[bonanova]

The Mother of all Truth-teller puzzles [Edits to clarify a point shown in red]

Citizens of the Land of KNLC are of four character types: Knights [K], Knaves [N], Liars [L], and Chameleons [C].

Citizens normally behave like this:

.

• [K] will tell the truth.
  .
  
• [N] statements alternate in truth value; the first statement that a Knave makes is freely chosen [TLT... or LTL...]
  If another citizen is available [i.e. is present and available to speak], a Knave will permit him or her to be the initial speaker.
  .
  
• [L] will lie.
  .
  
• [C] will mimic the truth value of the most recent previous speaker.
  If a lie has just been told, [C] will lie. etc.
  If no one has yet spoken, either today or the preceding day,
  then [C] will sit silently in the corner.
  Sometimes citizens ACT as if they were of a different character.
  
  Let's introduce the notation Character[ACTING_LIKE].
  Then, for example,
  .
  
  • K[L] is a Knight ACTING like a Liar: K[L] will lie.
    .
    
  • C[K] is a Chameleon ACTING like a Knight: C[K] will tell the truth.
    .
    
  • L[N] is a Liar ACTING like a Knave.
    If the LIAR's last previous statement was a lie, then L[N] will tell the truth. etc.
    .
    
  • L[C] is a Liar ACTING like a Chameleon.
    If the LAST PREVIOUS SPEAKER spoke truthfully, L[C] will also tell the truth. etc.
    This deviant behavior is confusing, but it's predictable.
    
    Here's the ACTING schedule in the land of KNLC:
    .
    

    
    
    	Mon: K[K], N[N], L[L] and C[C] - Every citizen ACTS according to his own character.
    
    	Tue: K[N], N[L], L[C] and C[K] - Knaves ACT like Liars, etc.
    
    	Wed: K[L], N[C], L[K] and C[N] - Liars ACT like Knights, etc.
    
    	Thu: K[C], N[K], L[N] and C[L] - Chameleons lie, etc.
    
    	Fri: K[K], N[N], L[L] and C[C] - Everyone's back to original character.
    
    	Sat: K[N], N[L], L[C] and C[K] - Back to Tuesday behavior.
    
    	Sun: Citizens are not allowed to speak on Sunday.
    
    [/code]
    
    
    [color=#afeeee].[/color]
    
    [b]Please meet four KNLC Citizens: Andy, Dave, Iago and Lisa. [/b]
    
    
    Here's a little anecdote to help you know them better. 
    
    Yesterday they were given a single written Y/N question to be answered verbally.
    
    [color=#afeeee] .[/color]
    
    [/font]
    [font=Verdana]Two of them, now senile and without any memory to speak of, independently blurted
    
    out contradictory answers, as they always do. 
    
    [color=#afeeee].[/color]
    
    [/font]
    [font=Verdana]Another was deaf, but answered easily after reading the question, only because
    
    some memory still remained.
    
    [color=#afeeee].[/color]
    
    [/font]
    [font=Verdana]The last citizen was deaf, memory intact, but needed a hearing aid to answer. [/font][/list][font=Verdana][color=#afeeee].[/color]
    
    [b]Now for the puzzle:[/b]
    
    
    Last week, each citizen made a series of statements, one statement on each of three consecutive days. [color=#8b0000][[b]Edit to clarify:[/b]] In all, twelve statements were made, over a period of six days.[/color]
    
    [color=#afeeee].[/color]
    
    [/font][list]
    [font=Verdana]No two citizens made their first statement on the same day.
    
    [color=#afeeee].[/color]
    
    [/font]
    [font=Verdana]On days when more than one statement was made, the statements that day were alphabetically
    
    ordered according to the character that was being ACTED: 
    
    [color=#afeeee].[/color]
    
    [/font][list]
    [font=Verdana]In any given day, therefore, the order was *[C], *[K], *[L], *[N].
    
    Where * is a wild card notation, denoting any citizen who may have spoken that day.
    
