Mathematics 102

Problem Solving

C. Vinsonhaler

Fall, 2006

Office Hours

C. Vinsonhaler
MSB 316

TTh  9:30 – 10:30, W 9:30-10:30
Phone: 486-3944


Meeting Times

8:00-9:15 PM on Tuesday and Thursday
MSB 215


PProblem SSSolving by DeFranco and Vinsonhaler

Additional References:
    Effective Problem Solving by Marvin Levine.
    Prentice Hall. ISBN 0-13-245481-5.

    Thinking Mathematically by John Mason with Leone Burton & Kaye Stacey.
    Addison-Wesley Publishing Company. ISBN 0-201-10238-2.

General Information

Goals: The basic goal is to foster problem solving skills that can be applied throughout the college experience and the rest of life.

Expectations: First, you are expected to come to class on time. There will be quizzes or exercises during almost every class that count as part of your grade.  In class, we will not be doing much lecturing - you will be working on problems. You are responsible for everything that happens in class. If you miss a class, you are expected to find out what happened, either from me or one of your classmates. Second, you should expect to do some of your learning outside the classroom, generally spending around 6 hours a week working on this class. Problem Solving, like most subjects, is learned by doing it. Third, it is expected that you will get excited about what you are learning and take delight in your own, perhaps unexpected, ability to solve intriguing problems.

Homework: Homework will be assigned, collected and graded each week. Homework is to be done outside of class and we will not devote extensive class time to the discussion of homework problems. Your written work is expected to be neat, accurate and contain written explanations using full sentences and standard English. All work must be shown; an answer without an explanation is not worth any credit. Homework will be graded on the basis of accuracy, presentation and creativity . It is your responsibility to get help if you can't complete an assignment. You can come to my office, work with other students, send me email, or use any reasonable method to figure out how to complete your assignments. No late assignments will be accepted.

Group Projects: You will be assigned projects during the semester to be worked on in groups. One write-up will be submitted for each group. Like homework, projects will be graded on accuracy, creativity and presentation. We will complete some of the projects in class, but frequently additional time outside of class will be required to complete them. Groups may be asked to present their project solutions to the class.


Your grade will be based on quizzes, homework and projects (55%), an exam (15%) and a final (30%).

Assignments (No late work accepted)

  1. Due 8/31     Automathography ,  Read Chapters 1 and 2.
  2. Due 9/5      Sofa variation of Chair Challenge, Use 3,3,7,7 to make 24, Letter on Bean Game 
  3. Due 9/12    Stretches 3,6,7 on page 90 (choose two)
  4. Due 9/19    Stretches 10-12 on page 90 (pick 2), Sandglasses (see PROBLEMS at bottom)
  5. Due 9/26    Stretches 14-16 (pick 2), Achievement Scene
  6. Due 10/3    Friends
  7. Due 10/10  Exam
  8. Due 10/17  Choosing Problems (see PROBLEMS at bottom)      
  9. Due 10/24  Stretches 24, 26, 27, 28 (choose 3), More Candy (see PROBLEMS at bottom)      
  10. Due 10/31  Stretches 39, 42         
  11. Due 11/7    Stretches 36,47,50 (choose 2)  5 style points            
  12. Due 11/14  Stretches 57,63, 3 style points          
  13. Due 11/28  Reflection on three problems from Chapter 7     
  14. Final 12/13




Bean Heaps


Chair Challenge


Changing $.50, Acrobats


20-minute Gamesworth on Chicken Nuggets


Green’s Party, Prom Problem


Grilled Cheese


Cycling Heaps


Memorization – learn rhyme


Changing Places


Chocolates and Mathematical Induction


Handshakes, Candy Conundrum


Review for exam, Mathematical Induction




Choosing Two worksheet


Commuter, Telescoping Sums


Telescoping sums (induction), Forty Thieves


 Twenty Unfaithful Husbands


 Twenty Unfaithful Husbands (revisited)


 Cryptarithmetic 1-6, Sudoku


 Grandfather, Faculty Debts


 House Hunt, p.97 - 41


 Should You Switch?


 Light Switches, Checkerboard Chase


 Multiple Locks, Jumping Frogs, Dating Service (plan of attack)


 Multiple Locks, Jumping Frogs, Dating Service (complete)

Review Topics for First Exam

Stretches 1-18, Acrobats, Bean game, Changing Places, Changing $.50, Chocolates, Green Party, Handshakes, Prom Problem, Gamesworth, PSSSP Strategies and other material from book.

Review Topics for Final

First Exam material: Bean game, Chocolates, Green Party, Handshakes, All Stretches, Two Bean Heaps, Cryptarithmetic, Twenty Unfaithful Husbands, Commuter, Forty Thieves, Faculty Debts, Jumping Frogs, Multiple Locks, Should You Switch? Checkerboard Chase, PSSSP Strategies and subheadings, Choosing Problems, Tower of Hanoi, induction (11 points).

Practice Final




Exam 1 


Final Exam 


Remember that no make-up exams will be given.

Problems for Solving

Sandglasses. You have two sandglasses, one that measures 9 minutes and the other 13. You want to boil a stew for exactly 30 minutes. Can you do this if you must turn over the glass(es) for the first time just as the stew starts to boil?


Choosing Problems. (a) Calculate C(6,2) and C(17,2). (b) How many ways to choose a committee of 2 from 11 people?  (c) Calculate C(7,3) and C(8,3). (d) Calculate C(6,4), C(6,5) and C(6,6).


More Candy. How many ways can 10 identical pieces of candy be divided among three people, if it is possible to give no candy to a person (or two). What does the answer have to do with choosing problems?


Bonus Problem:  Show that the tetrominoes S and Z can form a common region.

Problems posed by C. Vinsonhaler.

Problems posed by A. Stein.


Last modified September, 2006 by Charles Vinsonhaler <vinsonhaler@math.uconn.edu> .

[COMMENTS] to Professor Vinsonhaler.