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The solution of a 6x6 and a 9x9 puzzles with "strange cages" https://www.calcudoku.org/forum/viewtopic.php?f=16&t=105 
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Author:  giulio [ Tue Nov 29, 2011 1:47 pm ] 
Post subject:  Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca 
clm, Sorry for the delay in replying to your question of Mon Nov 14, 2011 8:43 am: Quote: is there any reason why you have initially excluded in your analysis the combination 66552211 for the 3600x? I thought I had subscribed to the thread but I hadn't. I just discovered that the discussion has been continuing... Is there a way to subscribe to all threads automatically, by default? Anyhow, I found again the printed puzzle I had used for the analysis, and saw that I had considered and then discarded 66552211. I confess, I cannot find out again why I did it . Clearly, there are several permutations that would be possible. I suspect that I discarded it by mistake... Or perhaps I had a moment of lucidity and brilliancy that I am unable to reproduce... Perhaps Patrick could search the thousand of solutions that his solver has generated and see whether any of them includes 66552211 for 3600x. If it did, it wouldn't prove that I was very clever, but at least it wouldn't exclude it... 
Author:  clm [ Tue Nov 29, 2011 3:49 pm ] 
Post subject:  Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca 
giulio wrote: clm, Sorry for the delay in replying to your question of Mon Nov 14, 2011 8:43 am: Quote: is there any reason why you have initially excluded in your analysis the combination 66552211 for the 3600x? I thought I had subscribed to the thread but I hadn't. I just discovered that the discussion has been continuing... Is there a way to subscribe to all threads automatically, by default? Hi, giulio, I do not see that option in the User Control Panel, "Manage subscriptions", it seems one must subscribe topics individually, let's Patrick to clarify. giulio wrote: Anyhow, I found again the printed puzzle I had used for the analysis, and saw that I had considered and then discarded 66552211. I confess, I cannot find out again why I did it . Clearly, there are several permutations that would be possible. I suspect that I discarded it by mistake... Or perhaps I had a moment of lucidity and brilliancy that I am unable to reproduce... Perhaps Patrick could search the thousand of solutions that his solver has generated and see whether any of them includes 66552211 for 3600x. If it did, it wouldn't prove that I was very clever, but at least it wouldn't exclude it... With respect to this subect on Nov 14, I was answering to your post :"... Apart of this, I can provide an initial premise. Considering the addition, 63, of three columns or three rows, it can be quickly seen that "2700x" (+) = 26 so the only combination is 65533211 having the other three combinations values of 24, 25 and 28. Now, the "28+" is made by the rest of the numbers in columns d, e and f, that is, 66443221. Similarly, "3600x" (+) = 27 and the only combination is 65543211, having the other four combinations sums of 25, 26, 28 and 29. Consequently, "31+" = [6, 6, 5, 4, 4, 3, 2, 1]. ... ". On Nov 15, after several posts and after correcting something that was not working properly in the solver, Patrick finally found for this 6x6, 42672 different solutions, but sure all of them are obtained by permuting those compositions I was referring to, in other words, it is mathematically impossible to include the 66552211, which sum is 28 and not 27, in any of the solutions, since being that sum 28 we would break the total sum of the three leftmost columns of the puzzle (63 = 3 x 21). Apologize for not replying you first with respect to your initial analysis but I thought you was following the thread. 
Author:  pnm [ Tue Nov 29, 2011 6:29 pm ] 
Post subject:  Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca 
clm wrote: Hi, giulio, I do not see that option in the User Control Panel, "Manage subscriptions", it seems one must subscribe topics individually, let's Patrick to clarify. An option is to use the "View unread posts" link at the top right. That should give you a list of all the posts you haven't read yet. Patrick 
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