    [color=#afeeee].[/color]
    
    [/font]
    [font=Verdana]This doesn't imply there were ever four speakers in a day; it just gives the order of any who did speak.
    
    For example, if K[L] and L[C] spoke on the same day, L[C] preceded K[L], because [C] comes before [L].
    
    [/font]
    [font=Verdana][color=#afeeee].[/color]
    
    [/font][*][font=Verdana]The characters that were being ACTED in the final two statements are in strict alphabetic order. [No ties.][/font]
    [font=Verdana][color=#afeeee].[/color]
    
    [b]Here are the twelve statements, in the order they were made:[/b]
    
    
    Note: Only declarative statements have truth value.
    
    Questions, exclamations and imperatives [commands] can safely be ignored.
    
    [color=#afeeee].[/color]
    
    [/font][list=1][*][font=Verdana]Snazzlefartz! [color=#8b0000][Note from OP: the meaning of this term is uncertain.][/color][/font][*][font=Verdana]Don't ask me what Snazzlefartz means. I never use that word.[/font][*][font=Verdana]Looking for Iago? Look somewhere else. He's not I.[/font][*][font=Verdana]Hi! I'm Lisa. Are you enjoying your visit to KNLC?[/font][*][font=Verdana]None of our initials agree with the initial letters of our real characters.[/font][*][font=Verdana]If the Knave's final statement is True, then my name is Lisa.[/font][*][font=Verdana]If the majority of these statements are True, then most of them are False.[/font][*][font=Verdana]If the Chameleon's final statement is false, then the Knight's first statement is true.[/font][*][font=Verdana]I hate having to appear in these puzzles. You'd think they'd at least pay us something.[/font][*][font=Verdana]I'm not Lisa. Can I leave now?[/font][*][font=Verdana]I'm not Lisa, either. Can I leave, too?[/font][*][font=Verdana]If all 4 of us have made at least two statements that appear consecutively in this list, then I am not Dave.
    
    [color=#afeeee].[/color]
    
    [/font]
    [font=Verdana]
    
    Now you should know the character types of the four Citizens and the order in which they spoke.
    
    
    [color=#8b0000][color=#0000ff]Which was Andy's final statement?[/color]
    
    
    [b][color=#000000]Enjoy![/color][/b] 
    
    
    [/color][/font][font=Verdana][spoiler=A very weak hint and a hint about hints]A precise  sequence of 8 steps leads to the solution. i.e., there are eight puzzles, and solving the first permits solving the second, which permits solving the third, etc. Thankfully, they get easier as you go along.
    
    
    One hint would be to describe the sequence: e.g., first determine ...... then find out whether .... 
    
    
    I'll wait a while before giving these hints.[/spoiler][/font]

Edited October 3, 2010 by bonanova
Clarification

[Guest]

Just to through this out there..you have got WAY too much time one your hands to be coming up with stuff like this..but, i give you credit..it's always good..i shall see what i can figure out

[Guest]

I asked a question but then I saw it was silly and now I can't delete it, just edit

Edited October 1, 2010 by MaybeMyNameIsStine

[Guest]

Last week, each citizen made a series of statements, one statement on each of three consecutive days.

No two citizens made their first statement on the same day.

I dont understand these two parts of the puzzle...

It says only 1 statement per day can be spoken by any given citizen...

then it says no 2 citizens speaks their first statement on the same day...so..

Day 1..only one statement by 1 person

Day 2..maximum of 2 statements, by 2 different peopl (1 of them being day 1s speaker)

Day 3..maximum of 3 statements made by 3 different people ( 2 of them spoke previous days)

so I get a total of 6 statements made, and 1 person not speaking..

What did I read incorrectly?

[bonanova]

I dont understand these two parts of the puzzle...

It says only 1 statement per day can be spoken by any given citizen...

then it says no 2 citizens speaks their first statement on the same day...so..

Day 1..only one statement by 1 person

Day 2..maximum of 2 statements, by 2 different peopl (1 of them being day 1s speaker)

Day 3..maximum of 3 statements made by 3 different people ( 2 of them spoke previous days)

so I get a total of 6 statements made, and 1 person not speaking..

