#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: p14
#with an attachment called
#p14FirstLast.txt
#(e.g. p14DoronZeilberger.txt)

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


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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

1. Where and when was Herbert S. Wilf born?
1931 in Philadelphia, PA

2. Let m:= age of Donald Trump, n:= Age of Joe Biden
What is the probability that if you take a random lattice talk from [0,0] to [n,m] you will anways stay in the region x>=y?
m = 74, n = 77
NuGPaths(77, 74) = 9212324866083276752554588862297816271201000

3. What is a Wilf-Zeilberger pair?
A Wilf-Zeilberger pair is a pair of functions that can be used to certify certain combinatorial identities.

4. What nationality was Catalan? What is the constant named after him?
French and Belgian 
Catalan's constant, G

5. Do the same for [1,1,-1,-1,1] and get a set of 10 such lists that is the whole of Paths(3,2).
{[1, -1, 1, -1, 1], [1, -1, 1, 1, -1], [1, 1, -1, -1, 1], [1, 1, -1, 1, -1], [1, 1, 1, -1, -1]}

6. You are in a circular track in the desert. At random places there are gas containers with random amounts of gas a1,a2,...,ak such that the a1+a2+...+ak gallons are exactly what you need to drive in this track
{[0, 1.1], [0.2, 0.5], [0.7, 0.4]}
Prove that there exists a location on the circular track such that if you start there you don't run out of gas.
Devise a method for doing it.