giulio wrote:
Ditto. I joined on 2011-11-03, and I only managed to solve two of those 8-W puzzles (on 2011-12-27 and on 2012-02-21).
My apologies for being picky, but if you say "with minimum trial and error", it means that they are not solved analytically. I consider a puzzle to be analytically solvable only when I am certain of all numbers that I write in them. Even if sometimes, to do so, I need to make lists and consider how permutations of different cages eliminate each other. And even if, sometimes, my certainties are misplaced, I make mistakes, and have to start from scratch.
clm wrote:
However, I think they all can be solved analytically (with minimum trial and error) using simultaneously all techniques (after we have obtained all possible combinations for all cages): addition property of rows and columns, multiplication property, parity, maximums and minimums in the sum of cages, "X-ray", common numbers in the intersection areas to make "visible" the "hidden" numbers, possible location of some prime numbers like 5, 7, 11 ... , etc.) but it's true that sometimes they take time (those 9x9's on tuesdays are not very suitable for timed puzzles ![[smile]](./images/smilies/msp_smile.gif "Smile")
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)My apologies for being picky, but if you say "with minimum trial and error", it means that they are not solved analytically. I consider a puzzle to be analytically solvable only when I am certain of all numbers that I write in them. Even if sometimes, to do so, I need to make lists and consider how permutations of different cages eliminate each other. And even if, sometimes, my certainties are misplaced, I make mistakes, and have to start from scratch.
But you are right, giulio, it is not well expressed, I missed part of the phrase " ... I think they all can be solved analytically (though this can be accelerated with minimum trial and error) ... ". Once you have obtained the numbers that compose all cages, for instance, and a big part of the puzzle filled, to "position" one of those numbers in a cage and see the global effect could be considered part of the analysis (this was already discussed, in some way it's like when you have to break 667 into its prime factors, you make attempts ... "it is not divisible by 2, 3, 5, 7, 11, ... ", until you reach the 23 and thus the 29), you could do it mentally, virtually, in abstract, but if you can gain time there is no sense when just writing the number with the pencil (or in the screen) helps (this is more or less what you are saying with ... "consider how permutations of different cages eliminate each other"). In other words, a puzzle would not be analytically doable if the only possibility to solve it is to be "lucky" among many many trials randomly performed and when you have spent a lot of hours. Perhaps we could define a "probability of solution"
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![[thumbsup]](./images/smilies/msp_thumbsup.gif "ThumbsUp")
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