What did I read incorrectly?

The statement in the OP

each citizen made a series of statements, one statement on each of three consecutive days.

Should be interpreted: each citizen speaks on three consecutive days and makes one statement each of those days. Three days applies to each citizen, not the entire group. As we see later on, that makes 12 statements in all. You're correct as far as you go, just don't stop after three days.

I'll edit the OP to make that point clearer.

Thanks!

- bn

[Guest]

If another citizen is available, a Knave will permit him or her to be the initial speaker.

On days when more than one statement was made, the statements that day were alphabetically

ordered according to the character that was being ACTED:

This makes no sense.

[Guest]

And, as an example, if a Knave told the truth Monday, and a Knight speaks Tuesday (thus acting like a Knave), will he then lie, because the [C] was true the day before? Or can he just as well tell the truth, because he's a different person?

Okay, I know this doesn't make much sense, but I don't know how else to explain it. I hope bonanova understands.

[bonanova]

If another citizen is available, a Knave will permit him or her to be the initial speaker.

This makes no sense.

To get the intent of this, you may change "available" to "present"

Initial speaker = someone who speaks before anyone else has spoken. "Initial" refers to the first of the twelve statements.

If no one has spoken [yet] and a Knave is with a Knight, for example, the Knave will permit the Knight to speak first. You may also assume the four speakers come together and stay in a group from the 1st statement to the 12^th.

On days when more than one statement was made, the statements that day were alphabetically

ordered according to the character that was being ACTED:

This makes no sense.

Quoting from the OP: For example, if K[L] and L[C] spoke on the same day, L[C] preceded, i.e. spoke before, K[L], because [C] comes before [L].

Since the Liar ACTED as a Chameleon, he speaks before the Knight. That's because the Knight ACTED as a Liar, and C comes before L in the alphabet. The order is alphabetical according to the ACTED character.

[bonanova]

And, as an example, if a Knave told the truth Monday, and a Knight speaks Tuesday (thus acting like a Knave), will he then lie, because the [C] was true the day before? Or can he just as well tell the truth, because he's a different person?

Okay, I know this doesn't make much sense, but I don't know how else to explain it. I hope bonanova understands.

Your question makes sense, and it's an important point. When a person acts as a Knave, that person looks back to his OWN previous statement.

In your example, What the Knave said on Monday doesn't matter. What matters is whether the Knight that is acting as a Knave has just told the truth, or lied. Since the Knight is acting like a Knave, he does what Knave would do - look back to his OWN previous statement and alternate the truth value for his next statement.

Again, quoting the OP: L[N] is a Liar ACTING like a Knave.

If the LIAR's last previous statement was a lie, then L[N] will tell the truth. etc.

Also, if L[N] is making his [the Liar's] first statement, he [the Liar] can choose T or F, just as a real Knave could do when making his first statement. So L[N] means the character is a Liar, but he ACTs exactly the way he would if he were a Knave.

Hope that helps.

[phaze]

Aaaarrrrrgghhhhhh!

:shrug: Well someone had to say it..

[bonanova]

Aaaarrrrrgghhhhhh!

:shrug: Well someone had to say it..

phaze, I added a little guidance in the spoiler at the bottom. If may help you think about what to figure out first. Or, better, what can you figure out first. Order matters, and it's not the usual order for this type of puzzle. Ask yourself, what are all the things I eventually need to know. Then, which of these can I figure out from the clues given. Make any charts or schedules or grids that need to be filled in, and go as far as you can ...

Good Luck.

[bonanova]

The solution proceeds in steps.

Generally, each step requires the result of the preceding steps.

So they must be done in a particular order.

Index numbers in bold have been assigned to statements in OP.

This facilitates referring to particular pieces of information used in the solution.

Citizens of the Land of KNLC are of four character types: Knights [K], Knaves [N], Liars [L], and Chameleons [C]. The normal Citizen behavior is ...

01 [K] will tell the truth.

