Let's trick the brain

Knight always tells the truth so the Knight is either A or C.
Since the Knave always lies, it must be that the Knave is A or C.
This leaves only B, so the Jester is B.

B's statement "I am the knave" obviously mean he's not the knave, otherwise he's telling truth, also not a knight since if he is, he has just lied. Thus, B is a jester.

Take two cases.. 1.if A says true .this will lead to B is jester 2.if A lies, this will again lead to that B is jester Work it out!

Neither a knight or a knave can say that he is a knave so it is B

• Knight always tells the truth.

• Knave always lies.

Now,

Knight must be either A or C

Knave must be A or C

Now only B is left

Therefore B is Jester.

We need to find friend B, so let's just focus on him.

If friend B is a knave, he would say that he is a joker or knight, which makes it impossible to for B to be a knave. The same goes if friend B is a knight. If he is a knight, he could only say that he is a knight, so he's impossible to be a knight, too. Now we obviously know that friend B is a joker, but let's see why. The joker could either say a lie or the truth, but in this case, the joker lied because if the joker said the truth, he could only say that he is a joker, which is impossible to be a knave. On the other hand, if he lied, then he could only saw that he is a knight or a joker, which means it is possible to say he is a knave.

So, this means that friend B is a joker.

Knights always tell the truth, Knaves always lie, and Jesters can do both.

A can be any three, since this statement would work for all three of them.

If B was the Knave, they would not say that they were the Knave since Knaves always lie. They also can't be a Knight since Knights will always tell the truth. So by process of Elimination, B must be the Jester.

(If you wanted to make sure, here's why C isn't the Jester)

C made the same statement as A, so we could only find out that C was not the Jester by looking at B's statement.

Let's just assume that A=Knight , B= Knave C= Jester. Now read the conditions. A says I am not Knave, and he is telling the truth. B says I am the Knave and he is telling the truth ( which doesn't meet the condition since Knave always lies). So that leaves us with only one option. B is not Knave, B is Jester ( who can lie or say the truth. But in this case, he is lying). C is Knave but since he always lies so he is saying that he isn't Knave (which is a lie) !!.

Knight would tell the truth so he's either friend A or C. Knave, however, will lie so there's a 100% chance that he will say that "he's not the knave." That would mean he could also be either friend A or C. Now, if Knight and Knave could be both A or C, that tells us that friend B is definitely the Jester.

If b is the liar, then he would say he is not the Knave. If he was A, the same thing happens. No Knave or Knight says that they are the Knave. B says that he is the Knave, so B is the Jester.

Since the knight always tells the truth, the knight is either A or C. Since knaves always lie, they would claim to not be a knave as well, making them A or C as well. This leaves B, which is a statement neither knights or knaves will ever make.

if B is a knave it will be paradox, if B is a knight it will be also paradox, so B is a jester

One of the earlier questions said that, if on an island with knights and knaves, you will always get “No” to the question “Are you a knave?” Therefore, B, who said he was a knave, must not be a knight or a knave, and is the jester.

Knave will say I am not a knave because it always say lies. Knight will say I am not knave it always say the truth.Neither knight or knave will say I am the knave. So the answer is B.

Earlier in this same challenge they state that the knights and knaves can't actually say "I am a knave." Therefore, the Jester must be B.

B is impossible for either a Knight or a Knave to say. A knight cannot say they are a Knave, and a Knave cannot say it is a Knave. The only one capable of making the statement that they are a Knave is a Jester.

In this case, we also cannot tell which is the Knight or the Knave. We only know they are NOT B, and that if one of them is a Knave, then the other is the Knight. B also only tells us that A and C are not the Jester, but nothing else as to which they might be

As the knight always tells the truth, he/she is either A or B, but let's assume it's A for the sake of this explanation. That leaves B and C, and since the knave will always lie, he won't say that he is the knave, meaning C is the knave, which leaves B, the Jester. Two reasons for why this is,

• That's the only option left
• The jester can either lie or be truthful, he takes the lying route which only the knave and jester can do, and it has already been established that the knave will never tell the truth, so it's B.

This one is quite simple.

Simply look at $B$ 's statement. If $B$ were the Knight, $B$ would be lying which is impossible. Similarly, if $B$ were the Knave, $B$ would be telling the truth which is impossible. This implies that $B$ is a Jester.

Because the knave always lies we know that he will always say he isn't not the knave. Therefore he cannot be B and is either A or C. The knight always tells the truth so he will always say he is not the knave. Therefore he is not B either. So we know that the jester must be B.

The Knight can either be A or C as he always tells the truth.

The Knave can also be A or C as he always lies.

The Jester must be B as he can lie or tell the truth, and is the only remaining option.

The Knight will always tell the truth, thus their response will be 'I am not the Knave', from the responses listed.

The Knave will always lie, this their response will also be 'I am not the Knave', from the responses listed.

As a result, only one response remains, that of 'I am the Knave'. This is a possible response of the Jester, and also the only remaining possibility.

The Jester is B.

B must be the Jester, since it would otherwise lead to a contradiction (of the kind "This sentence is false")