#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:6

#attendance question 1
#where and when was Herbert S. Wilf born
#answer:He was born in Philadelphia on June 13, 1931.

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#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
#Answer: 
m:=74
n:=77
NuGPaths(77, 74)
9212324866083276752554588862297816271201000
NuPaths(77, 74)
179640334888623896674814482814807417288419500
%%/%
2/39

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#attendance question 3
#What is Wilf-zelberger pair?
#Answer: Wilf?Zeilberger pair, or WZ pair, is a pair of functions that can be used to certify certain combinatorial identities.



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#attendance question 4
#What nationality was catalan? what is the constant named after him
#answer: 
#Eugene Charles Catalan had both Belgium and France nationalities.
#Catalan's constant G, which appears in combinatorics, is defined by

Sum((-1)^n/(2n+1)^3,k=0..)

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#attendance question 5
#Do the same for [1,1,-1,-1,1] and get a set of 10 such lists
#manually,
[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], [1,-1,-1,1,1]

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], [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]}

#probably the same

#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
#[[0,0.1],[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
#device a method for doing it