2 problems

Let $m=\Omega(n)$ balls be allocated to $n$ bins in the two-thinning setting, and let the overseer two-thin the allocations. More-balls conjecture. The asymptotically optimal maxim…

Let $n$ bins receive balls in the two-thinning setting, where the overseer may iteratively reject up to $k$ suggested allocations for each ball. More-choice conjecture. The asympto…