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Question

A restaurant offers three desserts, and exactly twice as many appetizers as main courses. A dinner consists of an appetizer, a main course, and a dessert. What is the least number of main courses that the restaurant should offer so that a customer could have a different dinner each night in the year 2003?

Accepted Answer

Let m denote the number of main courses needed to meet the requirement. Then the number of dinners available is 3 m 2m = 6m^2. Thus m^2 must be at least 365/6 61. Since 7^2 = 49<61<64 = 8^2, 8 main courses is enough, but 7 is not.