Let m be the number of muffins, s the number of students, and let f(m,s) be the largest possible size of the smallest assigned muffin piece. Scaling conjecture. For all k,m,s∈N, f(km,ks)=f(m,s). This conjecture is solved; the paper states that it is proved therein, while the second muffin conjecture was previously proved by Cui et al.

Muffin problem scaling conjecture

The conjecture asserts that multiplying both the number of muffins and students by the same positive integer leaves the optimal smallest-piece size unchanged, namely $f(km,ks)=f(m,s)$ . No proposer or original date is identified in the retrieved sources.

July 2019 claimed complete solution

On July 19, 2019, Richard E. Chatwin's paper An Optimal Solution for the Muffin Problem claimed a recursive algorithm that solves every muffin instance and always produces an optimal solution. A 2020 exposition by James Propp explicitly says Chatwin's proof shows that $f(m,s)$ depends only on the ratio $m/s$ , which implies $f(km,ks)=f(m,s)$ .

Current status (as of September 2026): The scaling identity $f(km,ks)=f(m,s)$ is claimed to follow from Chatwin's complete solution, but the retrieved record provides no independent verification, so the claim remains unverified here.

Muffin problem scaling conjecture

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