Data inadequate

Logic Level 2

There are two doors $\text A$ and $\text B$ , and two individuals are before the doors. One door leads you to $\text{treasure and happiness}$ while the other leads you to $\text{sadness and misery}$

One of the individual always lies , while the other always tells truth .
You are supposed to ask only one question to any one person .

Can you get to the door containing $\text{treasure and happiness}$ ?

If you think there's a way out, provide a solution as to what question you would ask. If you think there's no way out, provide a proof explaining why. And if you think that the data is inadequate, explain what should be added to the question.

My friend had asked me this question.

Yes None of these choices No Data inadequate

2 solutions

Sravanth C.
Jul 12, 2015

Yes. There's a way out. You just need to ask:

Where would the other person point when asked, to point the door containing treasure and happiness?

So, we can consider these two cases:

$1$ : If we ask this question to the truth teller, he would point the door containing $\text{sadness and misery}$ .

$2$ : If we ask this question to the liar, he would also point the door containing $\text{sadness and misery}$ .

Now, we know that both the individuals point the wrong door, we will choose the other door and get what we need!

Moderator note:

Yes. In questions like this, it's (almost) always better to frame your question in the form of asking what another person will do (or will not do).

Here's an unsolicited advice on setting up questions like this:
It's always better to set your answer choices as
1. "Yes, by doing action X"
2. "Yes, by doing action Y"
3. "Yes, by doing action Z"
4. "No, it's not possible"

This lets the reader ponder on whether action X, Y or Z are applicable instead of making a wild guess and hoping that "Yes" is the correct answer. It is very unlikely the answer is no given that you have already set up a very strict constraint, "You are supposed to ask only one question to any one person". So it's not a bad guess to think that the answer is yes. However, do not give away the full answer in the given choices, else readers will just apply trial and elimination to solve your problem which defeats the purpose of this question.

In this case, you should frame your correct answer choice as "Yes, we should ask one individual what the other individual would do given a certain circumstance".

Interesting question nonetheless, keep sharing more problems! Thank you!

Firdous Fatma
Jul 14, 2015

We have to ask that what the other person would say So we have two cases 1. if we ask truth teller then he would say the path sadness and misery. 2. if we ask liar he would also choose the door of sadness and misery. So we can choose up

Data inadequate

My friend had asked me this question.

2 solutions

Moderator note:

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