Physics
An egg sinks in soft water but floats in a concentrated solution of salt because

The density of salt solution exceeds the density of eggs
Egg absorbs salt from the solution and expands
Water has high surface tension
Albumin dissolves in salt solution and egg becomes lighter

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Physics
Ice is packed in saw dust because

Saw dust does not stick to the ice.
Saw dust is poor conductor of heat.
Saw dust will not get melted easily.
Saw dust is a good conductor of heat.

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