Calcudoku puzzle forumhttps://www.calcudoku.org/forum/ The solution of a 6x6 and a 9x9 puzzles with "strange cages"https://www.calcudoku.org/forum/viewtopic.php?f=16&t=105 Page 2 of 5

 Author: pnm  [ Mon Nov 14, 2011 6:04 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9possible solutions had been tried (testament to the poor quality of my solver I'm thinking the 9x9 is too "open ended", and most likely completely unsolvableby a human (unless there's some key solving technique that I'm missing)Patrick

 Author: pnm  [ Mon Nov 14, 2011 7:18 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca My solver took half an hour to compute all solutions for the 6x6.It found 6492 solutions.The difficulty rating is 183.Here are a few solutions:465123126345342561514632231456653214645123326541214635563412431256152364542163326541614325453612231456165234142635326541465312654123231456513264(these were solution number 10, 100, 1000, and 6492 found)Patrick

 Author: clm  [ Mon Nov 14, 2011 11:38 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca pnm wrote:Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9possible solutions had been tried (testament to the poor quality of my solver I'm thinking the 9x9 is too "open ended", and most likely completely unsolvableby a human (unless there's some key solving technique that I'm missing)Patrick Very curious. If a 6x6, even knowing the exact compostion of the cages, has 6492 solutions (by spinning those numbers around the central "hole" of the cages and combining the 4 cages to a valid grid) (I suppose excluding symmetries), how many a 9x9 would have?. The number of different diagrams (excluding symmetries), just the "configuration", before stablishing the cages, that is, the restrictions, is 3 for a 3x3 (with the 1's in the diagonal, the 2's in the diagonal and the 3's in the diagonal); for the 4x4 I think is 108 (in three classes, 36 with one pair of equal corners, 36 with two pairs of equal corners, and 36 with all four corners different), etc. The number of valid grids grows almost "in vertical" and we know the very high number, 6,671 x 10 ^ 21 of valid "sudoku grids" (9x9). The case of the 6x6: with a rating of 183 it would be solvable by a human, even if the solution is not unique (one of those 6492), the program could return the "congratulations"; perhaps you may introduce some type of complementary (additional challeging puzzles), without points, without time limitation (neither 24 hours or 72 hours...) and just indicate (without names) "solved by 12 puzzlers..." and after some time, a month or so, put new ones, just for hobby.

 Author: pnm  [ Tue Nov 15, 2011 12:12 am ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca clm wrote:perhaps you may introduce some type of complementary (additional challeging puzzles), without points, without time limitation (neither 24 hours or 72 hours...) and just indicate (without names) "solved by 12 puzzlers..." and after some time, a month or so, put new ones, just for hobby.What I should introduce is a "user puzzle" feature: simply upload a filein that format, and it becomes a puzzle created by clm.The solver would assign points to it based on difficulty level, etc...Patrick

 Author: clm  [ Tue Nov 15, 2011 12:17 am ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca pnm wrote:Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9possible solutions had been tried (testament to the poor quality of my solver I'm thinking the 9x9 is too "open ended", and most likely completely unsolvableby a human (unless there's some key solving technique that I'm missing)Patrick Perhaps there are not many solutions and because of the high number of combinations in the case of the 9x9 it would have required more time to find the first solution. Here is the solution:

 Author: beaker  [ Tue Nov 15, 2011 1:59 am ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca This kenken is beyond my ken

 Author: clm  [ Tue Nov 15, 2011 12:37 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca pnm wrote:My solver took half an hour to compute all solutions for the 6x6.It found 6492 solutions.The difficulty rating is 183.Here are a few solutions:465123126345342561514632231456653214645123326541214635563412431256152364542163326541614325453612231456165234142635326541465312654123231456513264(these were solution number 10, 100, 1000, and 6492 found)Patrick Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time. Here is one of those 6492 solutions:

 Author: pnm  [ Tue Nov 15, 2011 3:06 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca clm wrote: Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time. What's also interesting is how to modify the puzzle so there's exactly one solution...I'm wondering if this could be programmed. The solver determines there are >= 2 solutions(determined quite quickly), and then the puzzle is modified in a way that is known to reducethe number of solutions (simple example: split a large cage into two), etc.Patrick

 Author: clm  [ Tue Nov 15, 2011 8:38 pm ] Post subject: Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca pnm wrote:clm wrote: Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time. What's also interesting is how to modify the puzzle so there's exactly one solution...I'm wondering if this could be programmed. The solver determines there are >= 2 solutions(determined quite quickly), and then the puzzle is modified in a way that is known to reducethe number of solutions (simple example: split a large cage into two), etc.Patrick We could try your idea and see what happens, I broke (in my solution) a big cage into two parts:631,+,a1b1c1a2c2a3b3c32,+,b2150,x,d1d2d3e3f34,+,e22,-,e1f1f23600,x,a4b4c4a5c5a6b6c63,+,b528,+,d4e4f4d5f5d6e6f65,+,e5 Here is the graphic anyway

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