The Burnt Pancake Problem
Python 2, 83
Input is expected to be the list of (size, orientation) tuples with the stack's top at the end. The output is a list of sizes to flip separated by various kinds of whitespace.

a=input()
while a:i=a.index(max(a));print len(a)-i,a[i][1],len(a),i;a=a[i+1:]+a[:i]