Given a necklace with $d$ types of beads and $p$ people it is well known we can fairly divide the necklace with at most $d(p-1)$ cuts. I am curious if it is known which necklaces require $d(p-1)$ cuts. I cannot seem to find it in any of the literature but maybe one of you is aware of this result. Clearly a necklace which groups all of the beads of a type together will require the maximum number of cuts. You can also vary this idea and repeat a necklace of this type a specific number of times based on $p$. Is this it?