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Question
LIst all possible(64) combinations of AaBbCc taken 6, 5, 4, 3, 2 and 1 at a time.
I want to find the number of valid states in the problem of "Three Jealous Husbands" which is the famous River Crossing Problem.
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Answers
Wowww......
THANKS A LOT....!!
I GOT A WAY TO RECHECK...!!
I am glad... you replied..!!
Highly appreciated.
Maybe you meant possible states at any one location, not counting the rule that that no woman can be in the presence of another man unless her husband is also present.
which would be (64) combinations
But it that's what you meant, then you already know that the number of such states is 64
so I may be confused what you are asking.
I listed states that are valid under the constraint that no woman can be in the presence of another man unless her husband is also present, where state includes people on each shore and in the boat
6C6 = 1 (Cases having all 6 chars)
6C5 = 6 (Cases having 5 chars)
6C4 = 15 (Cases having 4 chars)
6C3 = 20 (Cases having 3 chars)
6C2 = 15 (Cases having 2 chars)
6C1 = 6 (Cases having 1 chars)
6C0 = 1 (Cases having 0 chars)
Tot = 64
A a B b C c Len Res
1 1 1 1 1 1 6 AaBbCc
1 1 1 1 1 0 5 AaBbC
1 1 1 1 0 1 5 AaBbc
1 1 1 0 1 1 5 AaBCc
1 1 0 1 1 1 5 AabCc
1 0 1 1 1 1 5 ABbCc
0 1 1 1 1 1 5 aBbCc
1 1 1 1 0 0 4 AaBb
1 1 1 0 1 0 4 AaBC
1 1 1 0 0 1 4 AaBc
1 1 0 1 1 0 4 AabC
1 1 0 1 0 1 4 Aabc
1 1 0 0 1 1 4 AaCc
1 0 1 1 1 0 4 ABbC
1 0 1 1 0 1 4 ABbc
0 1 1 1 1 0 4 aBbC
0 1 1 1 0 1 4 aBbc
1 0 1 0 1 1 4 ABCc
1 0 0 1 1 1 4 AbCc
0 1 1 0 1 1 4 aBCc
0 1 0 1 1 1 4 abCc
0 0 1 1 1 1 4 BbCc
1 1 1 0 0 0 3 AaB
1 1 0 1 0 0 3 Aab
1 1 0 0 1 0 3 AaC
1 1 0 0 0 1 3 Aac
1 0 1 1 0 0 3 ABb
0 1 1 1 0 0 3 aBb
1 0 1 0 1 0 3 ABC
1 0 1 0 0 1 3 ABc
1 0 0 1 1 0 3 AbC
1 0 0 1 0 1 3 Abc
0 1 1 0 1 0 3 aBC
0 1 1 0 0 1 3 aBc
0 1 0 1 1 0 3 abC
0 1 0 1 0 1 3 abc
1 0 0 0 1 1 3 ACc
0 1 0 0 1 1 3 aCc
0 0 1 1 1 0 3 BbC
0 0 1 1 0 1 3 Bbc
0 0 1 0 1 1 3 BCc
0 0 0 1 1 1 3 bCc
1 1 0 0 0 0 2 Aa
1 0 1 0 0 0 2 AB
1 0 0 1 0 0 2 Ab
0 1 1 0 0 0 2 aB
0 1 0 1 0 0 2 ab
1 0 0 0 1 0 2 AC
1 0 0 0 0 1 2 Ac
0 1 0 0 1 0 2 aC
0 1 0 0 0 1 2 ac
0 0 1 1 0 0 2 Bb
0 0 1 0 1 0 2 BC
0 0 1 0 0 1 2 Bc
0 0 0 1 1 0 2 bC
0 0 0 1 0 1 2 bc
