#ATTENDANCE QUIZ FOR LECTURE 13 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p13
#with an attachment called
#p13FirstLast.txt
#(e.g. p13DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 20, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER

1) Describe the problem that Euler solved regarding 7 bridges

The problem is about the city of Konigsberg in Germany, which had seven bridges. People asked Euler to figure out if there was a way to cross all of the bridges exactly once. He figured out that it was not possible, and this is how he started the field of graph theory.

2) Draw it on a piece of paper with a line segment representing every edge
V={1,2,3,4}
G=[{2,3},{1,3,4},{1,2,4},{2,3}]

***Picture is separate from this txt file***

3) If you toss a fair coin 2000 times what is the probability that you get exactly 1000 heads (and exactly 1000 tails)

(2000 Choose 1000)/2^2000 = 2000!/(1000!1000!2^2000) - This is really small

4) If you roll a fair die 6000 times what is the probability that each of the possible outcomes {1,2,3,4,5,6} occurs exactly 1000 times

(6000 Choose 1000) * (5000 Choose 1000) * (4000 Choose 1000) * (3000 Choose 1000) *  (2000 Choose 1000) / 6^6000 - Yeah it is really small

I wasn't sure if I was supposed to use one of the Maple code functions for 3 & 4? it doesn't seem like it.

5)Pick 5 random facebook friends
For each of them pick 3 friends
For each of the friends of friends pick 3 friends

Label the people picked 1,2,...n
Write the graph in our data structure

I will use initials to safeguard their privacy.

DC 1
RS 
JY 
BL 
KW 
VF 
BV 
WS 
AL
KZ
WK 
VSO 
GB 2

JC 3

VF 4

SD 5

I don't think I can actually do this one, it is too tedious. There will 5*3*3=45 people and I have to check friendships between all of them which will take 45*45=2025 comparisons. 

6) Look at the cities that border piscataway
And for each of them those that border them
and again until you get to princeton

(i) construct the graph
(ii) Find the number of paths from piscataway to princeton
(a) find the actual set using paths (and list them)
(b) by using nuPaths
(c) using GFt