1. Suppose you have a yam with n-1 cuts. Carefully slice the yam in two and look at the freshly cut faces. What do you see? Does this explain any earlier observations you made? A laser cutter will cut through just about anything. It might even be able to cut a k-dimensional vegetable such as a hyper beet. Consider this situation if you dare . . . .
2. Suppose you want the maximum number of hyper beet pieces to result from making n cuts. What properties should your sets of cuts have in order to obtain the maximum number of hyper beet pieces?