#ATTENDANCE QUIZ FOR LECTURE 15 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p15
#with an attachment called
#p15FirstLast.txt
#(e.g. p15DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 27, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

#attendance problem 1

#i)what is erdos number?
#ii)what a the bacon number
#iii)what is the erdos-bacon number
#iv)what is the erdos-bacon number of doctor z

#answer
#i)The Erd?s number is the number of "hops" needed to connect the author of a paper with the prolific late mathematician Paul Erd?s.

#ii)Originated from six degrees of kevin bacon, Bacon number of an actor or actress is the number of degrees of separation from kevin Bacon.

#iiiA person's Erd?s?Bacon number is the sum of one's Erd?s number?which measures the "collaborative distance" in authoring academic papers between that person and Hungarian mathematician Paul Erd?s?and one's Bacon number?which represents the number of links, through roles in films, by which the person is separated from American actor Kevin Bacon.

#iv)Professor has 2 as erdos number because he is a coauther of 4 coauthers with Erdos(CANFIELD, EARL RODNEY, GILLIS, JOSEPH E,JANSON, SVANTE,REZNICK, BRUCE ARIE)
#moreover, professor has 3 bacon number because he stated that in his website lolol
#1.Doron Zeilberger and Steven Berkoff both appeared in To Infinity and Beyond (in the BBC Horizon documentary)
#2.Steven Berkoff and Duncan J. C Mayers both appeared in The Rapture
#3.Duncan J. C Mayers and Kevin Bacon both appeared in The X-Men: First Class

#so total his erdos-bacon number is 5, like it is revealed in wikipedia

######################################################################################

#attendance question 2

#what does it mean for a problem in cs to be np-hard?

#answer: NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally "at least as hard as the hardest problems in NP"
#in other words, A decision problem H is NP-hard when for every problem L in NP, there is a polynomial-time many-one reduction from L to H.


#######################################################################################

#attendance problem #3

#cook-up a graph with 6 vertices called 1,2,3,4,5,6
#with 12 edges that you know for sure has a hamiltonian

#answer: if it has 12 edge, we can easily think of the 6 vertices graph corresponding with hexagon.
#then G:=[{2,3,4,5,6},{1,3,5},{1,2,4,5,6},{1,3,5},{1,2,3,4,6},{1,3,6}]

#this is not a complete graph but has 12 edge

#hamiltonian cycle that uses all 6 vertices would be 1-2-3-4-5-6-1

########################################################################################

#attendance probem #4.

#using ComboProject1.txt, find the first ten terms of the following sequence
#the number of 3xn King's Tours n=1..10

#in other words use SAW with KiG

#to get the number of king's tours we use KiG to plot the king's graph and put it in SAWnu to get the total number of hamiltonian paths

#so each i, we are finding SAWnu(KiG(3,i)) from 1 to 10

seq(SAWnu(KiG(3,i)),i=0..10)
#it would stop at i=9, so lets look for sequence

SAWnu(KiG(3, 1));
                               0
SAWnu(KiG(3, 2));
                               8
SAWnu(KiG(3, 3));
                               32
SAWnu(KiG(3, 4));
                              240
SAWnu(KiG(3, 5));
                              1488
SAWnu(KiG(3, 6));
                              9844
SAWnu(KiG(3, 7));
                             63808
SAWnu(KiG(3, 8));
                             416236

seq till 8th term is 0,8,32,240,1488,9844,63808,416236

#as far as my computer lets me, this is the possible compiled result till the 8th term.