A really cool looking and easy way to do this is with either normal printer paper or with straws.
Roll the paper or use straws to make the edges for an open 8x8x8 cube.
Secure corners with masking tape.
Make a smaller cube with rolled paper or straws to hold the egg.
Wrap egg in tissue paper to make it fit better into the small cube.
From the corners of each cube, place an S Shaped paperclip ("open" the paper clip to an S shape)
From each clip then place a small rubber band. Band should be small enough to be pulled tight at the distance, but not near breaking.
all in all, it should look vaugly something like this:
Code:
_______
|\ /|
| \___/ |
| |EGG| |
| /ŻŻŻ\ |
|/ \|
ŻŻŻŻŻŻŻ
The rubber bands create a pretty good quality suspension sytem, preventing th egg from ever feeling the full force of the impact with the ground.
Works great if part of the challange is speed of drop. (Parachutes = Slower)