The egg drop challenge is not mostly a "shock absorption" exercise; the springiness of the padding around the egg is the determining factor.

If your "padding" is too soft, it will work well until the padding has compressed, and then the egg will experience a large g-force and break. If your padding is too hard, then the egg will break while the padding is being compressed. What is desired is padding that will compress at a rate that gives the egg the longest time to stop. We believe that the best solution is to have increasingly soft padding surrounding the egg in multiple (in our case, 3) layers. Our guess is that firm foam around the egg with softer foam outside of that and still softer foam further outside will give the desired results. It is also imperative that the foam in direct contact with the egg fit the egg's shape as well as possible, to help evenly distribute the forces on the egg. Also, if you can get the egg to fall vertically rather than horizontally it will endure much more force because of the oval shape of the egg. This point is easily demonstrated by the fact that it is very difficult to break an egg in your hand when you apply the forces on the top and bottom of the egg, while it is much easier to break the egg by compressing it's sides. The final point we will make is that the larger your package, the further the egg travels during its stop, thus decreasing the impulse that the egg experiences, so we have done our best to ensure that the container for our egg is as close to 12 cm3 as possible.