02 [N] statements will alternate in truth value; the value of the first statement is freely chosen [i.e., TFT... or FTF...] When speaking in a group, a Knave will permit another citizen to be the initial speaker.

03 [L] will lie.

04 [C] will mimic the truth value of the most recent previous speaker. e.g., If a lie has just been told, [C] will lie. If no one has yet spoken today or the preceding day, then [C] will become confused and sit silently in the corner.

But on some days, Citizens change their behavior and ACT like a different character. If we use the notation Character[ACTING_LIKE], then for example,

1A K[L] is a Knight ACTING like a Liar: K[L] will lie.

2A C[K] is a Chameleon ACTING like a Knight: C[K] will tell the truth.

3A L[N] is a Liar ACTING like a Knave. If the LIAR's last previous statement was a lie, then L[N] will tell the truth. etc.

4A L[C] is a Liar ACTING like a Chameleon. If the LAST PREVIOUS SPEAKER spoke truthfully, L[C] will also tell the truth.

Each day the ACTED character is the next in the K,N,L,C,... sequence. Specifically, here's the cyclic ACTING schedule in the land of KNLC:

05 Mon: K[K], N[N], L[L] and C[C] - Every citizen ACTS according to his own character.

06 Tue: K[N], N[L], L[C] and C[K] - Knaves ACT like Liars, etc.

07 Wed: K[L], N[C], L[K] and C[N] - Liars ACT like Knights, etc.

08 Thu: K[C], N[K], L[N] and C[L] - Chameleons lie, etc.

09 Fri: K[K], N[N], L[L] and C[C] - Same as Monday.

10 Sat: K[N], N[L], L[C] and C[K] - Same as Tuesday.

11 Sun: Citizens are not allowed to speak on Sunday.

Last week, I forget which day, four KNLC Citizens, Andy, Dave, Iago and Lisa, were given a simple, written Y/N question to be answered verbally.

12 Two of them, now senile and without any memory to speak of, immediately blurted out contradictory answers, as they always do.

13 Another, now deaf, answered easily after reading the question, but only because memory was still intact.

14 The last citizen, also deaf but with memory intact, needed a hearing aid to answer.

15 Each of them then made a series of statements - one statement on each of three consecutive days. Twelve statements in all, covering a period of six days. Here's what we know:

16 No two citizens made their first statement on the same day, but the four first-statement days were consecutive.

17 On days when more than one statement was made, the statements that day were alphabetical according to the character that was being ACTED. For example, if K[N] and L[C] spoke on the same day, L[C] preceded K[N], because [C] precedes [N].

18 The characters that were being ACTED in the final two statements were in strict alphabetic order. [No ties.]

Here are the twelve statements, in the order they were made:

19 S01 Snazzlefartz!

20 S02 Don't ask me what Snazzlefartz means. I never use that word.

21 S03 Looking for Iago? Look somewhere else. He's not I.

22 S04 Hi! I'm Lisa. Are you enjoying your visit to KNLC?

23 S05 None of our initials agree with the initial letters of our real characters.

24 S06 If the Knave's final statement is True, then my name is Lisa.

25 S07 If the majority of these statements are True, then most of them are False.

26 S08 If the Chameleon's final statement is false, then the Knight's first statement is true.

27 S09 I hate having to appear in these puzzles. You'd think they'd at least pay us something.

28 S10 I'm not Lisa. Can I leave now?

29 S11 I'm not Lisa, either. Can I leave, too?

30 S12 If all 4 of us have made at least two statements that appear consecutively in this list, then I am not Dave.

Which was Andy's final statement?

We know there are four Citizens - Andy, Dave, Iago and Lisa.

How many Knights, Knaves, Liars and Chameleons are there among the four Citizens?

Little other progress can be made until this is known.

Which statements provide this information?

[Guest]

I think I finally have it!!!!!

If all 4 of us have made at least two statements that appear consecutively in this list, then I am not Dave.

Here is my spreadsheet. Please let me know if you see any mistakes.

Edited October 6, 2010 by Drexlin

[bonanova]

I think I finally have it!!!!!

