The Muffin Problem
Guangiqi Cui, John Dickerson, Naveen Durvasula, William Gasarch, Erik, Metz, Jacob Prinz, Naveen Raman, Daniel Smolyak, Sung Hyun Yoo

TL;DR
This paper investigates the Muffin Problem, establishing the existence and computability of the optimal minimum piece size, and providing formulas and methods to approximate or determine it for various cases.
Contribution
It introduces a formal framework for the Muffin Problem, deriving bounds and formulas for the optimal minimum piece, and develops methods to handle exceptional cases.
Findings
f(m,s) exists, is rational, and computable
f(m,s) often equals FC(m,s), with exceptions
Developed formulas and methods for many cases
Abstract
You have muffins and students. You want to divide the muffins into pieces and give the shares to students such that every student has muffins. Find a divide-and-distribute protocol that maximizes the minimum piece. Let be the minimum piece in the optimal protocol. We prove that exists, is rational, and finding it is computable (though possibly difficult). We show that can be derived from ; hence we need only consider . We give a function such that, for , . It is often the case that . More formally, for all , for all but a finite number of , . This leads to a nice formula for , though there are exceptions to it. We give a formula , which has 6 parts, such that for many of the exceptional , . This works…
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