bonanova Posted February 16, 2008 Report Share Posted February 16, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 16, 2008 Report Share Posted February 16, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 16, 2008 Report Share Posted February 16, 2008 i think that Chuck is a knight Dave is a knave Elliot is a liar Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted February 16, 2008 Author Report Share Posted February 16, 2008 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. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 18, 2008 Report Share Posted February 18, 2008 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 Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 18, 2008 Report Share Posted February 18, 2008 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 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted February 18, 2008 Author Report Share Posted February 18, 2008 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? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 18, 2008 Report Share Posted February 18, 2008 There are 8 statements to work with. Did you use all of them? After All that hard work .. I get this .. URGHHHH! Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 18, 2008 Report Share Posted February 18, 2008 (edited) 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 February 18, 2008 by Aatif Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted February 18, 2008 Author Report Share Posted February 18, 2008 The solution is not ambiguous if I include the information that Al and Bob each made four statements. My bad ... Quote Link to comment Share on other sites More sharing options...
Question
bonanova
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.
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