#Nathan Fox
#Homework 8
#I give permission for this file to be posted online

##Read old files
read(`C8a.txt`):

#Help procedure
Help:=proc() :
print(` checkRollLD() , checkRandGame1() , G2(n) `):
end:

##Problem 2
checkRollLD:=proc():
print(add(x[RollLD([1,1,1,1,1,1])],i=1..6000)):
print(add(x[RollLD([1,2,3])],i=1..6000)):
print(add(x[RollLD([1,1])],i=1..6000)):
print(add(x[RollLD([seq(j*(j+1)/2,j=1..10)])],i=1..6000)):
end:

##Problem 3
checkRandGame1:=proc():
print(add(x[RandGame1(10)],i=1..NuGames1(10)*100)):
end:

##Problem 4
#G2(n): inputs a positive integer n and
#outputs the set of all level-2 games of size n.
G2:=proc(n) local S,g1,g2,g3,g4,i,j,k,Gi,Gj,Gk,Gl:
option remember:
if n=1 then
    return {[{},{}]}:
fi:
S:={}:
for i from 1 to n-1 do
    Gi:=G2(i):
    for j from 1 to n-i-1 do
        Gj:=G2(j):
        for k from 1 to n-i-j-1 do
            Gk:=G2(k):
            if n-i-j-k-1>=1 then
                Gl:=G2(n-i-j-k-1):
                for g1 in Gi do
                    for g2 in Gj do
                        for g3 in Gk do
                            for g4 in Gl do
                                if g1<>g2 and g3<>g4 then
                                    S:=S union {[{g1,g2},{g3,g4}]}:
                                fi:
                            od:
                        od:
                    od:
                od:
            fi:
            if i+j+k=n-1 then
                for g1 in Gi do
                    for g2 in Gj do
                        for g3 in Gk do
                            if g1<>g2 then
                                S:=S union {[{g1,g2},{g3}]}:
                            fi:
                            if g2<>g3 then
                                S:=S union {[{g1},{g2,g3}]}:
                            fi:
                        od:
                    od:
                od:
            fi:
        od:
        if i+j=n-1 then
            for g1 in Gi do
                for g2 in Gj do
                    S:=S union {[{g1},{g2}]}:
                    if g1<>g2 then
                        S:=S union {[{g1,g2},{}],[{},{g1,g2}]}:
                    fi:
                od:
            od:
        fi:
    od:
    if i=n-1 then
        for g1 in Gi do
            S:=S union {[{g1},{}],[{},{g1}]}:
        od:
    fi:
od:
S:
end: