The following two facts are known about Adam, Bert, and Carl:

1) Of Adam, Bert, and Carl, there is one knight, one knave, and one liar.
2) Adam said once, "Bert said that Carl isn't a knight."

Can you ask one yes/no question to one person and figure out who is who? If not, how many questions must you ask?

Answered in 2 questions below. Haven't proofread it yet, but it seemed to check out last night. Are there any holes?

If Adam = Liar
EITHER  *Bert said nothing at all. (In this case we don't have enough information to solve the puzzle.); OR *Bert said "Carl is a Knight"
Bert would not say this if he himself was a Knight
THEREFORE *Carl = Knight, & *Bert = Knave (telling truth)

If Adam = Knight
THEN  *Neither Bert or Carl is a knight; and*Wher Bert said "Carl isn't a knight" he told the truth.
THEREFORE  *Bert = Knave (telling truth), & Carl = Liar

If Adam = Knave (telling truth)
THEN  *Bert and Carl are Knight and Liar, but we can't tell who is who.

If Adam = Knave (lying)

THEN  *Bert said "Carl is a Knight"; *Either Bert or Carl must be a Knight; *Bert would not say that if he himself was a Knight
THEREFORE  *Bert = Liar, & Carl = Knight

So we have 5 possibilities only:
A  LIAR                        A  KNIGHT
B  KNAVE (T)                B  KNAVE (T)
C  KNIGHT                   C  LIAR

A  KNAVE (T)                A  KNAVE (T)
B  KNIGHT                    B  LIAR
C  LIAR                        C  KNIGHT

A  KNAVE (L)
B  LIAR
C  KNIGHT

THEREFORE Carl is a Liar or a Knight, he can not be a Knave.

So I ask 2 Questions:

Q1  Adam, if I had asked you yesterday whether Carl is a Knave, what would you have said?

The correct answer to [Is Carl a Knave] is NO
IF Adam is a Liar he would have lied yesterday and said "yes", he will lie about this again today and say "NO"
IF Adam is a Knight he would tell the truth yesterday and today, saying "NO"
IF Adam is a Knave he would either *lie yesterday, saying "yes", then correctly report that answer today, saying "YES"; OR *Tell the truth yesterday, being "no", then lie about this answer today, saying "YES"

So to Q1 if Adam answers YES he is a Knave
so we have 2 options:
A  Knave          A  Knave
B  Liar              B  Knight
C  Knight          C  Liar

If to Q1 Adam answers NO, then Bert is a Knave and we have:
A  Liar              A  Knight
B  Knave          B  Knave
C  Knight          C  Liar

If Adam answers YES (he is a knave) then Question 2 is:
Q2  Adam, If I asked you yesterday whether Bert is a Liar, what would you have said?
IF the answer to [Is Bert a Liar] is NO, a knave will answer "yes", as shown above.
IF the answer to [Is Bert a Liar] is YES, a knave will answer "no"
SO if Adam answers NO then the correct answer is YES and Bert is a liar
                 A  Knave
                 B  Liar
                 C  Knight
IF the answer to [Is Bert a Liar] is NO, Adam answers "yes", so the correst answer must be "no and we have:
                 A  Knave
                 B  Knight
                 C  Liar

Sorry, no time to finish this today, but if Adam answers "No" to Question 1 then Bert is the knave. I follow the same pattern as above, asking Bert Question 2 instead or Adam

Posted by Amber on 2005-05-19 06:13:28