The Intrepid Waitress Problem

An intrepid waitress leaves a restaurant kitchen with a stack of n different sized pancakes. Before she reaches her patrons, she wishes to iterate through all possible stack orderings using only a spatula and performing flips of various sizes. But is this possible? This problem corresponds to constructing a Hamilton path in the “pancake network”, or equivalently, to find a Gray code for permutations where successive permutations differ by a prefix-reversal. We describe two such orderings based on a greedy approach. Simple recursive formulations are provided along with an analysis of the flip sequences which can easily be generated by a loopless algorithm. Additionally, we provide similar results for signed permutations. As an application, we apply the greedy approaches to a shared resource problem on both the pancake network and the burnt pancake network.