The Mother of all Truth-teller puzzles.

[bonanova]

[Caveat removed]

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 ...

[K] will tell the truth.
[N] statements will alternate in truth value; the truth 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.
[L] will lie.
[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,

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.

This deviant behavior is confusing, but it's predictable: 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:

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

Two of them, now senile and without any memory to speak of, immediately blurted out contradictory answers, as they always do.
Another, now deaf, answered easily after reading the question, but only because memory was still intact.
The last citizen, also deaf but with memory intact, needed a hearing aid to answer.

Each Citizen then made a series of statements - one statement on each of three consecutive days. Twelve statements in all. Here's what we know:

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

On days when more than one statement was made, the statements that day were ordered alphabetically 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] comes before [N].

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:

Note: Only declarative statements have truth value. Questions, exclamations and imperatives can logically be ignored.

01. Snazzlefartz!
02. Don't ask me what Snazzlefartz means. I never use that word.
03. Looking for Iago? Look somewhere else. He's not I.
04. Hi! I'm Lisa. Are you enjoying your visit to KNLC?
05. None of our initials agree with the initial letters of our real characters.
06. If the Knave's final statement is True, then my name is Lisa.
07. If the majority of these statements are True, then most of them are False.
08. If the Chameleon's final statement is false, then the Knight's first statement is true.
09. I hate having to appear in these puzzles. You'd think they'd at least pay us something.
10. I'm not Lisa. Can I leave now?
11. I'm not Lisa, either. Can I leave, too?
12. If all 4 of us have made at least two statements that appear consecutively in this list, then I am not Dave.

Now you should know the character types of the four Citizens and the order in which they spoke.

Which was Andy's final statement?
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_{Vidi, vici, veni.}

[jesternl]

And this took you how long to make up?

[Zag]

I saw there was a response to this thread and I thought, Oh good, at least somebody is willing to make a stab at this. But I guess not. It is clearly too much for me, though I admire the puzzle-making.

[bonanova]

[ralphmerridew]

Well, I guess the first question is On what day did everything start? And AFAICT, the answer must be Monday

The definition of Knave confuses me. Is the sentence about speaking in a group there for a reason? (There's also the fact that "Knave" is typically used for what you call a liar.)

I guess the second part is analyzing the Y/N question given before the others. That part really confuses me. My best guess is that it's supposed to mean that the four people are of different types. The knight and liar are the senile ones and can answer immediately. The knave answers next, needing only to remember his/her last statement. The chameleon needs the hearing aid, to know whether the knave told the truth or lied.

I'm not sure how the deaf / senile parts interact with the 12 statements. For example, can we be sure that the people who made statements 2 and 11 are not senile?

If all my logic up to this point is correct, I think the next step is go over the 24 possibly permutations of "person who spoke first on (mon, tues, wednes, thurs)" to (K,N,L,C). For each permutation, work out which person made each statement. Cross out any permutation that has a contradiction.

[bonanova]

RM,
You're right about Knave, but I've seen this defn as well. Chameleon is I think an original addition to the character types. You have the first two steps, and all your other points are spot on.

You ask two questions. The first is, Yes. The second was intended to be, It doesn't matter. But [my bad] in one case it does. I tweaked the statements to fix, but now I think it's too confusing to make changes.

So instead, just assume the Citizens wrote and signed their statements on a sheet of paper in the given sequence, and on the appropriate days. That removes the hearing and memory issue. We now see that paper, but with the days and signatures elided.
_________________
_{Vidi, vici, veni.}

[bonanova]

This puzzle has run its course and probably will stir up no additional apathy.
So ... giving it a proper burial ...

Step 1. Andy, Dave, Iago and Lisa are K, N, L C in some order.

Step 2. The statements were made Monday-Saturday staggered starts.

Step 3. The first-statement order of the four Citizens is LNCK

Step 4. The order of the statements is L[L] / L[C] N[L] / N[C] L[K] C[N] / K[C] N[K] C[L] / C[C] K[K] / K[N]

Step 5. The truth values of the statements are
S01 L[L] F
S02 L[C] F
S03 N[L] F
S04 N[C] F
S05 L[K] T
S06 C[N] T (F)*
S07 K[C] T (F)*
S08 N[K] T
S09 C[L] F
S10 C[C] F
S11 K[K] T
S12 K[N] F

Step 6. S06 and S07 are T So the four Citizens' statements are
L: F F T
N: F F T
C: T F F
K: T T F

Step 7. S06 C=Lisa. S12 K=Dave S03 N=Iago. L=Andy

Step 8. L=Andy's final statement is S05.
_________________
_{Vidi, vici, veni.}