2021 WSMO Team Round Problems/Problem 8

Problem

Isaac, Gottfried, Carl, Euclid, Albert, Srinivasa, René, Adihaya, and Euler sit around a round table (not necessarily in that order). Then, Hypatia takes a seat. There are possible seatings where Euler doesn't sit next to Hypatia and Isaac doesn't sit next to Gottfried, where is maximized. Find . (Rotations are not distinct, but reflections are).

Proposed by mahaler