IMC 2022 Problem 4

Let $n > 3$ be an integer. Let $\Omega$ be the set of all triples of distinct elements of $\{1, 2, \ldots , n\}$ . Let $m$ denote the minimal number of colours which suffice to colour $\Omega$ so that whenever $1\leq a<b<c<d \leq n$ , the triples $\{a,b,c\}$ and $\{b,c,d\}$ have different colours. Prove that $\frac{1}{100}\log\log n \leq m \leq100\log \log n$ .