FAQ   Search   Memberlist   Usergroups   Register   Profile   Log in          Games  Calendar Log in to check your private messages    symmetry ?          Sudoku Programmers Forum Index -> Programming sudoku View previous topic :: View next topic   Author Message bidule Joined: 03 Nov 2005 Posts: 1 : Items Posted: Thu Nov 03, 2005 2:26 pm    Post subject: symmetry ? hello, I'm wondering if it's possible to apply vertical or horizontal symmetry or maybe both on a sudoku grid ? if yes, is it possible to combine vertical AND horizontal ? or only one at a time ? regards. Back to top Ruud Site Admin Joined: 17 Sep 2005 Posts: 708 : Location: Netherlands Items Posted: Thu Nov 03, 2005 8:12 pm    Post subject: Most published sudokus have 180 degree rotational symmetry. You can also do 90 degrees, horizontal mirroring or vertical mirroring. The latter two can be combined. When you apply 90 degree rotational or both H & V symmetry, you need to place 4 clues at a time. This greatly reduces the chance to create a minimal puzzle (one when no clue can be removed). It makes the puzzle more attractive to the eye but less to the mind. Symmetrical puzzles are like full glasses of beer. They look great, but you know they won't last. Ruud. Back to top Lummox JR Joined: 07 Sep 2005 Posts: 202 : Items Posted: Sat Nov 05, 2005 5:06 pm    Post subject: Re: symmetry ? bidule wrote: I'm wondering if it's possible to apply vertical or horizontal symmetry or maybe both on a sudoku grid ? if yes, is it possible to combine vertical AND horizontal ? or only one at a time ? Yes, it's possible to have symmetry in many forms. My own generator now supports several, including classic crossword-style, quad-style (90° rotation), horizontal, vertical, horizontal and vertical, horizontal and vertical and diagonal, and both diagonals (together; I'm strongly considering allowing just one diagonal or the other). I prefer asymmetric puzzles because as Ruud mentioned, it's harder to find a minimal puzzle with symmetry. My generator only goes for "symmetrically minimal", meaning it keeps removing groups of symmetrical clues until it can't anymore. A truly minimal puzzle, though, is one that has a single solution but has multiple solutions if you remove any one clue. It is very hard for a puzzle to be both symmetric and minimal. Back to top Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First         Sudoku Programmers Forum Index -> Programming sudoku All times are GMT Page 1 of 1   Jump to: Select a forum Sudoku----------------Solving sudokuSetting sudokuProgramming sudokuThe mathematics of sudokuExotic sudoku Library----------------PuzzlesSoftwareSudoku elsewhere Not sudoku----------------Random thoughtsForum feedback  You cannot post new topics in this forum You cannot reply to topics in this forum You cannot edit your posts in this forum You cannot delete your posts in this forum You cannot vote in polls in this forum   Powered by phpBB © 2001, 2005 phpBB Group Igloo Theme Version 1.0 :: Created By: Andrew Charron