A restaurant offers three deserts, 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 a restaurant should offer so that a customer could have a different dinner each night in the year
?
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Let the number of appetizers be n. We have 3(2n)n = 6 n 2 possible dinners. We have 6 n 2 > 365 so smallest integral n=8.