The New Sudoku Players' Forum

[vidarino]

The fact that a default Sudoku has a unique solution is no more or less part of the game than that it has one of each digit in each row, column and box.

We do not *assume* that the puzzle has a unique solution. It is a *given* -- no more or less set in stone than the other *givens* within the grid -- that the puzzle has a unique solution.

I agree completely. When I solve puzzles, I want to find *the* solution. (If I didn't trust the source, I'd probably even check the puzzle before going to work on it.) Hence, techniques that rely on there being a unique solution are all fair game to me, because if the puzzle *did* have zero or multiple solutions, it wouldn't be logically deductable, and I honestly wouldn't bother with it.

Just my two øre.

Vidar

[emm]

I look in cells that have many filled cells in the same row, column and box, hoping that all but one digit will be accounted for.

I think that what qualifies guessing is the hoping part.

While there is an element of hope in my reasoning - it doesn't matter how simple or how complicated the technique or how far down the track I am with it - while I am not sure if it's going to fall together or not, then I am actually guessing. It doesn't matter if it's a BUG, an Xwing or a naked single, it doesn't matter if I recognise the BUG on my first scan or the Xwing on my 10th or if it takes me 81 checks to determine the 81st single, it's not until I know that my deduction is true, that I am no longer guessing.

It's a very individual thing, but unless you're able to see the whole solution at first glance, then somewhere along the way you have to be doing some guessing.

However, guessing is a value-laden term in this forum - no-one likes to own up to it - and 'searching where it looks promising' sounds better. It also sounds cleverer. It implies a measure of intuition based on experience rather than the 'piñata' method as described by Mac.

Mac, are you an elite group of one or are there people out there who support you in secret? I'm genuinely curious how many actually do fill out all those copies of grids with different values.

[QBasicMac]

But if your first or second possibility reaches a solution, I simply don't believe you usually try the remaining possibilities just to discover whether or not that solution is unique.

Sorry that I have no way of proving that indeed I do that every single time without fail. Otherwise, I have not solved the puzzle.

Since that is obviously a lot of work, I try to avoid T&E by using whatever techniques are easier, for example simple coloring. But I don't use techniques which might fail in case of multiple solutions, and I avoid "boring arcane techniques" - those which are more work than T&E.

I have a computer program I wrote which supports saving current progress. That makes making the copies and solving each a piece of cake. I would need access to a copy machine if I were doing them by pencil and paper. Might just write off difficult puzzles in that case, especially those that have too many solutions. (The puzzle isn't solved until you've found them all). I've found that the puzzles generated by Marco v/d Berg's "Sudoku Solver/Creator" often have multiple solutions.

Cheers,

Mac

[ronk]

But if your first or second possibility reaches a solution, I simply don't believe you usually try the remaining possibilities just to discover whether or not that solution is unique.

Sorry that I have no way of proving that indeed I do that every single time without fail. Otherwise, I have not solved the puzzle.

I stand corrected, and you have my sympathy.

Ron

[QBasicMac]

Mac, are you an elite group of one or are there people out there who support you in secret? I'm genuinely curious how many actually do fill out all those copies of grids with different values.

Heh - I don't know about the "elite" part, but I'm more-or-less sure about the group size.

But at least I now know why someone would try copies until one works and then stop. It is because they buy the "It is guaranteed and given that all puzzles have one and only one solution" concept. When you find a solution that works, you are done! Well, not me. I keep going. I don't accept that "given" and thus stand alone - not for the first time and not for the first topic.

Well, now that I think about it, puzzle-solving is such an unimportant part of the universe that I'm being silly wasting everybodies time and forum space promoting the benefits of T&E. Sorry, forum regulars. Won't happen any more.

Mac