Question 116
Consider a perfectly straight land having a canyon in the form of an infinite strip of width $\omega$. A polyhedron of diameter (maximum distance between any two points on or inside the polyhedron) $d$ is placed on one side of the canyon and a cavity of radius $d$ on the other. We want to roll this polyhedron and drop it inside the cavity in such a way that in any time during its motion, there is at least one contact point between the polyhedron and the ground (unlike the real world, the polyhedron will not fall into the canyon even if it has only one contact point with the ground). To this end, we have constructed a bridge of width $\frac{d}{10}$ over the canyon. Prove that it is possible to drop the polyhedron into the cavity.
