Final_Exam

Final_Exam - ArsDigita University Month 2: Discrete...

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ArsDigita University Month 2: Discrete Mathematics - Professor Shai Simonson Final Examination – 100 points Show all work for partial credit. You may use three hours for this exam. After two hours, raise your hand if you feel that the time constraint will be too tight. Name: ______________________________________________________________ 1. /25 2. /20 3. /20 4. /20 5. /15 Total: /100
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1. Pyramid Numbers (25 points) The Pyramid numbers are the number of balls in a triangular pyramid of height n. P(0) = 0. P(1) =1. P(2) = 1+3 = 4. P(3) = 1+3+ 6 = 10. Think of cannon balls in a pyramid pile. a. Write a recurrence equation for the pyramid numbers. b. Solve this equation and get a closed form for P(n). c. Write down the first 7 or 8 rows of Pascal’s triangle, and use this to find a simple formula in terms of binomial coefficients for P(n). d. Write down a generating function in closed form for the pyramid numbers.
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2. Euclid and Friends? (20 points) a. You have two containers, one of size 45 and one of size 19.
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Final_Exam - ArsDigita University Month 2: Discrete...

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