Abstract of  Tetrahedron ABCD of Width 1 with Minimum AB+BC+CD :  A woodborer, freshly hatched at a random point within a slab of timber of unit thickness, wants to tunnel its way out by making at most two changes in its randomly chosen initial direction, in such a way that the worst case distance is minimized. What strategy does it adopt?  We present the solution of this problem, also partial results about the analogous higher-dimensional problems.