The ironclad mathematical laws of the universe are what I was bemoaning to myself , something I don't normally do except in the case of sudoku. In which one is pretty much locked in to the fact that 3 x 3 equals 9, and 9 x 9 makes 81 squares to fill, minus the clues.
This is just a tad too much for my poor head. I am one who likes to not fill in candidate numerals, and so keep in my head the various possibilities. There are a few of us who like to solve sudoku without pencil marks. By this I mean we allow ourselves to only use a pen or pencil to fill in the correct numeral only when we know for certain that it is correct.
And recently I began using a little program that generates "jigsaw" sudoku. This is essentially the same as regular sudoku except the boxes, instead of being 3 x 3 are irregular. But they have 9 regions and 81 cells to fill, minus the clues.
I had an odd thought. Irregular subregions don't need to be symmetrical. A puzzle with 64 squares is certainly possible with jigsaw sudoku. You don't need boxes 2.828 x 2.828 cells, an impossibility. (The square root of 8)
So I cranked up my lovely little jigsaw sudoku generator and plugged in some odd initial inputs, and lo and behold: I got the above puzzle. I had it set on "extreme" difficulty but it's not so hard. Heh heh.
There are several popular sudoku variants. For me this is not too easy, not too hard. "Just right."
I got the original program from Simon Tatham's webpage for games. I was in such a rush to download the newer jigsaw version a while back, and because the earlier version was so intuitive and easy I didn't need a help file, that I didn't see or download the newer help file for the jigsaw variant explaining how to do unorthodox sizes of puzzles. I had to figure it out myself.
UPDATE: August 2010 My favorite Sudoku forum disappeared. I have changed the link that was at "solving without pencil marks." Apparently the original forum vanished. There is a new forum full of smart people. Many are the same old crowd.