Combinatorics Homework
A
Running Total
1.
Building a garden path (see also Exploration 19 #2; p. 196 of
the Cooney et al. book)
- Statement
of problem and description of activity
- A
visual re-presentation of the problem for some number smaller
than P choose 10
- Your
solution path and initial solution
- Class
solution and why it works (i.e., why are the solution numbers
Fibbonacci numbers, P10 = F11 = F10 + F9)... don't be afraid
to search the web for information on Fibbonacci numbers!
- Explanation
of solution in terms of sums of combinations
- Copy
of Pascal's Triangle
- Solution
of the "sum" problem (you can write the results by
hand; I am attaching the file Pascal Sums (or download in rich text
format) case you want to practice your skills with the equation
editor.
2. Coloring squares
- Skim
pp. 167-171
- Exploration
4 # 1 (statement of problem, solution, and brief explanation)
- Read
pp. 171-179 and answer the questions in Exploration 7 (1/2 to
1 page).
3.
Cube nets (see also
Exploration 4 # 3, p. 170 of the Cooney et al. book)
- Problem
statement
- a
visual re-presentation of the 11 possible cube nets
- Choose
one of the nets. Divide each face into four parts and color each
face with four colors so that the colors around each vertex match
(the class experiment)
- Choose
a different net and add the flaps for gluing the faces together
Due: Friday, March
30, 2001; 5:00 p.m.