  We analyze the problem solving strategies of physics professors in a case
where their physical intuition fails. A non-intuitive introductory-level
problem was identified and posed to twenty physics professors. The problem
placed the professors in a situation often encountered by students, and their
response highlights the importance of intuition and experience in problem
solving. While professors had difficulty in solving the problem under the time
constraint, they initially employed a systematic approach, e.g., visualizing
the problem, considering various conservation laws, and examining limiting
cases. After finding that familiar techniques were not fruitful, they made
incorrect predictions based on one of two equally important factors. By
contrast, other more familiar problems that require the consideration of two
important principles (e.g., conservation of both energy and momentum for a
ballistic pendulum) are quickly solved by the same professors. The responses of
students who were given the same problem reflected no overarching strategies or
systematic approaches, and a much wider variety of incorrect responses were
given. This investigation highlights the importance of teaching effective
problem solving heuristics, and suggests that instructors assess the difficulty
of a problem from the perspective of beginning students.