Here is my spreadsheet. Please let me know if you see any mistakes.

Nice work Drexlin. Very Close.

.

1. Statement 7
   
   This says, If the Knave's final statement is true, then my name is Lisa.
   The solution has this as C's first statement.
   Since C is acting as a Knave, C freely chooses its truth value. It could be T or F.
   I'm not sure: does making Statement 7 False matter to the solution?
   .
2. Statement 8
   
   This has the form If A, then NOT A. Where A = "the majority of these statements are true."
   Depending on the truth value of A, [if A then NOT A] either translates to [if T then F] or translates to [if F then T].
   In the first case the inference is False [T cannot imply F]; the second inference [F implies T] is True.
   To see that [F implies T] is valid, note that [A implies B] is logically equivalent to [NOT A] OR B.
   That is, the only False inference is [T implies F]. That's equivalent to [F OR F] and is logically False.
   [F implies T] is the same as [T OR T] and is logically True.
   We can count 7 False statements, so A is False and Statement 8 becomes [if F then T] which is True.
   But the solution has Statement 8 to be False.
   .
3. Statement 9
   
   The solution has the Chameleon's final statement as Statement 11, which it says is False.
   Statement 9 says in that case the Knight's first statement is True.
   The solution has the Knight's first statement to be Statement 8, which the solution says is False.
   .

There's another error, and it probably leads to the above inconsistencies.

My bad, probably, since the clue is stated a little obscurely.

There are 24 permutations of the order of the four Citizen's first Statements.

That is, 24 permutations of CKLN. You arrived at NLCK.

You have the Knave making Statement 1.

But look at the definition of Knave, and you'll see that he won't be the first to speak.

To arrive at that, you should assume the four Citizens are together as a group.

Even if they don't all speak on any given day, they're still all there.

I didn't make that explicitly clear, partly to make the puzzle more difficult.

I mentioned this point in post #8 tho.

Hint: the clues allow only one of the 24 permutations of CKLN.

That's the last difficult thing to determine.

Good luck!

[Guest]

The first 2 of your 8 steps are easy. But I can't really get further ):

[Gmaster479]

OWWWWW...Bonanova this was something else. However...I believe I have it

None of our initials agree with the initial letters of our real characters

[Gmaster479]

Okay...maybe not.

I have Andy or Dave being able to be whomever they want. The final statement, which I assume to be the one that determines whether that person is Dave or not Dave, I have as Lisa. Therefore Dave and Andy aren't explicitly determined.

There are also some annoying little things about 6 and 7 that I don't quite understand and if I interpreted them incorrectly could make my solution wrong. Oh well, I'll let Bonanova decide

Edited October 15, 2010 by Gmaster479

[Guest]

Too many information to calculate lol!

[Guest]

OWWWWW...Bonanova this was something else. However...I believe I have it

None of our initials agree with the initial letters of our real characters

At minimum, your last two statements fail this requirement:

The characters that were being ACTED in the final two statements are in strict alphabetic order. [No ties.]

Bonanova! I haven't given up on this yet, I just haven't had time to work on it.

[bonanova]

Gmaster479's result is very close.

Drexlin's observation is correct.

The coveted bonanova Gold Star awaits the final solution.

[Guest]

Attempt # 2. I think this is it.

Gmaster479 was correct. Andy said:

None of our initials agree with the initial letters of our real characters.

Here is the new spreadsheet.

C'mon, gimme that Gold Star!

[Gmaster479]

Attempt # 2. I think this is it.

Gmaster479 was correct. Andy said:

Here is the new spreadsheet.

C'mon, gimme that Gold Star!

Crap you beat me by 2 minutes! Your explanation is correct as is my new one seen below, though I was the first to know the statement .

But yay! We got it! Here are those gold stars

Edited October 18, 2010 by Gmaster479

[bonanova]

Gmaster had the correct answer first [but I couldn't say so without giving clues.]

Drexlin had the correct matrix of identities first.

Declaring a well fought contest with dual winners ... !

