Waste less time on Facebook — follow Brilliant.
×

Lying guard

You are traveling in a land where every inhabitant either always lies or always tells the truth. You come across two caves: in one lies treasure and in the other lies certain death. There is a guard in front of the caves, and a sign announcing that the guard will answer one yes/no question to any traveler.

You don't know whether the guard tells the truth or lies - what single yes/no question should you ask the guard if you want to find the treasure? (Or try to show that it is impossible for you to determine which cave has the treasure.)

I thought of this independently, but presumably someone has come up with this problem before.

Note by Maggie Miller
2 years, 4 months ago

No vote yet
1 vote

  Easy Math Editor

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 \( 2 \times 3 \)
2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
\frac{2}{3} \( \frac{2}{3} \)
\sqrt{2} \( \sqrt{2} \)
\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

Comments

Sort by:

Top Newest

"If I ask you whether the left cave has treasure, would you answer Yes?"

Vincent Miller Moral - 2 years, 3 months ago

Log in to reply

That's what I was thinking! :)

Maggie Miller - 2 years, 3 months ago

Log in to reply

is there more then one cave with treasure?

Rex Holmes - 1 year, 3 months ago

Log in to reply

Choose a random route, and ask him : You people have two kinds of folks, liars and truthful. If I asked one of the other kind of people if this is the right way he would say yes. Am I right?

If it was the right way: Liar: No Truthful: No

if it was the wrong way: Both will say yes.

Sherif El-Sabbahy - 2 years, 4 months ago

Log in to reply

Oh, I didn't think about just reducing it to two guards. That does the care of the problem, though.

Maggie Miller - 2 years, 4 months ago

Log in to reply

I don't really get what you mean by reducing it to two guards but yea I think this works out the problem. Took me a while though haha

Sherif El-Sabbahy - 2 years, 4 months ago

Log in to reply

@Sherif El-Sabbahy Well, there's a very famous problem where there are two guards: one who lies and one who tells the truth. The strategy there is to ask one guard what the other would say if asked if the left cave had treasure - which is essentially your answer here

Maggie Miller - 2 years, 4 months ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...