Knights and Knaves (Logic Puzzle)

this is for an extra credit thing. I don't actually HAVE to figure this out, but I want to, and I'm sure a few of you find this sort of thing interesting.

Ok so if you're not familiar with Knights and Knaves logic puzzles, the premise is this: On this island, there are two types of people. Knights, and knaves. Knights -always- tell the truth, and knaves -always- lie. So if a knight says P, P is true. If a knave says P, P is false, or, Not P is true. Simple.

K, so this is the puzzle:

You want to know whether there is any gold on this island.
You meet one person, A, but you don't know whether A is a knight or a knave. You can ask A one yes/no question.

What question can you ask that will tell you if there is gold on the island?



I'm usually pretty good with these puzzles, but this is the only one I can't get. If anyone would like me to post simpler puzzles (most of the other ones aren't like this, they're more like, determine who is a knight and who is a knave depending on what they say, save for one which is in the same vein as this one), let me know. It may be easier to think about this one if you get better acquainted with those.

thanks.

Is this not the same answer as the "What door do I go through?" version of the puzzle?

So, you ask: "Would someone who is of the opposite allegiance to you say this island has gold?"

Let's say the island has gold:
A Knight would know that Knave would say "no", and so would say "no".
A Knave would know that a Knight would say "yes", and so would say "no".

If the island has no gold:
A Knight would know that a Knave would say "yes" and so would say "yes"
A Knave would know that a Knight would say "no" and so would say "yes".

Originally Posted by John

A Knight would know that Knave would say
A Knave would know that a Knight would say
A Knight would know that a Knave would say
A Knave would know that a Knight would say

It doesn't matter what the other would say.
Knights ALWAYS tell the truth.
Knaves ALWAYS tell the lie.

Originally Posted by Glutexo

It doesn't matter what the other would say.
Knights ALWAYS tell the truth.
Knaves ALWAYS tell the lie.

Not in the standard version of the puzzle, no.

The most classic is the "Which door" puzzle, which is like this:
You come across two doors. Previously a Knight had told you that behind one of them was instant death and the other lead to paradise, but he refused to tell you which door to go through.

Standing in front of these two doors are two people. You know that one of them is a Knight, one a Knave.

You are allowed to ask one question to figure out which door to go through.

The best question to ask is: "What door would the other person tell me leads to paradise?" No matter which one you ask, they will point to the wrong door because if you ask the Knight he'll truthfully tell you what the Knave would say (which is the wrong door) and if you ask the Knave he'll lie about what the Knight would say (and so point you to the wrong door.)

This seems like it could work similarly, so long as you are allowed to ask my question. (I'm not sure if "What would someone with the opposite alignment as you say?" is actually a valid question to ask in these puzzles.)

Originally Posted by John

Not in the standard version of the puzzle, no.

The most classic is the "Which door" puzzle, which is like this:
You come across two doors. Previously a Knight had told you that behind one of them was instant death and the other lead to paradise, but he refused to tell you which door to go through.

Standing in front of these two doors are two people. You know that one of them is a Knight, one a Knave.

You are allowed to ask one question to figure out which door to go through.

The best question to ask is: "What door would the other person tell me leads to paradise?" No matter which one you ask, they will point to the wrong door because if you ask the Knight he'll truthfully tell you what the Knave would say (which is the wrong door) and if you ask the Knave he'll lie about what the Knight would say (and so point you to the wrong door.)

This seems like it could work similarly, so long as you are allowed to ask my question. (I'm not sure if "What would someone with the opposite alignment as you say?" is actually a valid question to ask in these puzzles.)

Ah. I think I understand what you're saying now.
At first your answers didn;t seem to answer the question, but I get it now.

Ahhh thank you. That seems so obvious. I hadn't heard of the door one. There is a puzzle that came after this one that is maybe sort of similar..?

It said there was an inhabitant, unidentified, and behind them was two paths. One leads to knights, one to knaves. You can ask one yes/no to find out which is knights.

I just said that you point to one path and ask them if that's where they're from. If it leads to knights they'll say yes if they're a knight or knave (because the first yes would be the truth, the second the lie), and the same idea if they say no. Although now I'm wondering if I'm allowed to include the pointing part in the question, but I don't see why not.

I don't know if you're method of answering my original puzzle would work for this though. I would figure it out but I have class. -.- I feel like it could work though, but I would have to write it out to make sure.

Anyway thanks so much again. I feel silly for not thinking it but now I'll have the concept of asking about the opposite alliance in my head for future puzzles.

Ask: Am I standing beside you?
Knight's answer: yes
Knave's answer: no

Originally Posted by bolter1

Ask: Am I standing beside you?
Knight's answer: yes
Knave's answer: no

But there goes your one question, so you can't then ask if there's any gold.