Calcudoku puzzle forumhttp://www.calcudoku.org/forum/ Step by step analytical solution of a 9x9 “very difficult”http://www.calcudoku.org/forum/viewtopic.php?f=3&t=196 Page 1 of 2

 Author: arjen  [ Sat Apr 21, 2012 10:03 am ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul Excellent, I restarted 2 times.I'm curious to see statistics.A graph of the last month with the lines started / finished / solver rating.@Patrick, when you are bored .... :)

 Author: pnm  [ Sat Apr 21, 2012 10:30 am ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul arjen wrote:I'm curious to see statistics.A graph of the last month with the lines started / finished / solver rating.@Patrick, when you are bored .... :)Interesting though.But at the moment I'm not logging when a puzzle is started (I can see of coursewhen it's loaded, but not if/when someone starts entering numbers)(so I maybeI should log that fact :)

 Author: jomapil  [ Sat Apr 21, 2012 1:58 pm ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul Clm, a pretty and clean analytical solution.In short, we must " transform " the products in sums and calculate a,b,c,d values.Thanks for your solution.

 Author: jomapil  [ Sat May 12, 2012 12:31 pm ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul At the beginning it looked like I must do many "trial and error" to solve the 9x9 of today (12-May-2012). But, after all, as far as I remember it was the first time I solved a 9x9 puzzle 100 % analytically.Has anyone any explanation about some characteristic of this puzzle that permitted that? ( It's only a curiosity of mine ).

 Author: jomapil  [ Wed May 16, 2012 12:33 pm ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul Clm: For the second time in less than a week I solved the 9x9 puzzle of today, exclusively by analytic and logical means ( in part due to your advices ). But the 9x9 of yesterday ( 15-May-2012 ) I used many trials and errors and it took many hours to complete ( with many restarts due to the mistakes ). So, it looks like many diagrams are not possible to use only analytical methods, isn't it?

 Author: clm  [ Wed May 16, 2012 6:09 pm ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul jomapil wrote:Clm: For the second time in less than a week I solved the 9x9 puzzle of today, exclusively by analytic and logical means ( in part due to your advices ). But the 9x9 of yesterday ( 15-May-2012 ) I used many trials and errors and it took many hours to complete ( with many restarts due to the mistakes ). So, it looks like many diagrams are not possible to use only analytical methods, isn't it? First of all congratulations for the two analytical solutions, on May 12 and May 16, we are in the good way. But I think that probably all diagrams, though difficult, can be solved with analytical methods, according to my previous assertion of: "If a calcudoku has a unique solution, it can be solved using only analytical means" (thread "A 6x6: Is the analysis enough to solve a calcudoku?"). This is not a theorem (it must be demonstrated and this demonstration is still pending). The yesterday's case, May 15, 2012, is not an exception, in my opinion. It's more difficult than usual, as every tuesday, of course. As it's a large 9x9 it will require several graphics and some time. I will try to send the step by step solution in the following days, opening a separate thread (in this same section "Solving strategies and tips"), in order to separate the discussion from this thread, which is more related to the 9x9 on tuesday Apr 17, 2012.

 Author: jotempe  [ Thu May 17, 2012 12:03 am ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul clm, as I have already written elsewhere, the validity of your assertion depends on your definition of "analytical solution". Look e.g. at "Note 1" and "Note 2" in the solution that you started the thread with. They essentally say someting like: 'it could be either x or y. However if this were x, then we would have a, and ths would lead to b, which is contradictory, because of c. So it must be y'. Now, a purist will tell you, that this is a reductio ad absurdum proof, or, in plain English, a trial and error method, only that you performed the entire trial "in your mind", without putting any numbers in the diagram - as you have good enough memory to "see" the diagram with them in. So, the question is "how many numbers can be put in the diagram when considering a hypothesis, before you stop calling it anaytical solution?"

 Author: jomapil  [ Thu May 17, 2012 8:56 am ] Post subject: Re: Step by step analytical solution of a 9x9 “very difficul Jotempe, in the end it looks like there will be ALWAYS " trial and error " ( TAE ). But what Clm intends to say is that we can reduce this TAE at a minimum of times. And the remaining few times we use TAE we can use them in a smarter way so as to mask that TAE component. Will it be so?