Given n pancakes, for each permutation we can compute the minimum number of pancake flips.  If we take the maximum over all possible permutations, we get the worst case pancake number $P_n$.I think I can prove that $P_n \geq n$.  My argument is that I can start from the sorted pancake, and do a anti-sorting of the pancake by first flipping at position n, then position at n-1, n-2, etc.For example, the case of n=5 would yield 34251.Sorting such a pancake would take at best n steps.Am I doing something wrong?
Lower bound on worst case pancake number?
sorting;lower bounds