0 0 0 0 1 1 2 Cc
1 0 0 0 0 0 1 A
0 1 0 0 0 0 1 a
0 0 1 0 0 0 1 B
0 0 0 1 0 0 1 b
0 0 0 0 1 0 1 C
0 0 0 0 0 1 1 c
0 0 0 0 0 0 0
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by: ozoPosted on 2009-05-01 at 22:23:33ID: 24284940
valid states are
AaBbCc
AaBbC c
AaBbC c
AaBb Cc
AaBb C c
AaBb c C
AaBb Cc
AaBCc b
AaBC bc
AaBC b c
AaB bc C
AaB b Cc
AaBCc b
AaBC c b
AaBC bc
AaB Cc b
AaB C bc
AaCc Bb
AaC Bb c
Aa BbCc
Aa BbC c
Aa Bb Cc
AaCc B b
AaC B bc
Aa BCc b
Aa BC bc
AaCc b B
AaC bc B
Aa bc BC
Aa b BCc
AaCc Bb
AaC c Bb
Aa Cc Bb
Aa c BbC
Aa BbCc
ABbCc a
ABbC ac
ABbC a c
ABb ac C
ABb a Cc
ABCc ab
ABC abc
ABC ab c
AB abc C
AB ab Cc
ABCc a b
ABC ac b
ABC a bc
ACc ab B
AC abc B
A abc BC
A ab BCc
ACc a Bb
AC ac Bb
A ac BbC
A a BbCc
ABbCc a
ABbC c a
ABbC ac
ABb Cc a
ABb C ac
ABCc b a
ABC bc a
ABC b ac
ABCc ab
ABC c ab
ABC abc
AB Cc ab
AB C abc
ACc Bb a
AC Bb ac
A BbCc a
A BbC ac
ACc B ab
AC B abc
A BCc ab
A BC abc
abc ABC
ab ABCc
ab ABC c
abc AB C
ab AB Cc
ac ABbC
a ABbCc
a ABbC c
ac ABb C
a ABb Cc
ac ABC b
a ABCc b
a ABC bc
abc AC B
ab ACc B
abc A BC
ab A BCc
ac AC Bb
a ACc Bb
ac A BbC
a A BbCc
BbCc Aa
BbC Aa c
Bb AaCc
Bb AaC c
Bb Aa Cc
BCc Aa b
BC Aa bc
B AaCc b
B AaC bc
bc AaBC
b AaBCc
b AaBC c
bc AaB C
b AaB Cc
Cc AaBb
C AaBb c
c AaBbC
AaBbCc
AaBbC c
c AaBb C
AaBb Cc
Cc AaB b
C AaB bc
c AaBC b
AaBCc b
AaBC bc
bc AaC B
b AaCc B
bc Aa BC
b Aa BCc
Cc Aa Bb
c AaC Bb
AaCc Bb
c Aa BbC
Aa BbCc
BbCc A a
BbC A ac
Bb ACc a
Bb AC ac
BCc A ab
BC A abc
B ACc ab
B AC abc
bc ABC a
b ABCc a
b ABC ac
Cc ABb a
C ABb ac
c ABbC a
ABbCc a
ABbC ac
Cc AB ab
C AB abc
c ABC ab
ABCc ab
ABC abc
abc BC A
ab BCc A
abc B AC
ab B ACc
ac BbC A
a BbCc A
ac Bb AC
a Bb ACc
abc C AB
ab Cc AB
abc ABC
ab c ABC
ab ABCc
ac b ABC
a bc ABC
a b ABCc
ac C ABb
a Cc ABb
ac ABbC
a c ABbC
a ABbCc
BbCc a A
BbC ac A
Bb ac AC
Bb a ACc
BCc ab A
BC abc A
B abc AC
B ab ACc
bc a ABC
b ac ABC
b a ABCc
Cc ab AB
C abc AB
c ab ABC
abc ABC
ab ABCc
Cc a ABb
C ac ABb
c a ABbC
ac ABbC
a ABbCc
BbCc Aa
BbC c Aa
Bb Cc Aa
Bb c AaC
Bb AaCc
BCc b Aa
BC bc Aa
B bc AaC
B b AaCc
bc BC Aa
b BCc Aa
bc B AaC
b B AaCc
Cc Bb Aa
c BbC Aa
BbCc Aa
c Bb AaC
Bb AaCc
bc C AaB
b Cc AaB
bc AaBC
b c AaBC
b AaBCc
Cc b AaB
C bc AaB
c b AaBC
bc AaBC
b AaBCc
Cc AaBb
C c AaBb
c C AaBb
Cc AaBb
c AaBbC
c AaBbC
AaBbCc