MathDB

Alice and Bob play a game on a sphere which is initially marked with a finite number of points. Alice and Bob then take turns making moves, with Alice going first:
- On Alice’s move, she counts the number of marked points on the sphere,

n

. She then marks another

n + 1

points on the sphere.
- On Bob’s move, he chooses one hemisphere and removes all marked points on that hemisphere, including any marked points on the boundary of the hemisphere.
Can Bob always guarantee that after a finite number of moves, the sphere contains no marked points?
(A hemisphere is the region on a sphere that lies completely on one side of any plane passing through the centre of the sphere.)
proposed by the ICMC Problem Committee

Problem Statement