Knights and Knaves argue with each other

Logic Level 2

You're a visitor on the island of Soldons, where there are only two kinds of people: Knights and Knaves. Knights always tell the truth and Knaves always lie. You are walking along a path when a group of four people approach. You ask one of them how many knights are there in the group. Instead, one of them mutters something,and another says: "He said he's a Knave." A third person says to the second person, "You're lying! He must have said he's a knight." The fourth person said to the third person,"Right you are."

So, can you work out how many knights can there be in the group?

Cannot be told 2 or 3 1 or 2 1,2 or 3 3 or 4

3 solutions

Www Www
May 6, 2016

Relevant wiki: Truth-Tellers and Liars

Everyone on the island will say that they're a knight, whether they're a knight or knave, because Knights always tell the truth and Knaves always lie. So the first person would've said he was a knight, whether he was a knight or knave. But the second person must be lying because he said that the first person said he's a knave, which couldn't be possible. So the second person must be lying, which means he's a knave. The third person said that the second person is lying, which is true, which means the third person is a knight. The fourth person said the third person is saying the truth, which is also true, which means the fourth person is a knight too. We cannot be sure if the first person is a knight or knave, so this equals that there are two or three knights in the group.

Saya Suka
Apr 26, 2021

The muttering / mumbling person is a possible knave while the second person is a confirmed knave. This amount to 2 or 3 Knights in the group.

Diana Bradish
Apr 14, 2020

Note: I’m going to assume that these 4 people are all boys. Reader(s), you can assume whatever you want.

Knights can’t lie and say they’re knaves, and knaves can’t tell the truth and admit that they’re knaves, so the first person must have said “I am a knight.” However, both knights and knaves can make this statement, so the first person is either a knight or a knave. (The “or” in the previous sentence is an exclusive “or”, not an inclusive “or”.)

The second person is obviously a knave, because he said that the first person said that he himself was a knave, and we already know that it’s basically impossible for any of the natives of Soldons to make the statement, “I am a knave” so the second person is lying, thus he is a knave.

This means that the third person is a knight, because he said that the second person was lying, and because the second person is a knave, that indicates that the third person is a knight!

The fourth person said that the third person was correct, and the fourth person was right! So that indicates that the fourth person is also a knight.

We still can’t figure out if the first person is a knight or a knave, but now we know what the types of the other three people are and what the answer is, which is 2 or 3 knights! Hooray! 🎉

Knights and Knaves argue with each other

3 solutions

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