Question 74
Let $n \geqslant 1$ be a strictly positive integer. On a wall, $n$ nails are hammered in. Each pair of nails is connected by a rope coloured with one of $n$ colours. We say that the wall is coloured if for every triple of pairwise distinct colours $a, b, c$, there exist three nails such that the three ropes connecting these nails have colours $a, b$ and $c$.
- Does there exist a coloured wall for $n=6$?
- Does there exist a coloured wall for $n=7$?
- Does there exist a coloured wall for $n=6$?
- Does there exist a coloured wall for $n=7$?