Meanie Genie, Fountain of Knowledge, Dodge Ball.
You should be familiar with these problems and their solutions.
(Note that complete solutions to each are presented in Sections 1.2 and 1.3.)
You may be asked to work on a problem that is similar to these.
Similar might mean only a small change (different sizes of cups in
Fountain of Knowledge), or a problem that can be solved using
similar thinking (like Cannibals and Missionaries).
The homework problems assigned from Chapter 1 give examples
of the types of problem solving activities you might see.
If I were to give you a problem solving task that you cannot solve,
be sure to show the work you do in a reasonably coherent manner, since
it is possible to get significant credit without actually solving the problem
if you show that you were using reasonable methods to attack the problem.
Locker problem.
You should have a good understanding of the solution to this
problem, including things like: relationship to factoring (divisors),
relationship to square numbers, relationship between square numbers
and the pattern of runs of closed lockers, facts that can be learned
from a round by round approach
Section 2.1: Counting
Pigeon-hole principle (sock hop problem, for example).
Making reasonable estimates (and knowing if they are too big or too small).
Section 2.2: Numerical Patterns in Nature
How Fibonacci sequence works.
Where Fibonacci sequence shows up in nature.
Relationship between golden ratio (j) and Fibonacci numbers.
Section 2.3: Prime Numbers
Definition of prime number, factor, divisor, multiple, remainder
Geometric interpretation of multiplication and remainders
(rectangular arrays).
Every number can be written as a product of prime numbers multplied together.
(Why?, How?)
Finding/recognizing prime numbers.
Sieve of Eratosthenes. Time saving observations when trying to
prove a number is prime. How to find a prime number larger than
any specified number and the proof that there is no largest prime
number.