#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: 4

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER
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1. 
(i) What is the Erdos number?
	The number of hops needed to connect the author of the paer to the mathematician Paul Erdos.   
(ii) What is the Bacon number?
	The number of degrees of seperation an actor has from actor Kevin Bacon.    
(iii) What is the Erdos-Bacon number?
	The sum of a person's Erdo's number and Bacon's number is their Erdos-Bacon number. 
(iv) What is the Erdos-Bacon number of Dr.Z?
	Dr. Z's Erdos-Bacon number is 5

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2. What does it mean for a problem in CS to be NP-Hard?
A2. In computational complexity theory, NP means non-deterministic polynomial. NP hardness means 
    non-deterministic polynomial - time hardness meanind the level of hardness of the problem.

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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 Cycle.
A3. [[1,1],[1,2],[1,4],[1,6],[2,2],[2,3],[2,4],[2,5],[2,6],[3,3],[3,4],[3,6],[4,4],[4,6],[4,5],
    [5,5],[5,6],[6,6]],[{1,2,3,4,5,6},{1,2,3,6,5,4},{1,2,3,4,6,5},{2,3,4,5,6,1},{2,5,4,3,6,1},
    {2,5,6,1,4,3},{2,1,4,5,6,3},{3,4,2,5,6,1},{3,2,1,6,5,4},{3,2,4,1,6,5},{4,3,2,1,6,5},
    {4,5,6,1,2,3},{5,6,1,2,3,4},{5,4,2,3,6,1},{5,4,3,2,1,6},{6,3,2,1,4,5},{6,1,2,3,4,5},
    {6,5,4,3,2,1}]

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4. Using ComboProject1.txt find the first 10 terms of the following the number of 3xn King's 
   tours n=1..10
   In other words use SAW with KiG
A4.  seq(SAW(KiG(3, n)), n = 1 .. 3);
{}, {[1, 3, 5, 6, 4, 2], [1, 3, 6, 5, 4, 2], [1, 4, 5, 6, 3, 2], 

  [1, 4, 6, 5, 3, 2]}, {[1, 4, 5, 7, 8, 9, 6, 3, 2], 

  [1, 4, 7, 5, 8, 9, 6, 3, 2], [1, 4, 7, 5, 9, 8, 6, 3, 2], 

  [1, 4, 7, 8, 5, 9, 6, 3, 2], [1, 4, 7, 8, 6, 9, 5, 3, 2], 

  [1, 4, 7, 8, 9, 5, 3, 6, 2], [1, 4, 7, 8, 9, 5, 6, 3, 2], 

  [1, 4, 7, 8, 9, 6, 3, 5, 2], [1, 4, 7, 8, 9, 6, 5, 3, 2], 

  [1, 4, 8, 7, 5, 9, 6, 3, 2], [1, 5, 3, 6, 9, 8, 7, 4, 2], 

  [1, 5, 4, 7, 8, 9, 6, 3, 2], [1, 5, 7, 4, 8, 9, 6, 3, 2]}


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