2 puzzles from Leo Moser, each explained in a minute and credited to the original work. Free on Savvy.
A hallway one unit wide turns a sharp right angle. What is the largest-area two-dimensional shape — the 'sofa' — that can be slid flat around the corner without ever lifting it? Th…
— Leo Moser, Moving furniture through a hallway (Problem 66-11)
Imagine every conceivable curve, straight or wiggly, that is exactly one unit long. Moser's worm problem asks for the smallest-area shape that can be laid down to completely cover …
— Leo Moser, Poorly Formulated Unsolved Problems of Combinatorial Geometry