Question 33
In the plane let S consist of points (x,y) with x,y∈{1,2,...,2013}. Two points of S are neighbors if their distance is 1. Each second a fly and spiders move on S as follows: first the fly either stays or moves to a neighboring point; then each spider either stays or moves to a neighboring point. Several spiders may occupy the same point, and the fly and spiders know all their positions.
a) Find the smallest integer k such that k spiders can always eventually catch the fly in finite time, regardless of all initial positions.
b) Answer the same question in ordinary space, where S consists of (x,y,z) with x,y,z∈{1,2,...,2013}.
a) Find the smallest integer k such that k spiders can always eventually catch the fly in finite time, regardless of all initial positions.
b) Answer the same question in ordinary space, where S consists of (x,y,z) with x,y,z∈{1,2,...,2013}.