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Nice try - but the original question doesn't state the egg has to be a chicken-egg, just "the egg".

Eggs were laid long before birds even evolved. If that's the criteria then the question becomes much easier to answer.

But a bird's heavier than feathers.

But when birds of a feather flock together, many hands make light work.

And it's known that a bird in many hands is just a gross bunch of fleshy bits with feathers sticking out.