Congratulations

[bonanova]

Step 1. Find what characters are present

Statements were

From [12], Only K and L always disagree. These are K, L in some order.

From [13], Only N and C need memory; C needs to hear. This is a N.

From [14], Only C needs to hear. This is a C.

So Andy, Dave, Iago and Lisa are K, N, L C in some order.

Step 2. Determine the days that the 12 statements were made.

Four 1-day staggered [15] sets of consecutive-day [15] statements that excludes Sunday [11].

The Citizens' first statements were made on M, T, W and Th:

31 Mon S1 - First speaker's first statement
32 Tue S2 S3
33 Wed S4 S5 S6
34 Thu S7 S8 S9
35 Fri S10 S11
36 Sat S12 - Last speaker's last statement.

Step 3. Determine the first-statement speaking order of the four Citizens. By [2] and [4], neither N nor C was first to speak, leaving 12 permutations:

KLNC LNCK
KLCN LNKC
KNLC LCNK
KNCL LCKN
KCLN LKNC
KCNL LKCN

Consider xxxN. Last two speakers would S11 = N[N] [by 9, 17, 35] and S12 = N[L] [10]. This violates [18]. Consider xxNx. S11's speakers' character is [N] [9, 17]. No character of S12 can strictly follow N. S [18] is violated. Consider XXXL. Speaker of S12 would ACT as [C]. No character of S11 can strictly precede C. [18] is violated. Consider xxxC. Speaker of S12 is C[K] [10,36]. By [18], S11 would have to be x[C]. But since Friday has two speakers [35], and ACTed characters don't appear twice in a day [5-10], a Friday x[C] would have to be S10 [35], not S11. Eliminating xxxN, xxxL, xxxC and xxNx leaves only one permutation: LNCK Step 4. Construct the order of the 12 statements, based on ACTED CHARACTER using [5-10], [31-36]

Mon L[L] => L[L]
Tue L[C] N[L] => L[C] N[L] ordered by acted character
Wed L[K] N[C] C[N] => N[C] L[K] C[N] ordered
Thu K[C] C[L] N[K] => K[C] N[K] C[L] ordered
Fri K[K] C[C] => C[C] K[K] ordered
Sat K[N]` => K[N]

Step 5. Determine the truth values of the statements, based on ACTED CHARACTER

S01 L[L] F [3]

S02 L[C] F Last previous statement was F [4]
S03 N[L] F Acting as Liar [3]

S04 N[C] F Last previous statement was F [4]
S05 L[K] T Acting as Knight [1]
S06 C[N] T (F)* Knave's first statement can be either T or F [2]

S07 K[C] T (F)* Mimicing last previous statement [4]
S08 N[K] T Acting as Knight [1]
S09 C[L] F Acting as Liar [3]

S10 C[C] F Last previous statement was F [4]
S11 K[K] T Acting as Knight [1]

S12 K[N] F K's last prev statement was T. Acting as Knave, he now lies. [3a]

Step 6. Remove the ambiguity of statements 06. and 07. Choose either of two methods. [26] is S08, which we know is True: If C's final statement False [s10 is F], then K's first statement [s07] is True. This makes S07 True. Because it mimics the truth of S06, S06 is also True. Alternate reasoning: S07 has the form If A, then NOT A. Where A = "the majority of the statemens are True". Even with 6 and 7 uncertain, seven other statements are False. So A is False. Since [F logically implies T] is True S07, and therefore S06, are True. The truth values of statements of the four characters, in order, are:

L: F F T
N: F F T
C: T F F
K: T T F

Step 7. Associate names with the characters:

S06 C[N][True] says [24] If N's final statement is True [it is] then my name is Lisa.

C = Lisa.

S12 K[N]{False] says [30] If all of us have made consecutive statements [they did: 1-2, 3-4, 7-8, 11-12] then I'm not Dave.

K=Dave.

S03 N[L][False] says [21] I'm not Iago.

N=Iago.

L=Andy.

Step 8. Solve the puzzle

L=Andy's final statement is S05.