MathDB

There is a tiger (which is treated as a point) in the plane that is trying to escape. It starts at the origin at time

t = 0

, and moves continuously at some speed

k

. At every positive integer time

t

, you can place one closed unit disk anywhere in the plane, so long as the disk does not intersect the tiger's current position. The tiger is not allowed to move into any previously placed disks (i.e. the disks block the tiger from moving). Note that when you place the disks, you can "see" the tiger (i.e. know where the tiger currently is).
Your goal is to prevent the tiger from escaping to infinity. In other words, you must show there is some radius

R(k)

such that, using your algorithm, it is impossible for a tiger with speed

k

to reach a distance larger than

R(k)

from the origin (where it started).
Find an algorithm for placing disks such that there exists some finite real

R(k)

such that the tiger will never be a distance more than

R(k)

away from the origin.
An algorithm that can trap a tiger of speed

k

will be awarded:
1 pt for

k<0.05

10 pts for

k=0.05

20 pts for

k=0.2

30 pts for

k=0.3

50 pts for

k=1

70 pts for

k=2

80 pts for

k=2.3

85 pts for

k=2.6

90 pts for

k=2.9

100 pts for

k=3.9

Problem Statement