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). 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.
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 :-) -- Hauke Reddmann <:-EX8 firstname.lastname@example.org Die Weltformel: IQ+dB=const.