17 replies to this topic

[bonanova]

In the land of Truth-tellers, Liars and Alternators, every citizen either always answers truthfully T,
always answers falsely L, or alternates true and false answers A. You encounter, and find yourself
extremely attracted to, a citizen. Before exploring a possible relationship, however, you wonder
whether you'll be dealing with a T, L or A. You may ask a number of yes/no questions to satisfy
your curiosity.

How many questions will it take?

[ujjagrawal]

Spoiler for Please use spoilers

In maximum 2 questions

1. Are you a alternator ?
2. Are you a Truth-teller?

based upon the answers -
If respective answers are - no, yes -> Truth-teller
yes, yes -> Liar
yes,no or no,no -> Alternator

[witzar]

Spoiler for ...

Two questions:
1. Is 2+2=4?
2. Is 2+2=4?

[bonanova]

Both right.
witzar's solution has the following

Spoiler for advantage

In the case of an Alternator, you know the parity of the alternation.
This is a great piece of information, should there be continued dialog.

[翁馬克]

There is a

Spoiler for flaw in ujjagrawal's logic

...or do I misunderstand it?
Let the person we are talking to be an Alternator and assume he is in the state where his next answer is the truth.

1. Are you an alternator? Answer: Yes
(Now, his next answer will be false.)
2. Are you a truth-teller? Answer: Yes.

According to ujjagrawal, he would now be considered a Liar, but he is an Alternator!

[WitchOfDoubt]

One question.

Spoiler for More than one bit of information, though

"Let's suppose that truthtellers are the opposite parity of liars. If I were to ask someone of the opposite parity of you whether they were a truthteller, what would they say - yes or no?"

A truthteller says "yes". A liar says "No." An alternator can't answer one way or the other, because the question is ill-defined for them.

[omthkkr]

Spoiler for Hint - Concentrate on the alternator

Answer is 2 - 1) Are you the alternator? 2) Are you the alternator? Yes & Yes = Liar Yes & No or No & Yes = Alternator No & No = Truth teller

Edited by omthkkr, 25 May 2012 - 12:02 PM.

[bonanova]

One question.

Spoiler for More than one bit of information, though

"Let's suppose that truthtellers are the opposite parity of liars. If I were to ask someone of the opposite parity of you whether they were a truthteller, what would they say - yes or no?"

A truthteller says "yes". A liar says "No." An alternator can't answer one way or the other, because the question is ill-defined for them.

I'm not sure why that question is Ill-defined for an Alternator.

Spoiler for Specifically

Let's do the thought experiment of first asking the the Alternator two questions 
1. Is 2 + 2 = 4?
2. Is 2 + 2 = 4?
And suppose his answers were Yes and No; then his next answer would be truthful. Thus a person, also an Alternator, of the opposite parity, call him an OPP, would next answer falsely, and if asked about being a T would answer Yes. So the truthful answer of the Alternator being questioned would be that the OPP would say Yes.

If the thought experiment answers had been No and Yes, then the Alternator's next answer will be false. The OPP would then next answer truly, and when asked about being a T would answer No. The false answer of the Alternator would then be that the OPP would answer Yes.

Thus an Alternator answers the proposed question just as a T would, and the question can't discriminate between the two, even if asked twice.

Two things can be noted: we must presume an Alternator remembers the truth value of his last statement, else he doesn't know how to answer any question at all. Given that, he can determine how to answer every question, alternately emulating a T or L.

[bonanova]

There is a

Spoiler for flaw in ujjagrawal's logic

...or do I misunderstand it?
Let the person we are talking to be an Alternator and assume he is in the state where his next answer is the truth.

1. Are you an alternator? Answer: Yes
(Now, his next answer will be false.)
2. Are you a truth-teller? Answer: Yes.

According to ujjagrawal, he would now be considered a Liar, but he is an Alternator!

You're right.

[phil1882]

Spoiler for my question

confuse the hell out 'em!
"how would the lair respond to the following question, "are you an alternator?""
it would be quite interesting seeing what the liar says.
no matter what he says he is telling the truth.