Moser's Worm Problem

Determine the infimum area of a plane set C that contains a congruent copy of EVERY curve of length 1 (a 'worm'). Best known covers have area ≈ 0.2604; the trivial lower bound is 1/4.

Posed alongside Moser's better-known sofa problem. Gerriets and Poole found an L-shaped 0.286 cover in 1979; successive hand-tuned and computer-searched shapes (Khandhawit–Sriswasdi's clever sector covers; Wang's 2021 refinement toward 0.2604) keep shaving area, while the lower bound has barely moved off the trivial 0.25 since the 1970s. A perfect laboratory for how little we can prove about covering one object with another.