Jump to content
BrainDen.com - Brain Teasers
  • 0


bonanova
 Share

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.

Link to comment
Share on other sites

9 answers to this question

Recommended Posts

  • 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.

Link to comment
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

Link to comment
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

Link to comment
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 :blush:

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
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

Guest
Answer this question...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

Loading...
 Share

  • Recently Browsing   0 members

    • No registered users viewing this page.
×
×
  • Create New...