Who are the space adventurers?

Question

I got this puzzle from a friend and thought it was a good one for this community:

In this space adventure, women from Neptune and Men from Jupiter always speak the truth, while men from Neptune and women from Jupiter always lie.

In this adventure, beings from Neptune and Jupiter live alongside each other. You’ll even find that pairs, consisting of one woman and one man, do not need to come from the same planet!

However, us earthlings are unable to determine if a being is from Neptune or Jupiter based on external features, and we're also unable to see or hear if it's a man or a woman we're talking to.

On one occasion, we meet a couple. We’ll call them A and B. They make the following statements: 


A: We are both from Neptune. 


B: No, that's not true!

Who is a man?

Answer 1

First, note that

A and B come from the same planet.

This is because

a man and a woman coming from different planets are either both honest people or liars. Since they are saying two opposite things, one and only one of them is telling the truth.

Now, we just need to check for two cases:

1. They're both from Neptune. Then A is telling the truth and B is lying, so B is the man.

2. They're both from Jupiter. Then A is lying and B is telling the truth, so B is the man.

Conclusion:

B is the man.

Answer 2

Assuming A and B are both from either Neptune or Jupiter (and not from a third planet) and both either Woman or Man (and no other gender)

There is, a priori, 16 combinations: WNWN; WNWJ; WNMN; WNMJ; WJWN; WJWJ; WJMN; WJMJ; MNWN; MNWJ; MNMN; MNMJ; MJWN; MJWJ; MJMN; MJMJ

The first sentence informs us that

They can't be both from Neptune and A being a man, because then the sentence would be true but said by a man from Neptune. This removes the MN.N combinations. Nor can one of them be from Jupiter while A being any combination that would make them truthful. This removes WN.J and MJ.

About the second sentence:

This simply means that A and B have a different "truthiness", so it only allows WNWJ, WNMN, WJWN, WJMJ, MNMJ, MNWN, MJMN, MJWJ.

When we put that together:

That leaves WNMN, WJWN, WJMJ, MNMJ. If we are looking for a Man then our best bet is B since, in the only case where B isn't a Man (WJWN), A isn't either.

Answer 3

One of the answers has to be true and one has to be false since B is calling A a liar. Either A is a liar and B is speaking the truth, or A tells the truth and B is lying by calling A a liar.

If we assume A is telling the truth, then they are both from Neptune. With people from Neptune, Women tell the truth and Men lie, so A is a woman and B is a man.

If we assume B is telling the truth, that is more difficult. We know A is lying, and by that we know they can't both be from Neptune.

As a liar, A must then be either a Man from Neptune or a Woman from Jupiter. As someone that tells the truth, B must be either a Woman from Neptune or a Man from Jupiter. If A is a Man from Neptune, then B cannot be a Woman from Neptune since the statement made by A is a lie, so B must be a Man from Jupiter. If A is a Woman from Jupiter, then B could be either a Woman from Neptune or a Man from Jupiter.

So we have several combinations:

1. Woman from Neptune, Man from Neptune
2. Man from Neptune, Man from Jupiter
3. Woman from Jupiter, Woman from Neptune
4. Woman from Jupiter, Man from Jupiter

Since the question states:

You’ll even find that pairs, consisting of one woman and one man, do not need to come from the same planet!

So, we are left with only two viable options:

1. Woman from Neptune, Man from Neptune
2. Woman from Jupiter, Man from Jupiter

And in both cases:

The Man is B