Let $A =\{a_1<a_2<\dots <a_h\}$ be a set of real numbers. Let $g(A):= \max_{1\leq i\leq h-1} (a_{i+1}-a_i)$ and

$c_n(A):= a_h-a_1- g(nA)$

Prove or disprove: the sequence $\frac{c_n(A)}{n+1}$ is non-increasing always.

UPDATES: worked on by Google's "AI-comathematician" on May 8, 2026. After 20 hours, it tried 2.5 millions example (up to 7 elements and span 50) without finding a counter-example.

(5/14/2026): An interesting conversation about this problem is unfolding on MathOverflow. See the original question and a spin-off.