BrainDen.com - Brain Teasers
• 0

## Question

In the land of Knights, Knaves and Liars [KKL]

Knights always tell the truth,

Knaves alternate telling the truth and lying: e.g. T F T F or F T F T and

Liars, of course, always lie.

Al and Bob are Knaves. They make the following statements.

You don't know who made which statement, but you know the time sequence is correct.

Edit: Al and Bob each made four statements.

1. Chuck is a liar.

2. Dave is a Knave.

3. Elliot is a Knight.

4. Chuck and Dave are the same type.

5. Dave and Elliot are of different types.

6. Chuck is a Knight.

7. Elliot is a Knave.

8. Dave is a liar.

Identify Chuck, Dave and Elliot as a Knight, Knave or Liar. They might all be of different types, but they needn't be.

## 9 answers to this question

• 0

Here is my solution:

Chuck

Chuck = Knight

Dave = Liar

Elliot = Knight

1. = False

2. = False

3. = True

4. = False

5. = True

6. = True

7. = False

8. = True

1A -F

3A -T

4A -F

6A -T

2B -F

5B -T

7B -F

8B -T

I double checked this but I am sick, so it may be wrong.

##### Share on other sites
• 0

i think that

Chuck is a knight

Dave is a knave

Elliot is a liar

##### Share on other sites
• 0
i think that

Chuck is a knight

Dave is a knave

Elliot is a liar

That would make statements 1,2,3,6,7,8 = F T F T F F so that statements 4,5 would be T T.

Thus C=D^=E.

Chuck and Dave would be the same.

##### Share on other sites
• 0

One possible solution is:

Chuck = Knave; Dave = Knave; Elliot = Knave

The only thing know by what Al & Bob say is that,

1. there can be no 3 straight T statements or 3 straight F statements (eg. TTTFFTT is not allowed)

2. After 2 straight T statement, there can be no 2 more straight T statement without 2 preceding F statements (eg. TTFTTFF is not allowed)

No lets assume that the statement 4. C,D are same to be True.

That means:

I)

1. T 2. F 3. T/F 4. T 5. F 6. T/F 7. T

There is no way of being certain that which of 3. or 6. are true or vice versa. Hence E can be either Knight or Knave and there is no way of knowing it.

Hence assumption that 4. is True is incorrect.

or

II)

1.F 2.T 3.F 4.T 5.F 6.T 7.F

Which would mean Chuck is Knave; Dave is Knave and Elliot is Knave

There are no other possible combinations for 4. being true.

Now lets look at 4. being False.

I did for 4 different combinations and all of them proved to be not possible, from the initial conditions. On doing more rigorously it can be shown that its not possible for 4 cannot be false (Also note that we have a viable solution above. So if there is another solution, then it makes the overall solution not unique and hence the puzzle void)

Thus, from the reverse logic only rational solution can be Chuck is Knave; Dave is Knave and Elliot is Knave

##### Share on other sites
• 0
One possible solution is:

Chuck = Knave; Dave = Knave; Elliot = Knave

The only thing know by what Al & Bob say is that,

1. there can be no 3 straight T statements or 3 straight F statements (eg. TTTFFTT is not allowed)

2. After 2 straight T statement, there can be no 2 more straight T statement without 2 preceding F statements (eg. TTFTTFF is not allowed)

No lets assume that the statement 4. C,D are same to be True.

That means:

I)

1. T 2. F 3. T/F 4. T 5. F 6. T/F 7. T

There is no way of being certain that which of 3. or 6. are true or vice versa. Hence E can be either Knight or Knave and there is no way of knowing it.

Hence assumption that 4. is True is incorrect.

or

II)

1.F 2.T 3.F 4.T 5.F 6.T 7.F

Which would mean Chuck is Knave; Dave is Knave and Elliot is Knave

There are no other possible combinations for 4. being true.

Now lets look at 4. being False.

I did for 4 different combinations and all of them proved to be not possible, from the initial conditions. On doing more rigorously it can be shown that its not possible for 4 cannot be false (Also note that we have a viable solution above. So if there is another solution, then it makes the overall solution not unique and hence the puzzle void)

Thus, from the reverse logic only rational solution can be Chuck is Knave; Dave is Knave and Elliot is Knave

I rechecked my logic and it seems there are multiple solutions possible.

Another one can be:

Chuck is Knight; Elliot is Knight and Dave is Liar

In this case:

1.F 2.F 3.T 4.F 5.T 6.F 7.T

A: 1,3,4,6,7 - F,T,F,T,F,T

B: 2,5 - F,T

##### Share on other sites
• 0
One possible solution is:

Chuck = Knave; Dave = Knave; Elliot = Knave

I rechecked my logic and it seems there are multiple solutions possible.

Another one can be:

Chuck is Knight; Elliot is Knight and Dave is Liar

There are 8 statements to work with.

Did you use all of them?

##### Share on other sites
• 0
There are 8 statements to work with.

Did you use all of them?

After All that hard work .. I get this .. URGHHHH!

##### Share on other sites
• 0
After All that hard work .. I get this .. URGHHHH!

Ok.. Now I include statement number 5, which I blissfully ignored in my 2 earlier posts

Solution 1:

Chuck = Dave = Elliot = Knave

1.F 2.T 3.F 4.T 5.F 6.F 7.T 8.F

A: 1,2,3,4,5,7,8 - F,T,F,T,F,T,F

B: 6 - F

Solution 2:

Chuck is Knight; Elliot is Knight and Dave is Liar

1.F 2.F 3.T 4.F 5.T 6.T 7.F 8.T

A: 1,3,4,5,7,8 - F,T,F,T,F,T

B: 2,6 - F,T

Edited by Aatif

##### Share on other sites
• 0

The solution is not ambiguous if I include the information that Al and Bob each made four statements.

## Create an account

Register a new account