is the difficulty real?

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is the difficulty real?

Postby jojojo » Sun Dec 09, 2007 12:56 am

this is kind of a stupid question.. but here goes anyway.. is the difficulty in solving sudoku puzzles real or imagined? surely the creators of the puzzles know the answers. we could be doing the same puzzle over and over with different empty cells. i guess it is just a reflection of life -- it's the journey that matters and not the destination.

how difficult must it be to create the puzzle? you cant just randomly group together 9 boxes of 9 squares. how do the puzzle creators know that they dont have duplicate numbers?
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Postby ab » Sun Dec 09, 2007 3:35 pm

You've asked several questions there. I'll try to answer them.

There are several different techniques for solving sudoku. The simplest involve finding one occurance of a number in a line or box or finding a cell which can only have one number in it. These are hidden and naked singles. You can also have hidden and naked pairs, triples and quads, which allow you to delete candidates fron cells. From an algorithmic standpoint you have to do more computational processes to find pairs than singles, so yes, the technique is harder. Also there are many other techniques, which would take forever to explain in a single post, so I suggest you look in the advanced solving techniques section, in particular, this post: http://forum.enjoysudoku.com/viewtopic.php?p=21804#p21804

is a good place to start.

Some puzzles, many of those published in daily newspapers for example, can be solved using just hidden and naked singles. but there are puzzles which can't be solved with just singles, but can be solved with pairs, or triples. Because these techniques are harder, then de facto, the puzzles are harder. You'll find some links to puzzles which can't be solved with singles in this post: http://forum.enjoysudoku.com/viewtopic.php?t=4609

Now if all the puzzles you have encountered have come from newspapers which publish puzzles which can be solved with a small set of techniques, then in a sense your comment 'we could be doing the same puzzle over and over' has an element of truth in it. I mean the puzzles aren't the same, in the sense that there's a simple mathematical map that maps one puzzle to the other, but there's no qualitative difference between them. For instance if you get all your puzzles from the Guardian newspaper in the uk you'll never need to know any techniques beyond singles, pairs and locked candidates. I guess if you take this argument to the extreme, then yes all puzzles are the same. But given the vast number of different solving techniquesthat are available, from the point of view of a human solver, there's plenty of stuff to keep you interested in the process of solving sudoku puzzles, if you get your puzzles from a source that employs a variety of solving techniques to generate the puzzles.

As for the difficulty of generating a puzzle, well generating a puzzle that can be solved using singles is, in my opinion, little more difficult than solving such a puzzle. Generating a harder puzzle is a bit more difficult. You might try to include an advanced technique in your puzzle, but in the process of creating the rest of the puzzle, it's likely that you include and alternative solving path which requires only singles. Up to this point I'm talking about generating a puzzle by hand. However you can use software to generate puzzles. Basicly if you have software which can solve a puzzle, then it's very easy for it to use the same process to generate a puzzle. It just has to keep adding clues until it has a puzzle with a unique solution. Such software can take moments to generate a puzzle, so some generators can make thousands of puzzles a second. Then they can check what's the hardest technique required to solve them.

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Postby Smythe Dakota » Mon Dec 10, 2007 5:04 am

Virtually all newspaper puzzles are computer-generated. And the computer also figures out the difficulty level, probably based on the techniques required to solve the puzzle.

But humans think differently from computers, so some puzzles regarded as easy by the computer might be harder for humans, or vice versa. Lots of times I find a puzzle to be "unusually difficult for a Monday puzzle" or "unusually easy for a Friday puzzle", etc.

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Postby daj95376 » Mon Dec 10, 2007 6:26 am

While randomly generated puzzles are to be expected, there's no guarantee. A very notable exception is the sample puzzles supplied with Simple Sudoku. If you solve all of the puzzles, including the advanced set of puzzles in the second ZIP file, then you will discover that many of them have the same solution. Since SS isn't a commercial venture, Angus Johnson is allowed to do whatever he desires ... and I won't fault him a bit because his solver made Sudoku solving a reality for me!
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