Archimedes' Principle relates the weight of a fluid displaced to the object placed in the fluid. If the weight of the fluid displaced is less than the object's weight ,then the object sinks. When the weights of the object and displaced water are equal, the object will float.
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When a body is immersed fully or partially in a fluid, it experiences an upward force that is equal to the weight of the fluid displaced and this is known as archimedes' principle.
The pigeonhole principle is merely the following observation - "If we are to place N balls into M boxes where N > M, at least one box will contain at least two balls." A generalized version of the pigeonhole principle says that if we place at least nk + 1 balls into n boxes, then at least one box will contain at least k+1 balls. I say "at least" a lot because these numbers are arbitrary and lower bounds.
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