Hi,
Consider the first 2 puzzles from the above example.
- Code: Select all
12345.67.47.1.652.6...7.4..28651.73.71.6.3285.3...7...8.....3...42............842
12.4.567..7.1.65.2..........8..6.73.71.3.8265.3.5.7..88...5432.24.8.3.56...6..8..
1111.111.11.1.11111...1.1..11111.11.11.1.1111.1.1.1..11...1111.1111.1.11...1..111 #union (56+25)
11.1..11..1.1.11.1..........1..1.11.11.1.1111.1...1...1.....1...1.............1.. #intersection (27+54)
Do you mean to represent every of the known puzzles so that the union of all givens over all puzzles has as less as possible givens (and therefore has as much as possible non-givens), and then to enumerate all puzzles within this/these pattern(s)?
Even if finding pattern(s) is achievable, the enumeration of, say, 60-cells pattern, seems too ambitious.
The alternate approach to find the maximal intersection of the givens (say 20 cells), and then to expand, seems unrealistic too.
In both cases we are anchoring the search to already known patterns and any new puzzle obtained in different way might reset the search.
Concerning gaps. My understanding is that
the_size_of_the_space = the_count_of_the_known_puzzles + sum(the_sizes_of_the_gaps). Different coordinate systems result in different gaps, but the sum of their sizes remains constant.
P.S. Attached are the 545 puzzles ordered by pattern so that the puzzles with same pattern are next to each other.
Edit: Replaced the wrongly ordered file with correct one.
