finalf03

# finalf03 - UNIVERSITY OF WATERLOO FINAL EXAMINATION FALL...

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UNIVERSITY OF WATERLOO FINAL EXAMINATION FALL TERM 2003 Surname: First Name: Id.#: Course Number MATH 239 Course Title Introduction to Combinatorics Instructor Professor Goulden 1:30 a Professor Mosca 2:30 a Professor Schellenberg 1:30 a Professor Verstraete 12:30 a Date of Exam December 13, 2003 Time Period 9 a.m. – 12 Noon Number of Exam Pages 12 pages (including this cover sheet) Exam Type Closed Book ADDITIONAL INSTRUCTIONS: 1. Write your name and Id.# in the blanks above. Put a check mark in the box next to your instructor’s name and lecture time. 2. There are 12 pages to this exam including the cover page. Please be sure you have all 12 pages. 3. Answer each of the problems in the space provided; use the back of the previous page for additional space.

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4. You may only use a non-programmable calculator. Show the reasoning used in any calculation. Problem Value Mark Awarded Problem Value Mark Awarded 1 12 6 15 2 15 7 13 3 10 8 14 4 13 5 8 TOTAL 100
1(a) For fxed positive integers n, k , determine the number o± integer solutions to the [5] equation t 1 + . . . + t k = n , where t 1 2 , . . ., t k 2. (b)

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## This note was uploaded on 07/28/2009 for the course MATH math239 taught by Professor ... during the Spring '06 term at Waterloo.

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finalf03 - UNIVERSITY OF WATERLOO FINAL EXAMINATION FALL...

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