I see a lengthy thread about the "smallest valid pattern".
What's the difference between that and a minimal clue puzzle?
Mathimagics wrote:Puzzles consist of clues, aka givens. Patterns are just templates that indicate the positions of those clues.
For example ..2..4..1 might be the first row of a puzzle, in which case the corresponding pattern would begin with ..X..X..X
A pattern is valid if there exists some choice of clue values that can replace the X's and be a valid puzzle (that is, has 1 solution).
dxSudoku wrote:I think I read somewhere the minimum number of givens and still have a solvable puzzle is 17.
dxSudoku wrote:So what does minimum pattern mean?
Mathimagics wrote:For a given grid/puzzle, if we generate all of the transformations, normalise them (which means relabelling so that row 1 = 123456789), then list these in one-line format, and then sort this list, then the first entry in the sorted list is the minlex form of the original grid/puzzle.
puzzle : ...7......7...5.3.....9.8..1.4...2......6...4.25....1...248.....6.9...7.8....1...
Norm puzzle: ...1......1...2.3.....4.5..6.7...8......9...7.82....6...875.....9.4...1.5....6...
grid : 946738125278615439513294867194357286387162954625849713752486391461923578839571642
Norm grid : 123456789846379251975812634712594863564738192389621475498263517237185946651947328