Search All of the Math Forum:
Views expressed in these public forums are not endorsed by
Drexel University or The Math Forum.



ZOMGbies! (A 1 person board game)
Posted:
Mar 10, 2013 12:01 PM


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 8cell 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 selfexplaining sketch:
444 4z33 11z3 1z23 222
 With k=2 and a woken human anywhere, you can protect a whole halfplane (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 fc3a501@unihamburg.de Die Weltformel: IQ+dB=const.



