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A Nose That Grows

Every time a man lies his nose grows to 150 percent of its size. Every time he tells the truth it shrinks to 50 percent of its size.

What will happen if he alternates between lies and the truth
For every pair of a truth and a lie his nose will shrink to 75 percent of its previous size prior to this truth and lie. So the correct answer is 0. As the number of times he tells a lie and the truth ((3/4)n) approaches infinity the length of his nose approaches 0.
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