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SudoCalcudoku https://www.calcudoku.org/forum/viewtopic.php?f=16&t=144 
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Author:  starling [ Sat Jan 14, 2012 2:10 am ] 
Post subject:  Re: SudoCalcudoku 
Turned into a sudoku way too fast. That is, everything that was a true cage solved almost instantly. Other than that, this is really cool. I'm not positive it has a unique solution, though. I got to a point where I couldn't conclusively prove anything, but this seemed to stem from the fact that I haven't done any sudoku in months. I could guess and test, and the trees I tried and didn't use didn't work, which makes me think it's likely the situation is unique, I just can't prove that because I had to guess and test. 
Author:  clm [ Sat Jan 14, 2012 3:09 pm ] 
Post subject:  Re: SudoCalcudoku 
starling wrote: Turned into a sudoku way too fast. That is, everything that was a true cage solved almost instantly. Other than that, this is really cool. I'm not positive it has a unique solution, though. I got to a point where I couldn't conclusively prove anything, but this seemed to stem from the fact that I haven't done any sudoku in months. I could guess and test, and the trees I tried and didn't use didn't work, which makes me think it's likely the situation is unique, I just can't prove that because I had to guess and test. Thank you for your comments. I think that if these type of puzzles were created with a software, more complex puzzles than this one of course, certainly, earlier or later in the solution process, the puzzle will turn into a pure sudoku. In this example we have "information" about 28 cells; if I am right (and I am not a very expert "sudoker") a really good and difficult sudoku has no more than 20 or 21 individual cells "given" (I would like to hear the opinion of the advanced "sudokers"  and they may also give an opinion about the unicity of this example). In those conditions and since the "given" numbers are usually separated and distributed over the 9x9 grid, it would be very difficult to group them in order to form cages with operations and results. With that purpose in mind the number of individual "given" numbers should decrease much in favor of the numbers grouped in cages, some compromise should be adopted. In the sudoku, the numbers 1 to 9 are independent and not linked to any operation, no mathematical knowledge (arithmetic or other operators) is required, and this is probably why the sudoku is attractive to a great variety of persons, but perhaps something intermediate could be realized (not in this site, of course) and that "SudoCalcudoku" would be in our borderland. 
Author:  starling [ Sun Jan 15, 2012 1:25 am ] 
Post subject:  Re: SudoCalcudoku 
I had no problem solving 60 of the 81 cells. I was missing A46, I46, D1, E1, F1, D9, E9, F9, and the middle section, and had no places where I could eliminate candidates. 
Author:  clm [ Sun Jan 15, 2012 3:15 pm ] 
Post subject:  Re: SudoCalcudoku 
starling wrote: I had no problem solving 60 of the 81 cells. I was missing A46, I46, D1, E1, F1, D9, E9, F9, and the middle section, and had no places where I could eliminate candidates. Hi, starling, I feel there is a 99% of probability of arriving to the situation you describe, so I am sure you have that part correct. The "difficulty" comes from this point. Try this: 1) A4 = 1 and complete the segment A4A6, then necessarily D5 = 9 and now there is no valid number for F4, so A4 <> 1. 2) Place then the 1 in its correct position and complete the segment A4A6. Place the 7 of row 6 in its proper position (it's inmediate). Now we have two possible places for the 6 in row 6. Consider D6 = 6 > I4 = 6 and, at the same time, D9 = 9 and now there is no place for a 9 in row 4, so D6 <> 6, the 6 of row 6 must go the other possible place in row 6. Completing the puzzle is now automatic. This process "looks" similar to the "trial and error" but, in some way, any logic process contains some "trial and error" inherently I think. (I will send the full solution anyway in a few days, perhaps any other puzzler wants to try it or find a different way) 
Author:  starling [ Sun Jan 15, 2012 10:07 pm ] 
Post subject:  Re: SudoCalcudoku 
clm wrote: starling wrote: I had no problem solving 60 of the 81 cells. I was missing A46, I46, D1, E1, F1, D9, E9, F9, and the middle section, and had no places where I could eliminate candidates. Hi, starling, I feel there is a 99% of probability of arriving to the situation you describe, so I am sure you have that part correct. The "difficulty" comes from this point. Try this: 1) A4 = 1 and complete the segment A4A6, then necessarily D5 = 9 and now there is no valid number for F4, so A4 <> 1. 2) Place then the 1 in its correct position and complete the segment A4A6. Place the 7 of row 6 in its proper position (it's inmediate). Now we have two possible places for the 6 in row 6. Consider D6 = 6 > I4 = 6 and, at the same time, D9 = 9 and now there is no place for a 9 in row 4, so D6 <> 6, the 6 of row 6 must go the other possible place in row 6. Completing the puzzle is now automatic. This process "looks" similar to the "trial and error" but, in some way, any logic process contains some "trial and error" inherently I think. (I will send the full solution anyway in a few days, perhaps any other puzzler wants to try it or find a different way) This was exactly what I actually ended up doing, and was what I was referring to as Trial and error. Reason why I think this is more trial and error was because I only did this after I tried a 7 in A4, and realized it was in error. I realize we've had the whole "Eventually everything boils into guessing that isn't a single cage," discussion, but past a certain point it's not really a question to me that it's trial and error. 
Author:  jaek [ Wed Apr 04, 2012 11:39 pm ] 
Post subject:  Re: SudoCalcudoku 
My experience was exactly the same as Starling's. I got the same 60 before stalling out. Maybe if you included the center value as a onecell cage? It definitely fell into place when I 'gave' myself the 5 there. Or maybe if you included 0,,e4e5e6? (result,operation,cells in case I am forgetting the standard notation.) [2,4,6] and [2,5,7] are the possible solutions once the first 60 cells are filled, but e1 prevents [2,4,6]. I didn't go back and try solving with either of those additional pieces of information so it may make the whole solution too easy. The one overarching drawback to me was that I mostly solved the few calcudoku cells before finishing the rest as sudoku. Almost like I had to solve the calcudoku parts in order to fill in the initial sudoku values. I think it may have been more enjoyable if there was more switching back and forth between the two styles. 
Author:  clm [ Thu Apr 05, 2012 2:05 pm ] 
Post subject:  Re: SudoCalcudoku 
jaek wrote: My experience was exactly the same as Starling's. I got the same 60 before stalling out. Maybe if you included the center value as a onecell cage? It definitely fell into place when I 'gave' myself the 5 there. Or maybe if you included 0,,e4e5e6? (result,operation,cells in case I am forgetting the standard notation.) [2,4,6] and [2,5,7] are the possible solutions once the first 60 cells are filled, but e1 prevents [2,4,6]. I didn't go back and try solving with either of those additional pieces of information so it may make the whole solution too easy. The one overarching drawback to me was that I mostly solved the few calcudoku cells before finishing the rest as sudoku. Almost like I had to solve the calcudoku parts in order to fill in the initial sudoku values. I think it may have been more enjoyable if there was more switching back and forth between the two styles. Thank you, your comments are very interesting. But if we gave more information (like values in e4 or e5 or e6, or for a cage "e4e5e6", etc.) the full puzzle would become very easy, since with the actual info it can be solved (with a unique solution I believe; in the next days I will try to provide the full solution process, if I find some time ). You are right that with more switching back and forth between the two styles it would be more enjoyable; in this "prototype" I tried to make it attractive to the "calcudokers" by solving initially the calcudoku part (very easy, unfortunately the "sudokers" do not read this page). To have more interaction we would need a software (I prepared this "manually" and it was just an "experiment"). Really, the difficulty is assigned to the "sudoku" part itself, and, as I commented to starling, the probability of arriving to those 60 cells is maximum. 
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