I have conducted a feasibility study and determined that such an experiment would be prohibitively expensive in both time and eggs:

situation 1: Imposible to ballance egg. I spend all day and night from now to Dec 22 holding the darn thing up.

situation 2: Egg ballances temporarily. Egg falls over, rolls downhill and I have to clean the mess up off the floor . Then I have to start over. It' 22 days to Dec 22 - that's at lesat 22 eggs and lord knows how many paper towels

Situation 3: Egg ballances. Kids, wife, or dogs get rambunctious in the Kitc... er lab. egg falls over. See situation 2\

Situation 4: Superglue the egg to the counter. Egg never falls over. Egg goes bad. egg cracks from a wandering graviton storm. Wife divorces experimenter because she can't get the smell out of the house.

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May you have a more understanding lab partner