MathDB

\mathbb{R}^3

some

n

points are coloured. In every step, if four coloured points lie on the same line, Vojtěch can colour any other point on this line. He observes that he can colour any point

P \in \mathbb{R}^3

in a finite number of steps (possibly depending on

P

). Find the minimal value of

n

for which this could happen.

Problem Statement