| [ QuizWit ] in KIDS 글 쓴 이(By): mkjung (한눈안팜 ) 날 짜 (Date): 2000년 8월 31일 목요일 오전 02시 58분 07초 제 목(Title): Re: [Q] Angel problem if the board is finite, then the devil wins. if ithas no boundary to start with, then the devil has to draw a big circle faster than the angel moves. After time n, the angel moves at most n squares from the original position while the devil can mark n squares. The angel has to move continuously while the devil do not. the best strategy for the devil is to pick out squares that will form a huge boundary so that the angel will be bounded by that continous line of squares. (more like by drawing a big circle) the devil does not need to draw the continous closed curve continously. he can draw here and suddenly move to the opposite direction. Unfortunately, the cardinality of the # squares inside radius r > # squares that makes up the boundary of the circle. Hence, the angel wins. QED. Hope I am correct thou i am no conway. kiki... ^^ HUMAN BRAiN좲APPiNG http://www.math.mcgill.ca/chung |