As far as I know there are 2 basic "flavours" for a standard (vanilla) Sudoku puzzle:
1. Symmetry: the pattern of given clues are rotationally or reflectionally symmetrical.
2. Minimality: no given clue is redundant (i.e. if any given clue is removed the puzzle no longer has a unique solution).
Also, certain people like to have the puzzle stays "purely logical", i.e. no arithmetical ingredient is allowed. In particular, the digit symbols (1-9) can be replaced by any other set of 9 incomparable symbols. Thus consecutive/non-consecutive, greater-than/less-than, odd/even, magic squares or killer cages shouldn't be used.
And, most importantly, the additional variant constraint(s) should be as simple and short as possible. Nothing is more inattractive than a puzzle with 7 or 8 complex rules which take several minutes to read, let alone to understand.
For example, here is an example of such a simple constraint:
- Code: Select all
Big square
. . . . . . . . .
. . . . . . . . .
. . x x x x x . .
. . x . . . x . .
. . x . o . x . .
. . x . . . x . .
. . x x x x x . .
. . . . . . . . .
. . . . . . . . .
All the x cells can't have the same value as the o cell
(Hint: in JSudoku, this constraint can be implemented by putting Anti-kNight and Anti-Elephant together.)
So if all 81 cells have this constraint (ignoring out of bound cells), the following puzzle has a unique solution:
- Code: Select all
. . . . . . . . .
. . . 1 . . . . .
. . . . . 2 . . .
. . 4 . . . . 3 .
. . . . . . . . .
. 7 . . . . 6 . .
. . . 8 . . . . .
. . . . . 9 . . .
. . . . . . . . .
Note this puzzle is perfectly symmetrical (90 degree rotational). Also it is obviously minimal because it has only 8 clues. (For any puzzle using 9 incomparable symbols 8 is the absolute minimum number of clues.)
It is also diagonal (Sudoku X) and have 9 disjoint groups (e.g. r147c147) but you don't need these constraints to achieve a unique solution. (However using both will probably make the puzzle more human solvable.
)This is the only simple constraint I found working for this clue pattern. However there are at least 2 other constraints which, combined with a couple of more well known constraints, give a unique solution.
The first one is this:
- Code: Select all
Big cross
. . . . . . . . .
. . . . . . . . .
. . x . . . x . .
. . . x . x . . .
. . . . o . . . .
. . . x . x . . .
. . x . . . x . .
. . . . . . . . .
. . . . . . . . .
All the x cells can't have the same value as the o cell
(Hint: in JSudoku, this constraint can be implemented by putting Anti-King and Anti-Elephant together.)
Combined with DG (Disjoing Group) and Windoku, the clue pattern above yields a unique solution. (Note the puzzle is also diagonal but it is not a necessary constraint.)
The second one is this:
- Code: Select all
Anti-Ostrich
(Ostrich = (1,5) leaper)
. . . . . . . . .
. . . . . . . x .
. . o . . . . . .
. . . . . . . x .
. . . . . . . . .
. . . . . . . . .
. . . . . . . . .
. x . x . . . . .
. . . . . . . . .
All the x cells can't have the same value as the o cell
Again, combined with DG (Disjoing Group) and Windoku, the clue pattern above yields a unique solution. (And again the puzzle is also diagonal but it is not a necessary constraint.)
But most important is the "Big Square" 8-clue puzzle above. I will see if anyone can find such a puzzle with a simpler constraint.
