Sample Problems

1
Sample Problems

• Teds weekly income is 100.00 less than double
  Garys weekly income. If Ted makes 500.00 a
  week, what does Gary make?
• Paul makes 25.00 a week less than the sum of
  what Fred and Carl together make. Carls weekly
  income would be triple Stevens if he made 50.00
  more a week. Paul makes 285.00 a week and Steven
  makes 75.00 a week. How much does Fred make?

2
Investigation and Argument

• Solving a problem has two phases
• Investigation Find a solution
• Argument Get the solution across to a client
• Too often, we only see the polished argument in a
  book
• Hopefully this course helps you with
  investigation
• But you also have to be good at argument

3
Argument

• Bad argument
• Coercing through force of will or personality
• Irrespective of correctness
• Good argument
• Clear presentation
• Logical progression of steps
• Enough and not too much
• Successful

4
When Do You Argue

• Anytime you write
• Email
• Letters
• Tests
• Homework
• Proposals
• Mechanisms
• Proofs
• Essays, papers, books

5
Chessboard Problem
Problem Completely tile defective chessboard
with dominos
6
Chessboard Problem
Claim Tiling the defective chessboard with
dominos is impossible.
Proof?
Must be a convincing argument
7
First Proof Attempt
There are more black squares than white
squares. Therefore, tiling the defective
chessboard with dominos is impossible.
Why is this not an adequate argument?
8
Second Proof Attempt
Every domino covers one black square and one
white square. The defective chessboard has two
more black squares than white squares. Therefore,
any tiling with dominos will leave at least two
black squares uncovered. We conclude that tiling
the defective chessboard with dominos is
impossible.
Is this an adequate argument?