> #Attendence Q1:
> #Where and when was Herbert S.Wilf born?
;
> #Look up his paper about "random generation of combinatorial objects"
;
> #Advances in Mathsmatics ca, 1980 and at least skim it.
;
> #
;
> #He was born on June 31, 1931.
;
> #Sorry I don't find this book, but find a similar book named ""
;
> 
;
> 
;
> #Attendence Q2:
> #Let m: age of Donald Trump=74
;
> #n:= age of Joe Biden=77
;
> #What is the probability that if you take a random lattice walk from [0,0] to [m,n]
;
> NuGPaths:=proc(m,n) option remember:
> if (m<0 or n<0 or m<n)  then 
> 0:
> elif m=0 and n=0 then
> 1:
> else
> NuGPaths(m-1,n)+NuGPaths(m,n-1):
> fi:
> end:
> G:=NuGPaths(77,74)
Typesetting:-mprintslash([(G := 9212324866083276752554588862297816271201000)],[
9212324866083276752554588862297816271201000])

;
> NuPaths:=proc(m,n) option remember:
> if m<0 or n<0 then 
> 0:
> elif m=0 and n=0 then
> 1:
> else
> NuPaths(m-1,n)+NuPaths(m,n-1):
> fi:
> end:
> F:=NuPaths(77,74)
Typesetting:-mprintslash([(F := 179640334888623896674814482814807417288419500)]
,[179640334888623896674814482814807417288419500])

;
> G/F
2/39

;
> 
;
> 
;
> #Attendence Q3:
> #What is a Wilf-Zeilberger Pair
;
> #Two function F,G form a WZ pair, if 
;
> #F(n+1,k) - F(n,k) = G(n,k+1) - G(n,k), and lim M->infinity G(n,M) = 0
;
> 
;
> 
;
> #Attendence Q4:
> #what nationality was Catalan? What is the constant named after him? 
;
> #French and Belgian
;
> #Catalan's constant: G = 0.915965594177219015054603514932384110774… 
;
> #A6752 in OEIS
;
> 
;
> #Attendence Q5:
> #Do the same for [1,1,-1,-1,1] and get a list 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]}
;
> Paths:=proc(m,n) local S1,S2,s:
> option remember:
> 
> if m<0 or n<0 then
>  RETURN({}):
> fi:
> if m=0 and n=0 then
>  RETURN({[]}):
> fi:
> S1:=Paths(m-1,n):
> S2:= Paths(m,n-1):
> {seq([op(s),1], s in S1)  , seq([op(s),-1], s in S2)  }:
> end:
> 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]}

;
> #Identical
;
> 
;
> #Attendence Q6:
> #If you are in a circular track in the dessert. Ar random places there are gas containers with random amount of gas 
;
> #a1,a2,...,ak
;
> #such that the a1+a2+a3+...+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 exist a location on the circular track such that if you start there, you dont run out of gas.
;
> #Device a method for doing it. 
;
> #Extra credit: write a maple function 
;
> #Prove: Since the amount of gallons of gas is exactly what I need to drive in this track, so let g(i) be the miles that I have for the location i, where i = 0,0.2,0.7 for example
;
> #and so g(0)=0.1, g(0.2)=0.5, and g(0.3)=0.4. For any location where the gas is lower than i needed to get to the next location, this location i=0 cannot be set to a Start location. 
;
> #But for the other location where the gas is equal or larger than the amount of needed gas to get to the next location can be set to Start location.  Since this is a circular location, 
;
> #there must exist at least one locoation which can be set to a Start location. 
;
> 
;