#Please do not post homework
#Ravali Bommanaboina, 10/25/20, Assignment 13

#Question 1
#{1,2,3,4,5,6,7,8,9}
#A:={r,v,l,b,m,n,a,i,o}
# The list A above shows the letters in my full name with a number assigned to it. For example r=1 v=2 and so on.
#L:=[{7,8,9},{7,8,9},{7,8,9},{7,8,9},{7,8,9},{7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9}]
#The graph L represented above represents all the neighbors of each letter in A where no two consonants can be neighbors.
#To compute the total number of paths I used the function NuPaths and computed all possible paths starting and ending at any two letters using L.
#B := 3*(NuPaths(L, 9, 1, 100) + NuPaths(L, 9, 2, 100) + NuPaths(L, 9, 3, 100) + NuPaths(L, 9, 4, 100) + NuPaths(L, 9, 5, 100) + NuPaths(L, 9, 6, 100) + NuPaths(L, 9, 7, 100) + NuPaths(L, 9, 8, 100) + NuPaths(L, 9, 9, 100))
#C := 6*(NuPaths(L, 2, 1, 100) + NuPaths(L, 2, 2, 100) + NuPaths(L, 2, 3, 100) + NuPaths(L, 2, 4, 100) + NuPaths(L, 2, 5, 100) + NuPaths(L, 2, 6, 100) + NuPaths(L, 2, 7, 100) + NuPaths(L, 2, 8, 100) + NuPaths(L, 2, 9, 100))
#B + C;
#The equation above gave me the result below.
#5226548988000567248773522137264977941817881695114675433474341352228679239341009


#{1,2,3,4,5,6,7,8,9}
#A:={r,v,l,b,m,n,a,i,o}
# The list A above shows the letters in my full name with a number assigned to it. For example r=1 v=2 and so on.
#L:=[{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6,7,8,9},{1,2,3,4,5,6},{1,2,3,4,5,6},{1,2,3,4,5,6}]
#The graph L represented above represents all the neighbors of each letter in A where no two vowels can be neighbors.
#To compute the total number of paths I used the function NuPaths and computed all possible paths starting and ending at any two letters using L.
#B := 3*(NuPaths(L, 9, 1, 100) + NuPaths(L, 9, 2, 100) + NuPaths(L, 9, 3, 100) + NuPaths(L, 9, 4, 100) + NuPaths(L, 9, 5, 100) + NuPaths(L, 9, 6, 100) + NuPaths(L, 9, 7, 100) + NuPaths(L, 9, 8, 100) + NuPaths(L, 9, 9, 100))
#C := 6*(NuPaths(L, 2, 1, 100) + NuPaths(L, 2, 2, 100) + NuPaths(L, 2, 3, 100) + NuPaths(L, 2, 4, 100) + NuPaths(L, 2, 5, 100) + NuPaths(L, 2, 6, 100) + NuPaths(L, 2, 7, 100) + NuPaths(L, 2, 8, 100) + NuPaths(L, 2, 9, 100))
#B+C=
#202754070861600536180436660918725228517598077673149561660158560432399425152362436796384018432


#{1,2,3,4,5,6,7,8,9}
#A:={r,v,l,b,m,n,a,i,o}
# The list A above shows the letters in my full name with a number assigned to it. For example r=1 v=2 and so on.
#L:=[{7,8,9},{7,8,9},{7,8,9},{7,8,9},{7,8,9},{7,8,9},{1,2,3,4,5,6},{1,2,3,4,5,6},{1,2,3,4,5,6}]
#The graph L represented above represents all the neighbors of each letter in A where no two vowels can be neighbors and no two.
#B := 3*(NuPaths(L, 9, 1, 100) + NuPaths(L, 9, 2, 100) + NuPaths(L, 9, 3, 100) + NuPaths(L, 9, 4, 100) + NuPaths(L, 9, 5, 100) + NuPaths(L, 9, 6, 100) + NuPaths(L, 9, 7, 100) + NuPaths(L, 9, 8, 100) + NuPaths(L, 9, 9, 100))
#C := 6*(NuPaths(L, 2, 1, 100) + NuPaths(L, 2, 2, 100) + NuPaths(L, 2, 3, 100) + NuPaths(L, 2, 4, 100) + NuPaths(L, 2, 5, 100) + NuPaths(L, 2, 6, 100) + NuPaths(L, 2, 7, 100) + NuPaths(L, 2, 8, 100) + NuPaths(L, 2, 9, 100))
#B+C;
#5222371523228586691507591059411304343770770758809435324721135616


#Question 2
#The farmer can take the sheep to point B first because the wolf and the cabbage can be left alone together. The farmer then returns to point A.
#Then the farmer can either take the wolf or the cabbage over to point B returning with the sheep to point A.
#The sheep is left at point A and the farmer takes whatever is left at point A over to point B (could be either the cabbage or the wolf).
#Then the farmer returns from point B to point A to carry the sheep over to point B.

#Question 4
#C=Canibal, M=Missionary
#CCCMMM          --
#        MC->
#CCMM            MC
#        <-M
#CCMMM           C
#        CC->
#MMM             CCC
#        <-C
#MMMC            CC
#        MM->
#MC              MMCC
#        <-MC
#MMCC            MC
#        MM->
#CC              MMMC
#        <-C
#CCC             MMM
#        CC->
#C               MMMCC
#        <-C
#CC              MMMC
#        CC->
#                MMMCCC