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 Author: giulio  [ Thu Mar 08, 2012 3:27 am ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? clm wrote:“If a calcudoku has a unique solution, it can be solved using only analytical means.”As the number of permutations increases, you are likely to employ strategies that approach guessing. For example, sometimes, I write down beside the puzzle (I only solve puzzles with pencil after printing them out) all possible permutations of adjacent cages, and eliminate them one by one by checking whether they lead to contradictions. How far can I go with it and still consider the solution analytical? In fact, by checking whether a permutation in a cage leads to a contradiction, I am just trying it out without completely admitting it. The difference with what I call "trial and error" is subtle, and becomes more subtle as the my checks involve more and more cages and cells. I go only as far as I can while still keeping all possibilities open. Trial and error, for me, means writing a solution in a cell or a cage and see whether it works. But the distinction is purely subjective.In other words, the distinction between "trial and error" and "analysis" is not an absolute distinction. It depends both on the solver and on how far the solver is prepared to go to eliminate alternatives before writing numbers in the grid.I agree with you that, as the solution is unique, it is certainly possible to solve the puzzle by eliminating the wrong alternatives. But, if in order to do so I have to deal with half a dozen "1- " and "2-" cages and/or with more than one large cage containing sums (which result in too many (whatever "too many" means to me) alternatives), I am going to consider the puzzle, for all practical purposes, only solvable by trial and error.

 Author: beaker  [ Thu Mar 08, 2012 5:38 am ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? That pretty much sums up the way I do it for the difficult 6's or greater.

 Author: sneaklyfox  [ Thu Mar 08, 2012 5:49 am ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? I know somewhere else in the forum there was a discussion about being analytical or doing things by trial and error, whether it is termed "guessing" or not. Someone else said that it is called "guessing" if you write anything down (even on the side I think?) to determine later that it in fact leads to a contradiction and that it doesn't count as "guessing" if you do it all in your head. I would "write things down" so I don't have to stress my brain too much by keeping it all only my head. But does guessing in one's head now count as "guessing" or something like "logic by process of elimination"? So perhaps giulio's assertion that "the distinction is purely subjective" has merit.

 Author: giulio  [ Thu Mar 08, 2012 6:41 am ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? IMO, "guessing" and "trial and error" are synonyms. After all, when you "try" a number, it means that you are making a "guess". Regardless of whether you write things down or not, when you write a single number in a cell, either you have a sequence of logical steps that leads you to the conclusion that it is the correct solution, or you are guessing.Obviously, the better you are at keeping logical steps and numbers in your head, the less you need to write things down. But without writing things down, I wouldn't be able to solve the more difficult puzzles, and I do like to solve them. If for somebody that means that I am guessing, then so be it!

 Author: sneaklyfox  [ Thu Mar 08, 2012 7:20 pm ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? giulio wrote:IMO, "guessing" and "trial and error" are synonyms. After all, when you "try" a number, it means that you are making a "guess". Regardless of whether you write things down or not, when you write a single number in a cell, either you have a sequence of logical steps that leads you to the conclusion that it is the correct solution, or you are guessing.Obviously, the better you are at keeping logical steps and numbers in your head, the less you need to write things down. But without writing things down, I wouldn't be able to solve the more difficult puzzles, and I do like to solve them. If for somebody that means that I am guessing, then so be it! Yes, but is guessing in your head "guessing" or "being analytical"?

 Author: beaker  [ Thu Mar 08, 2012 10:31 pm ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? LOL

 Author: giulio  [ Fri Mar 09, 2012 3:05 am ] Post subject: Re: A 6x6: Is the analysis enough to solve a Calcudoku? As I see it, the only difference between "guessing" and "trial and error, is that "guessing" implies that we choose one of possible alternatives, while "trial and error" sounds completely neutral: perhaps meaning that we go through all possibilities in an order that doesn't depend on the status of the particular puzzle (e.g., from the smallest to the larger numbers, or even throwing a die). In that vein, it could be argued that "guessing" is then a better strategy, because choosing a number without following a pre-defined strategy inevitably relies on heuristics. If you have played enough puzzles and have learned the "puzzle language" (who was saying that? Gee, my apologies, but my memory is completely shot!), you are more likely to "guess" the right solution.Don't you just love splitting hairs?

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