> #Attendence quiz 14
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> #THE NUMBER OF ATTENDANCE QUESTIONS WERE: 6
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> 
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> #Q1
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> #Where and when was Herbert S. Wilf born? Look up his paper about "random generation of combinatorial objects." 
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> # Herbert S. Wilf was born on June 13, 1931 in Philadelphia
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> 
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> #Q2
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> #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. 

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> #Trump 74 yrs old and Biden 77 yrs old so 
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> m:=74
m := 74
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> n:=77
n := 77
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> #NuGPaths(77,74) = 9212324866083276752554588862297816271201000
> #NuPaths(77, 74) = 179640334888623896674814482814807417288419500
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> #%%/% = 2/39
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> 
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> #Q3
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> #What is Wilf-zelberger pair?
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> #It is a pair of functions that can be used to certify combinatorial identities. 

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> #Q4
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> #What nationality was Catalan? What is the constant named after him? 
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> #Catalan is French and Belgian.
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> #Catalan's constant is G = 0.915965594177219015054603514932384110774...
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> 
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> #Q5
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> #Do the same for the other [1, 1, -1, -1, 1] and get a set of 10 such lists that is the whole of Path(3, 2)
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> #[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]}
> #OVERALL {[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]}
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> 
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> #Q6
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> #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 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 it.
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> 
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> #
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