Xan

Logic Level 2

In the country of Xan there are three classes of people:

Knights who always tell the truth.
Knaves who always lie and
Jesters who sometimes tell the truth and sometimes lie.

Alan, Brian, Calvin and Guillermo are 4 inhabitants of Xan. Alan says: "There are 3 knights among us." Brian says: "There are 3 knights among us." Calvin says: "There are 2 knights among us." And Guillermo says: "There are no knights among us."

What kind of person is Guillermo?

Guillermo is a Jester. Guillermo is a Knight. There is no sufficient information. Guillermo is a Knave. This is an impossible scenario.

3 solutions

Zee Ell
Mar 1, 2018

Alan and Brian cannot be Knights, since this would mean,. that the third Knight would also say that there are 3 Knights amongst them.

This leaves Calvin and Guillermo. Calvin cannot be a Knight either for similar reasons (Guillermo would have to say that there are 2 Knights amongst them).

Now, Guillermo cannot be a Knight, because then he would say that there is 1 Knight amongst them. So there are no Knights amongst them, which makes his statement true. This implies that Guillermo must be a:

$\boxed { \text {Jester} }$

Hm, I found it slightly difficult to follow your logic (though yes, it is all true). It might be better to phrase it as

If there were 3 knights, then (at least) 3 people will say "There are 3 knights among us". Since this did not happen, we conclude that Alan and Brian cannot be knights.
Similarly, we conclude that Calvin is not a knight.
Thus, if Guillermo was a knight, then he would say that there is 1 knight amongst us, so he is not a knight.
Since Guillermo spoke the truth and is not a knight, hence he must be a jester.

Generally, it can be tricky figuring out whether to state the conclusion first, or the supporting evidence first. In cases where the sequence of steps is short (IE 1 step for each of these mini-conclusions), then it is often to put the supporting evidence first. In cases where there are a lot of steps, it might be helpful to state the conclusion first, so that people have some sense of where it is headed.

Calvin Lin Staff - 3 years, 3 months ago

Chukwuka Odigbo
Apr 4, 2018

Alan and Brian are not knights.

By picking their statements,

if there are three knights among them, then a third person would attest to their truthfulness.

This shows they are Knaves or even Jesters, since they have lied.

Calvin is not a knight. By his statement, if there are two knights there, at least one should attest to his truthfulness. However, none did. He is a knave.

Guillermo, on the other hand, said that there was no knight present. He cannot be a knave, because if, in fact, he is lying; then there can be one or more knights there, and they should have said the truth.

Thus he is a Jester, and a truthful one at that.

Adios!

Saya Suka
Jun 16, 2019

More than half of the four men were making different statements on the same thing, about the same subject of the number of Knights among themselves. Amongst the four, there are three distinct statements, of which only one of those, at most, might be the truth. If one of the statements had to be the truth, then the number of people saying that there were n Knights amongst them MUST AT LEAST be n, and that's from the Knights who were there themselves. Remember that there could be more, from the truth telling Jester(s). Since both n(3 Knights) = 2 < 3 and n(2 Knights) = 1 < 2, then these must be lies. This leaves us with Guillermo who said none of them are Knights. n(0 Knight) = 1 ≥ 0, so it is validated for its truth value. Since G's no Knight statement is the truth, then he cannot be one, so he must be a truth telling Jester.

Xan

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