two thoughts while drifting off to sleep last night

[zwol]

The (paranormal) magic of the Shadowrun RPG is not suited to duplicating many classical effects of stage magic, especially those that involve making things appear and disappear. There's no teleportation, unless you count a special ability possessed by a very small number of extremely overpowered NPCs and thought to be impossible by everyone else. You could use illusion, but that's not notably different from the way stage magicians do it.

In a Sudoku puzzle, what is the smallest number of "givens" that can appear while the puzzle still has a unique solution? Wikipedia tells me this is unsolved and the best anyone has done is 17. I can't find any proved lower bound, but it seems intuitive that 8 or fewer cannot possibly work, and last night it seemed plausible that 9 could. Now I'm not so sure.

Comments

[vvvexation.livejournal.com]

It's unsolved? Wow. Seems like it shouldn't be all that different from a non-attacking queens problem. Then again, I guess the extra order of magnitude might make a qualitative difference.

[zwol.livejournal.com]

Well, it's nine concurrent non-attacking rooks problems with an additional constraint (the subregion rule) ... but I don't think the solution techniques that apply to that are going to help much with this.

Solving "what is the least number of rooks that can be placed on a 9x9 chessboard such that they permit exactly one solution to the non-attacking rooks problem on that board" should give an upper bound, but I don't think it's tight, because interactions between numbers give additional constraints.