#ATTENDANCE QUIZ FOR LECTURE 14 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p6
#with an attachment called
#p6FirstLast.txt
#(e.g. p6DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Sept. 24, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:6

Attendance problem 1 - Where and when was Herbert Wilf born? Look up his paper about random generation of combinatorial objects. Advances in Math ca. 1980 and at least skim it. 
Answer: He was born in 1931

Attendance problem 2 - Let m - Age of Donald Trump, n = Joe Biden, What is the probability from the origin from [0,0] to [n,m] you will always stay in the region x>=y

Answer: m = 74 n = 77
9212324866083276752554588862297816271201000

Attendace problem 3: What is the Wilf-Zeilberger pair?

Answer: a Wilf–Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities. WZ pairs are named after Herbert S. Wilf and Doron Zeilberger, and are instrumental in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series. A function's WZ counterpart may be used to find an equivalent and much simpler sum. Although finding WZ pairs by hand is impractical in most cases, Gosper's algorithm provides a sure method to find a function's WZ counterpart, and can be implemented in a symbolic manipulation program.

Attendance problem 4: What nationality was catalan? What is the constant named after him?

Answer: Belgian, Cassini's identity

Attendance problem 5: Do the same for the other [1, 1, -1, -1, 1] and get a set of 10 such lists that is the whole of Path(3, 2)

Answer: Confirmed using maple and hand, they're the same

Attendace problem 6
You are in a circular track in the desert at random places there are gas containers with random amounts of gas
#a1, a2, a3, a4,..., ak
Such that a1+a2+a3+a4+...+ak gallons are exactly what you need to drive thistrack 
Prove that there exists a location on the circular track such that you can drive the whole track

Answer 6: We use induction to prove this
for n = 1, it is pretty trivial, you just start at the gas tank
for n = 2 since a1+a2 = 1 (for generality the distance for the track is 1) the corresponding segments on x1+x2 =1. We must have a1>y1 or a2>y2. If x1>y1 then we start at can 1 otehrwise start at can 2. 

Now the inductive step
We have a1+a2+a3+a4..an = 1