Let n>3 be an integer. Let Ω be the set of all triples of distinct elements of
{1,2,…,n}. Let m denote the minimal number of colours which suffice to colour Ω so that whenever
1≤a<b<c<d≤n, the triples {a,b,c} and {b,c,d} have different colours. Prove that 1001loglogn≤m≤100loglogn. logarithmscombinatoricsSetsgraph colouringcollege contestsIMC 2022