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## Question

In the familiar Land of Knights and Knaves [LKK], Knights could be

always counted on to tell the truth, and Knaves would reliably lie.

That's how it was. But then a careless tourist, infected with the rare

averitas flu virus, visited LKK to solve a puzzle; and some of the inhabitants

were hit. Immediately their behavior was reversed: Sick Knights found

themselves incapable of truth, and infected Knaves could no longer lie!

As it turns out, the AFV vaccine is very costly, and only those verified

to be sick can be given shots. You have been assigned by FEMA to

determine those who truly need shots and, if possible, to sort out

the Knights from the Knaves.

To start things off, a group of six LKK citizens is brought to your office,

and they venture the following information:

A: Exactly three of the others are sick. B is not to be trusted.

B: Exactly three of the others are Knaves. You can trust C.

C: Exactly three of the others are well. D lies through his teeth.

D: Exactly three of the others are lying. E is one of them.

E: Exactly three of the others are Knights. F can be trusted.

F: Unintelligible. [An emergency helicopter drowns out F's voice.]

How many shots do you give, and to whom?

And who are the Knaves?

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A = Sick Knight

B = Healthy Knight

C = Sick Knave

D = Healthy Knave

E = Sick Knave

F = Healthy Knave

First step was to figure out who was telling the truth and who was lying. I started by assuming that A was telling the truth, but that led to a contradiction. Then I knew that A was a liar, and from that followed that D was also a liar and the others were truth tellers.

Knowing that B and E were truth tellers, by their statements I knew that B was a Healthy Knight and E was a Sick Knave.

From there I tried to deduce things, but it got confusing, and so I wrote out all the remaining possibilities (there were only 16 at that point... 4 unknowns and 2 choices for each) and applied the original statements to see that only one solution was left.

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To find out who tells the truth and who lies, following the trail of what they say about each other's honesty puts them into two camps: A & D on one side, B,C,E and F on the other. D's statement that exactly 3 of the others are lying cannot be true in this case, so A & D are the liars.

B's statement tells us there are at least 3 knaves. E's statement tells us there are at least 3 knights. So there are 3 of each, and B must be a well knight and E a sick knave.

C tells us that 3 of the others are well. We know B is well and E is sick, so that leaves two healthy specimens among A, D, and F and only one sick one.

A,C,D and F must consist of two knights and two knaves. There are also two liars and two truth tellers, so there must be an even number of sick cases, split evenly between knights and knaves.

There is only one sick member in A, D and F, so C must be sick, and a knave. It also means that the one remaining sick case is a liar (a sick knight), so F must be a healthy knight.

That leaves A and D, one of whom is a sick knight and one is a healthy knave. A's statement tells us which is which. If D were sick he would be telling the truth.

A: sick knight

B: healthy knight

C: sick knave

D: healthy knave

E: sick knave

F: healthy knight

It seems the gauntlet has been thrown down. I shall return! huh huh. ha ha ha. MUHAHA!! MWUHAHAHAHAARGH!!!! (but not for a few days coz I'm off skiing)

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Kudos to schmod54 and octopuppy <- don't break a leg .... !.

Perhaps I was too easy with this one ...

There will be others.

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