#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

#Q1: 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.

	#A: Herbert S. Wilf was born june 13 1931.

#Q2 (38:18): let m:= Age of donald Trump = 74
     let n:= Age of Joe Biden = 77
	#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

	#A:2/39

#Q3: What is a Wilf-zeilberger pair?

	#A: is a pair of functions that can be used to certify certain combinatorial identites (wikipedia).

#Q4: What nationality was Catalan? What is the constant named after him?

	#A: Catalan was Belgian-french. Catalan's constant (G) is equal to (pi)^3/32

#Q5(1:09:38): Do the same [1,1,-1,-1,1] and get a set of 10 suchy lists that is the whole of paths(3,2)

	#A: {[-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]}

#Q6: 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 sum of a1->ak gallons are
     what you need to drive 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.

	#A:{[[0, 0.1000000000], [0.2000000000, 0.5000000000], [0.7000000000, 0.4000000000]], [[0.2000000000, 0.5000000000], [0.7000000000, 0.4000000000], [0, 0.1000000000]], [[0.7000000000, 0.4000000000], [0, 0.1000000000], [0.2000000000, 0.5000000000]]}