The late Bernard Scott, founding professor of the Mathematics department of the University of Sussex, had two toys that I remember. One was a pair of pajamas with stripes going down the legs, with the bottoms of the legs sewn together so that the stripes matched up. By pulling the waist-cord tight a torus is obtained, with stripes going round. But when you turn the torus inside out, by loostening the waist-cord and reaching in and pulling and then retightening, you find that the stripes now go round the other way. The other toy was a pair of small solid cylinders. Each weighed the same (easily demonstrated in a balance). Each had the same external dimensions. Each was made from homogeneous material, but one of them was hollow (so it was made of denser material). The student was asked to demonstrate which was hollow by suggesting a physical experiment. The problem was intended to discover whether the student understood the concept of moment of inertia. The answer was to roll both cylinders down an inclined plane and explain the differing behaviours.