MA 310 Homework #1
Solutions
The Game of 100. Consider the positive integers that are congruent to 2 mod 7; i.e., those
for which the remainder is 2 when divided by 7. Call these integers key positions. Note
that the goal position 100 is itself a key posi
Final Exam Review
1. Review Log of Class Activities from Wednesday, February 27, through Friday, April
26.
2. Review Homework #7 and #8 and the solutions.
3. Review Exam #3.
4. Be able to do all of the problems that we did in class, for homework, and for
MA 310 Exam #3
Due Monday, April 8, in class
This is a take-home exam assignment. You may consult with other class members and
with me.
You are to personally nd real-world examples to illustrate 16 dierent symmetry types.
Read the Log of Class Activities
MA 310 Exam #1
Solutions
1. One of Polyas pieces of advice is, If you cannot solve the proposed problem try to solve
rst some related problem. Could you imagine a more accessible related problem?
Write a few sentences describing a time when you used this
MA 310 Homework #2
Solutions
1. Short answer only; do not provide justication (though, of course, you should be able
to if asked).
(a) If two people are playing a game like the Game of 100, but this time the goal
number is 1, 000, 000 and you are allowed
MA 310 Homework #4
Solutions
1. Solve Planar Clusters parts (3) and (4).
Solution (3): Recall or reconstruct the formula for the measure of the interior angle
n
of a regular n-gon: 180(n 2) . Then systematically consider triples a, b, c, a b c,
where a, b
MA 310 Homework #7
Solutions
1. Solve Piano Tuning.
Solution. The piano is tuned according to a geometric sequence. From C4 to C5 the
frequencies are a, ar, ar2 , . . . , ar12 . C5 has twice the frequency as C4, so ar12 = 2a.
Then r12 = 2, so r = 21/12 1.
MA 310 Homework #8
Solutions
1. Solve Complex Numbers and Transformations #9, 11, 13.
9. Reect across the line y = a:
Translate by (0, a) using f1 (z ) = z ai, then reect across the x-axis using
f2 (z ) = z , then translate back by (0, a) using f3 (z ) =
MA 310 Homework #6
Solutions
1. Solve Five Houses. For this problem, you do not have to explain all of the steps in
your reasoning, but simply provide a nal list of the houses, indicating for each the
color, nationality, pet, drink, and food.
Solution:
Ho
Exam #1 Review
1. Review Notes, sections (1) and (5.4).
2. Review Log of Class Activities through Friday, February 1.
3. Review Homework #1 through #4 and the solutions.
4. Be able to do all of the problems that we did in class and for homework. The expla
MA 310 Homework #3
Solutions
1. Prove that the number z in Animal Colors must always be 1089.
Solution: Let the starting number x have digits abc, with c < a. Its reversal is cba.
Because a is greater than c, we must regroup within x to get digits a, b 1,