who wants a lovely desert?!!!

Algebra Level 3

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 2003 2003 ?

1 7 3 6 5 8 2 4

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1 solution

Noel Lo
Mar 31, 2015

Let the number of appetizers be n. We have 3(2n)n = 6 n 2 6n^2 possible dinners. We have 6 n 2 6n^2 > 365 so smallest integral n=8.

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