Well frankly, as a aero/mech engineer I'd definitely pull out the UTM and the aero chamber. Your vice grip isn't going to be enough. [For those wondering, first

Well frankly, as a aero/mech engineer I'd definitely pull out the UTM and the aero chamber. Your vice grip isn't going to be enough. [For those wondering, first the aero chamber to determine Cd and terminal velocity. Then the UTM be used to determine the compressive strength.] After that I'd scan the other egg in a 3D scanner and generate a super accurately detailed model. Once the model is ready, it's just a matter of plugging these values into Ansys explicit dynamics or Comsol multiphysics and find out the exact height at which the egg will break. Granted, you might require a bunch of the world's fastest super computer clusters and a few days to solve this problem, but hey you have a very high accuracy and precision. [Probably +_ 1cm even]. But yeah, since the author has stated it's a math problem we've just left it as a thought experiment.