Question 29
Let $n \ge 3$ be an integer, and consider a set of $n$ points in three-dimensional space such that:
(i) every two distinct points are connected by a string which is either red, green, blue, or yellow;
(ii) for every three distinct points, if the three strings between them are not all of the same colour, then they are of three different colours;
(iii) not all the strings have the same colour.
Find the maximum possible value of $n$.
(i) every two distinct points are connected by a string which is either red, green, blue, or yellow;
(ii) for every three distinct points, if the three strings between them are not all of the same colour, then they are of three different colours;
(iii) not all the strings have the same colour.
Find the maximum possible value of $n$.