tag:blogger.com,1999:blog-8883034.post116292050480180386..comments2024-10-02T09:09:09.121+02:00Comments on atdotde: Two Sudoku ProblemsRoberthttp://www.blogger.com/profile/06634377111195468947noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-8883034.post-63593017904174104032006-11-22T17:14:00.000+01:002006-11-22T17:14:00.000+01:00I've read that most 'zines use a group of basic, h...I've read that most 'zines use a group of basic, human tactics as a measure for difficulty of the puzzle. (there's actually a solid library of quite a _lot_ of tactics... a puzzle that requires, from any some set, a particular strategy, requires that tactic's level of abstraction: so it isn't entirely ill-founded.)<br /><br />As for your difficulty rating not scaling, just some thoughts (I'm no mathematician so forgive me): <br /><br />can you combine leaf-count with backtrackings required?<br /><br />Backtracking by itself may not show difficulty correctly, because it is required in places where, when working the puzzle yourself, you would just use an abstraction (for hard puzzles in the Washington Post, it is common-place to have to look at a 3x3 cell and mark possibilities, such that one square may just happen to only have one possibility: it's the pigeon hole principle!) So you need some further refinement..Robbie Muffinhttps://www.blogger.com/profile/05205133232844714580noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1162981853795211182006-11-08T11:30:00.000+01:002006-11-08T11:30:00.000+01:00As far as I can tell this is not a 17 but an 81 cl...As far as I can tell this is not a 17 but an 81 clue puzzle and thus even Die Zeit would not rate it as "hard".<BR/><BR/>Georg raises an interesting point: I think what I wrote about the symmetry group of all sudokus is correct. However, not all orbits will be of this full size, some puzzles will not change under specific transformations. You could imagine a puzzle where a permutation of row blocks could be undone by a relabeling of the symbols for example.<BR/><BR/>These transformations which leave a specific puzzle invariant form a subgroup of the full symmetry group called the stabiliser. This opens the possibility for a third sudoku problem: Find a puzzle with a large (the largest?) stabiliser!Roberthttps://www.blogger.com/profile/06634377111195468947noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1162940000737833542006-11-07T23:53:00.000+01:002006-11-07T23:53:00.000+01:00I haven't thought about this for very long, but ar...I haven't thought about this for very long, but are you sure that for the Sudoku symmetry group the operations you named are actually all independent generators? I was wondering whether the operation of renaming digits 1-9 couldn't possibly always, or at least sometimes, be reformulated as a sequence of row and column permutations, given that the entries in each row, column and square are distinct. In that case the real symmetry group would be reduced by some relations between the different generators.Georg v. Hippelhttps://www.blogger.com/profile/15355104409462033075noreply@blogger.comtag:blogger.com,1999:blog-8883034.post-1162938367600421682006-11-07T23:26:00.000+01:002006-11-07T23:26:00.000+01:00Just another 17 clue puzzle79862431531587924626431...Just another 17 clue puzzle<BR/><BR/>798624315<BR/>315879246<BR/>264315978<BR/>129587463<BR/>683241759<BR/>457936182<BR/>942158637<BR/>531762894<BR/>876493521<BR/><BR/>www.onedollarsudoku.comAnonymousnoreply@blogger.com