MidtermA-SOLUTIONS.pdf - Introduction to Combinatorics MATHC44 Midterm\u2013A University of Toronto Scarborough Instructor Stefanos Aretakis Last Name

# MidtermA-SOLUTIONS.pdf - Introduction to Combinatorics...

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Introduction to Combinatorics MATHC44 Midterm–A University of Toronto, Scarborough Instructor: Stefanos Aretakis February 14, 2018 Last Name: First Name: Student #: Instructions: Duration: 2 hours Do not turn this page and start the exam until you are told to do so. Please do not make use of personal notes, computers or books. No aids are allowed. Provide a solution to all of the seven problems in pages 2–8. Write your solution only on the designated space. You might request extra paper for your draft, but this will not be graded. Maximum points 100 (Problem 1 is worth 16 points and each other problem is worth 14 points). Good Luck! 1
Problem 1. (16 points) Early in the morning of January 31 there was a rare eclipse of a full moon which was also a blue moon . A blue moon happens when there are two full moons in the same calendar month. Prove that there must be a blue moon every 2.71 years. [Every year has 365 days and 12 calendar months. A full moon happens every 29 days.] Solution (please write your answer in the space below only).

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