Smallest limited snakes

A (topological) disk is a subset of the euclidean plane homeomorphic to the unit ball. If two disks have a common interior point then we say that the disks overlap. A sequence C = 〈C1, . . . , Cn〉 of mutually non overlapping congruent disks where Ci ∩ C j = ∅ if and only if |i − j | ≤ 1 is called a snake. If the snake C is not a proper subset of another snake of disks congruent to the members of C then we say that the snake is limited. We are concerned with the following question: What is the minimum number of mutually non overlapping congruent disks which can form a limited snake? Here we prove