It's interesting that we are reaching an era where we can prove things through computational brute force before coming up with an elegant proof, even if it means running computers for 12 months.
I wonder what implications this has for other mathematical complexities. Obviously it helps that Sudoku involves concepts that are very discrete... you can't really do brute force regarding the number line... but there have to be other discrete issues. (For example, every now and then I have the occasional fleeting terror that a sudden technology breakthrough will instantly render all pre-existing SSL encryption worthless.)
Back to the Sudoku, I'm also now interested in how many 17-clue solutions there are, and how many 18-clue, and if there's any sort of pattern.
I wonder what implications this has for other mathematical complexities. Obviously it helps that Sudoku involves concepts that are very discrete... you can't really do brute force regarding the number line... but there have to be other discrete issues. (For example, every now and then I have the occasional fleeting terror that a sudden technology breakthrough will instantly render all pre-existing SSL encryption worthless.)
Back to the Sudoku, I'm also now interested in how many 17-clue solutions there are, and how many 18-clue, and if there's any sort of pattern.