statement in computing.

Given the plethora of people springing up who are creating these puzzles, it can't be that hard to do, so couldn't someone (on this site perhaps, in the programmers forum?) create especially hard puzzles for those that wanted them? There does seem to be a market for it.

Then again, I suppose that you'd make more money catering to the masses who are average solvers, which is why the specialist market isn't catered for. Perhaps Mensa will come up with especially hard puzzles for its members.

Why are the specialist solvers waiting for someone else to cater for them? If these solvers want especially hard puzzles that require specialist solving techniques why don't they create their own?

Wayne has stated his reasons for not creating these advanced puzzles and that's up to him, but if the specialist solvers aren't following his lead what's to stop them from creating their own especially hard puzzles/programs/techniques/website?

Note : I'm not being sarcastic when asking these questions, I'm looking for the information.

"Yet one after the other, Sudoku puzzle makers follow Wayne's lead and choose NOT to make the hardest possible puzzles -- and even denounce those who do." All the more reason for someone who cares to stand up and say that they are doing something different (all the puzzles are beginning to look the same to me). If it crashes and burns because the mass market is of average solvers who can't get further than Medium, for example, then so be it.

The puzzles sell newspapers and books. If all of the puzzles were excruiatingly hard all of the time nobody would do them and sales would fall.

If, however, a solver is in the game for the beauty and logic of it and wants/needs very advanced puzzles then there is nothing to stop that solver creating the more advanced puzzles necessary and creating a market for them.

In my opinion.

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Postby Karyobin » Wed Jul 06, 2005 12:12 pm

I think it might be fun to collate all the posts relating to bifurcation/logic/T & E/T & I/guesswork etc. and count all the different words there are in total. I reckon you'd be struggling to get past thirty.
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Postby scrose » Wed Jul 06, 2005 7:04 pm

tso wrote:Though not a normal Sudoku, take a look at puzzle number 8 in the most recent Internet Puzzle Solver's Test.


tso, could you please tell me if I have interpreted this puzzle correctly. First I have to arrange the nine blocks, A through I, in such a way that they will "fit" onto the grid on the left without creating any contradictions. For example, I can't place block B onto blocks 2, 5, or 6. Then, assuming I have the blocks arranged properly, I have to try and solve the grid. Have I got this right?
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Postby tso » Thu Jul 07, 2005 4:51 am

scrose wrote:tso, could you please tell me if I have interpreted this puzzle correctly. ...

Yes. Each of the nine shapes will have the all nine digits. No row or column will have the same digit twice. You can consider the top and bottom incomplete rows to be a single row; same with the right and left incomplete columns.
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Re: When unable to solve with reasoning/logic is it ok to gu

Postby arunprasadk_mba » Wed Jul 13, 2005 5:06 am

Hi Puzzlers,

The soultion for the partially done puzzle is given below:


I solved this puzzle only with reasoning and logic. As every sudouku puzzle has an unique solution, guessing will work only if u were damn lucky to fit a number in its exact location without ascertaning its place by logic. This , I feel , is the toughest puzzle I had solved till date.

chester wrote:I unable to solve this with reasoning and logic. Do I resort to guessing or am I missing something?

When it's a tough puzzle I usually put 1-9 in all the spaces I have left after the initial work through and go systematically through them until eventually something jumps out.
In this case I must be going blind as I can find no more.

This is as far as I have managed to get. Help!

* 2 * 9 * 8 * 3 *

* 8 * * * * * * 9

9 * 4 2 3 * * 8 1

4 * 5 * 8 1 9 * *

2 * 9 * * * * 1 8

7 1 8 6 9 2 4 5 3

8 * * * 5 9 1 * *

1 * * * * * * 9 *

* 9 * * * * * 6 *
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Is guessing logic?

Postby logician » Thu Jul 14, 2005 2:05 pm

I have only recently started solving su doku puzzles, and only today discovered this website and read this discussion. The relationship between logic and search is a topic about which there is much disagreement, even among world authorities.

Paul Thagard, in his Introduction to Cognitive Science, states page 45): “In logic-based systems the fundamental operation of thinking is logical deduction, but from the perspective of rule-based systems the fundamental operation of thinking is search.”

Jonathan Baron (1994) in his textbook, “Thinking and Deciding” writes on page 4:

“Thinking about actions, beliefs and personal goals can all be described in terms of a common framework, which asserts that thinking consists of search and inference. We search for certain objects and then make inferences from and about the objects we have found.”

Implicit in this statement is the assumption that logic is involved in inference, but not in search.

I maintain that although the inference rules of logic do not include search, any attempt to use logic to solve problems needs to include a search strategy for exploring alternative applications of the inference rules. The incorporation of search in the logic programming language, Prolog, is a good example of the relationship.

In terms of the discussion on this wenbsite, I would say that trial and error is included in the use of logic. But Thagard and Baron would disagree.
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