#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
#Attendance Question 1
#where and when was Herbert S. Wilf born?
#Look up his paper about "random generation of combinatorial objects"
#Advances in Mathematics ca. 1980 and at least skim it.
#Attendance Answer 1
#Herbert S. Wilf was born in Philadelphia, PA on June 13, 1931.

#Attendance Question 2
#Let m:= Age of Donald Trump 
#n:=Age of Joe Biden 
#What is the probability that if you take a random lattice walk from [0.0] to [n,m] you will always stay in the region x>=y
#Attendance answer 2
#[77,74]
#the probability is 322/4224

#Attendance Question 3
#What is a Wilf-Zeilberger Pair
#Attendance Answer 3
#A pair of functions that can be used to certify certain combinatorial identities.
#Used in the evaluation of many sums involving binomial coefficients, factorials, and in general any hypergeometric series.

#Attendance Question 4
#What nationality was Catalan? What is the constant named after him?
#Attendance Answer 4
#Eugene Charles Catalan was French and Belgian.
#Catalan's constant is the Dirichlet beta function at 2 
#Approximately 0.915965594177219

#Attendance Question 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)
#Answer Question 6
#[-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]
#[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]

#Last Attendance Question
#You are in a circular track in the desert. At random
#places there are gas containers with random amounts of gasoline
#a1,a2,...,ak
#such that the a1+a2+...+ak gallons are exactly what you need
#to drive in this track
#[[0,0.1],[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
#Answer question 6
#all the gasoline on the track adds up to the full mile needed to travel 
#all the distances from each point also adds up to a mile
# if at one point if there are only two points in the track such that 
#the first point is [x1,y] then the second point must be [x2,1-y]
#if y<x2-x1 then 1-y must be greater and therefore would be enough
#to get you to x1 from x2