6 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…

Pálvölgyi's conjecture. For each $j$ such that $a_j$ is not divisible by $q$, it is possible to decide which thieves get $\lfloor a_j/q\rfloor$ and which get $\lceil a_j/q\rceil$ a…

Let an open necklace have $q$ types of beads, with the number of beads of each type divisible by $k$, and let a $k$-splitting divide the necklace among $k$ thieves so that every th…

Two-part necklace coloring conjecture. For $q=2$, this bound is tight.

Let $d,k,t\geq 1$, and let a measurable $k$-coloring of $\mathbb{R}^d$ assign one of $k$ colors to each point. A $d$-dimensional necklace is a measurable object in $\mathbb{R}^d$,…