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Solution:
7 eggs. The first person bought one half of his eggs plus one half an egg (3 1/2 + 1/2 = 4 eggs) This left him 3 eggs. The second person bought one-half of his eggs plus one half an egg, (1 1/2 + 1/2 = 2 eggs) leaving the man 1 egg. The last person bought one-half of his eggs plus one-half an egg, (1/2 + 1/2 = 1 egg) leaving no eggs.