I won ours using a very similar design: we were given a couple of sheets of paper and some tape. I rolled one of the sheets of paper into a tube the diameter of the egg, and placed the egg snugly near the bottom end of the tube so that it would have a low center of mass. I softly crumpled the other piece of paper into a small cylinder the diameter of the tube, and placed it under the egg in the tube to be used as cushioning.

I was honestly surprised to see that such little cushioning helped it survive three 2 m drops, although it did get a hairline crack after the third drop!