SudoCue - Minimum Windoku-X Collection
The program I wrote to find Sudoku-X puzzles with the minimum number of 12 (probably) clues has been adapted to broaden
the search to other variants, such as Windoku with a current 11 clues minimum and Windoku-X with a current 9 clues minimum.
This Windoku-X starts with a series of 51 empty cells. That's 5 empty boxes!
You can download a zip with the current collection of 233576 puzzles.
I started with some 20000 Windoku-X puzzles from my puzzle generator with 15 or fewer clues. With this collection, I performed the following steps:
Using this method, the first 9 clue results quickly appeared. To my surprise, this collection keeps growing by replacing any of the 9 clues with a random other clue. Unlike Sudoku-X and Windoku, this collection is still growing on its own and requires no fresh input. This gives me hope that we may even find an 8 clue puzzle someday.
Because of the many constraints, Windoku-X puzzles have far fewer permutations than other Sudoku variants.
Using reflection and rotation gives 8 equivalent puzzles. These transformations do not change the relative position of
cells, but only operate on the complete puzzle.
In phase 2, the digits are relabeled in order of appearance on the string of 81 numbers. When multiple permutations in phase 1 were pattern-equivalent, their relabeled clues are compared from left to right and the lowest value is chosen as the canonical form.