<email@example.com> writes: > Da Rulez! > 0. All rules may be pimped for moar lulz. > 1. You play on a m*m torus square grid board. > 2. The cells are in one of three states: > human, zombie or asleep. > 3. Initially all cells are asleep. > 4. Your move is "awakening" k cells. > 5. On awakening, the cell will become human > with probability p. (Alternatively, the state > is preset but unknown to you, like in Minesweeper).
And they become zombies otherwise? Or do they fall back asleep again?
> 6. A zombie cell will infect all "sleeping" cells > in its vicinity (The usual LIFE 8-cell neighborhood). > Already woken humans carry a chainsaw and are immune. :-) > (The infection is computed after the awakening, but > see Rule 0.) > Protect mankind! > > Some analysis: > - For k>=8, your job is trivial: awake all the neighborhood > of any zombie. > - Still, k=4 is enough to stamp out any breakout if zombies > appear only sparingly. See self-explaining sketch: > > 444 > 4z33 > 11z3 > 1z23 > 222 > > - With k=2 and a woken human anywhere, you can protect a > whole half-plane (since the infection spreads with v=1 > to both sides and your protective wall too). Oops, did I say > we play on a torus? Goto 0 :-) Also, I assumed there is > just one zombie hidden on the board.
No you didn't. You assumed "3. Initially all cells are asleep." combined with "2. The cells are in one of three states: human, zombie or asleep." that means there are no zombies on the board.
> So, any strategies for k=1 and a board starting with one > awoken zombie (and no more hidden)? > > P.S.: > oo. Anyone making a browser game out of my idea and not > sharing the million$ will meet Cindy, the rusty chainsaw :-)
You can't kill what's already dead!
Phil -- "In a world of magnets and miracles" -- Insane Clown Posse, Miracles, 2009. Much derided. "Magnets, how do they work" -- Pink Floyd, High Hopes, 1994. Lauded as lyrical geniuses.