Cutting a Melon
Source: Tournament of Towns Fall 2015 Senior A - level
February 23, 2017
combinatorics
Problem Statement
Basil has a melon in a shape of a ball, in diameter. Using a long knife, Basil makes three mutually perpendicular cuts. Each cut carves a circular segment in a plane of the cut, deep ( is a height of the segment). Does it necessarily follow that the melon breaks into two or more pieces if
(a) ? (6 points)
(b) ? (6 points)