2 problems

Binary necklace-splitting conjecture. Given a necklace with $n$ kinds of beads and $r\geq 4$ thieves, there exists a binary necklace splitting of size $(r-1)n$.

Equitable distribution conjecture. It should be possible to cut at most $(r-1)m$ cookies and distribute them so that each child has the same amount of each kind of frosting and at…