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

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

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Physics
Skating on ice is possible because

Ice is cold
The pressure on the ice due to skate raises its melting point
The pressure on the ice due to skate melts the ice by lowering its melting point forming a thin film of water
The surface of ice is smooth

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