No Knaves, No Knights

Logic Level 2

You have been awoken in an island full of people. A voice has been greeting your mind to certain information.

"All of these people surrounding you are jokers. I am a knight. You don't belong here, and I will help you get back to your world and your memory will return." said the voice.

Upon exploration, you find a secret underground basement, leading to 5 different portals. With knowledge, the voice tells you that one of these is the portal to your world.

You ask a random group of people about the basement. They respond with simple sentences.

Person 1: Person 2 is not lying.

Person 2: Person 3 is lying.

Person 3: Person 4, 5 and 7 tell the truth.

Person 4: The first portal leads to your world.

Person 5: Person 6 is lying.

Person 6: The third portal leads to your world.

Person 7: The fourth portal leads to your world.

Person 8: Only four of us are speaking the truth.

The voice in your mind tells you that Person 1 and Person 8 are speaking the truth.

Determine all of the people who are lying.

3, 4, 5, and 7 2, 5, 6, and 7 It is impossible to tell 7, 6, 2, and 3 2, 3, 6, and 4 6, 2, 4, and 7 3, 4, 5, and 6

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3 solutions

William Huang
Jul 19, 2017

The problem doesn't clearly state but assuming from past experiences of these type of questions, a knight always tells the truth and a joker can either tell the truth or lie.

The voice in your mind states that Person 1 and Person 8 are speaking the truth.

Person 1 states that "Person 2 is not lying" - which is true. So Person 2 is not lying.

Person 2 states that "Person 3 is lying" - which is true. So Person 3 is lying.

Person 3 states that "Person 4, 5 and 7 tell the truth" - which is false. So Person 4, 5 and 7 are all lying

Person 4 states that "The first portal leads to your world" - which is false.

Person 5 states that "Person 6 is lying" - which is false. So Person 6 is not lying.

Person 6 states that "The third portal leads to your world" - which is true. This is the portal we need to go through!

Person 7 states that "The fourth portal leads to your world" - which is false.

Person 8 states that "Only four of us are speaking the truth" - which is true. The question asks who is telling the truth. The voice in your mind originally stated that Person 1 and Person 8 are telling the truth so that's 2 people. Then, we have Person 2 and Person 6 who are also telling the truth. Person 8 said that four people were speaking the truth and it is in fact, true!

Our final answer is that Person 1, 8, 2 and 6 are telling the truth.

That person 3 lies and 'Person 4, 5 and 7 tell the truth' is false doesn't means that Person 4, 5 and 7 are all lying, it means that they three can't be saying the truth at the same time. Person 1, 2 and 8 tell the truth so there can only be one more person telling the truth. Person 5 states 'Person 6 is lying', so, or Person 5 tells the truth and Person 6 lies, or Person 5 lies and Person 6 tells the truth; both cases are possible so really it is impossible to tell.

Caleb Garcia Quispe - 3 years, 10 months ago

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Well, I think it only really depends on how you look at it. But from your point of view, yes, I agree with you. I think the writer should do something about it.

William Huang - 3 years, 10 months ago

The voice states that P1 and P8 are telling the truth. So there can only be 2 more people telling the truth since P8 says that only 4 Persons are telling the truth. If P2 is lying then P3 must be telling the truth. P3 says that P4, P5, and P7 are telling the truth, but if you add that to P1 and P8, that makes 5 Persons, when only 4 are telling the truth. So P3 is lying and P2 is telling the truth. So P3 lies that P5 is telling the truth, so now P5 is lying that P6 is lying. So P6 is telling the truth. We now have our four truth-tellers, who are P1, P2, P6 and P8.

The remaining persons are 3 , 4 , 5 , 7 \boxed{3, 4, 5, 7} .

Saya Suka
Apr 25, 2021

The third portal leads to your world.

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