Aliens Exist!

[Guest]

An alien, Jynor, lands and tells you that earth’s future is in your hands! Another alien, Mukl escaped from a high security intergalactic prison. Mukl is very, very evil and very, very dangerous. He’s being chased by yet a third alien, Qirit who is the only chance to stop Mukl. Jynor gives you a blaster and tells you that you must blast Mukl so Qirit can overcome him. If you accidentally blast Qirit though, Mukl will eat him and you and all of humankind are doomed.

To help you out, Jynor gives you the following information:

Mukl is a known Fosling and Foslings always lie. In fact, only Foslings lie. Qirit is a known Arfid and Arfids always tell the truth. Also, all Arfids are Borfids. Some Borfids are Arfids, and some are Cofids. All Cofids are Borfids. All Dorfids are either Borfids or Goslings. All Goslings are Foslings, but no Foslings are Borfids. If a Dorfid is a Borfid, he’s also a Huggl.

Later that day …

A spaceship crashes to the ground followed quickly by a second. Two aliens pop out. They see you and the first yells, “Don’t shoot, I’m an Arfid!” The second yells, “Don’t shoot, I’m an Arfid!” The first yells again, “I’m also a Borfid!” The second follows with, “blast him, he’s lying, he’s a Gosling!” The first retorts, “He’s the liar, he’s a Huggl Dorfid! Shoot him!”

They both then charge toward you. Which of the two do you blast and why?

[bonanova]

An alien, Jynor, lands and tells you that earth’s future is in your hands!

it was written in the high school men's room.Which of the two do you blast and why?

the second alien

I'll use initial letters, and denote first alien by [1] and second alien by [2].

Suppose [1] is M and [2] is Q.

Then the statements lead to this:

[1] is A, ^F, B and ^G

[2] is ^A, F, H, D -> BvG -- that is, [2] is B or [2] is G

Because No F's are B, that means [2] is G

which means .... OK I'm lost.

I think the clues aren't sufficient. Let me ask:

Does "Some Borfids are Arfids, and some are Cofids." allow for B's that are neither A nor C?

Does "only Foslings lie" and "All Goslings are Foslings" lead to a contradiction?

i.e. Goslings don't lie, because only Foslings lie, but Goslings do lie beacause they are Foslings?

This is interesting, but I'm stuck.

I'll revisit after some zzzzzzzzzzzzzzzz's

[Guest]

Just to clarify - Jynor told me that a Fosling is a Fosling by any definition. Therefore it doesn't matter what else you are, if you are a Fosling also you will always tell a lie.

In fact, only Foslings lie.

This is meant to exclude non-Foslings from being able to tell a lie.

[Guest]

You shoot the first one.

BECAUSE

The first ones last sentence is " he is a liar He is a huggl dorfid shoot him.

You would not shoot a non liar if you are chasing a liar.

[Guest]

Well, one of you is in deep trouble. Who is it?

[bonanova]

Using cap first letters for names. Blue is given; Red is conclusion.

M is F; F iff Liar

Q is A; If A then Truthteller.

----------------------

M will lie; Q will tell truth.

All A is B; Some B is A; Some B is C; All C is B.

All D is either B or G; All G is F; No F is B.

If DB then H.

----------------------

Truthtellers are A, B, C and H

Liars are F and G.

D's are mixed: and [G].

=============now the story==============

[1]: I am A. Innocuous. T or F.

[2]: I am A. Innocuous. T or F.

[1]: I am B. Innocuous. T or F.

[2]: [1] lies; [1] is G. Innocuous; consistent. Both T or both F.

[1]: [2] lies; [2] is H; [2] is D. Inconsistent. Cannot all be true.

[1] is M, and I shoot him.

[Guest]

... and Bona saves the world!

[bonanova]

You shoot the first one.

BECAUSE

The first ones last sentence is " he is a liar He is a huggl dorfid shoot him.

You would not shoot a non liar if you are chasing a liar.

I think this is very close to a solution.

On first read, I didn't appreciate how close. It is the last utterance that gives it away; the rest of what's said doesn't help us.

As it stands, tho, the imperative "shoot him" has no truth value, so it can't contradict anything.

But change it to a declarative "you should therefore shoot him" and it becomes an incorrect conclusion for "he is a liar."

[1] thus exposes himself as the liar.

... or a poor logician ... or a good candidate for Survivor! <!-- s;) --><!-- s;) -->

[Guest]

Ok, to explain this one.

Maybe my logic is off, as this is original work under stress of waiting for bar results

Ok, we have:

Mukl is a known Fosling and Foslings always lie. In fact, only Foslings lie. Qirit is a known Arfid and Arfids always tell the truth. Also, all Arfids are Borfids. Some Borfids are Arfids, and some are Cofids. All Cofids are Borfids. All Dorfids are either Borfids or Goslings. All Goslings are Foslings, but no Foslings are Borfids. If a Dorfid is a Borfid, he’s also a Huggl.

and

A spaceship crashes to the ground followed quickly by a second. Two aliens pop out. They see you and the first yells, “Don’t shoot, I’m an Arfid!” The second yells, “Don’t shoot, I’m an Arfid!” The first yells again, “I’m also a Borfid!” The second follows with, “blast him, he’s lying, he’s a Gosling!” The first retorts, “He’s the liar, he’s a Huggl Dorfid! Shoot him!”

We know one alien will always lie, and one will never lie.

Both say "Don't shoot I'm an arfid!" - We know one is lying and one is not. No help.

#1 is a Borfid - If he's a liar this is a lie, if he's a truth teller, it could be the truth - no help.

#2 says #1 is a Gosling and he's lying. This gets us somewhere as we know that Goslings will lie because all Goslings are Foslings and all Foslings lie. To make this statement untrue, you would have to separate the fact of being Gosling from the principal of lying. The and in the sentence logically connectes the two concepts, so this must be a truth. #2 just told a truth.

But just to make it more clear, #1 says that #2 is a Huggl Dorfid and a liar. We know that if a Dorfid is a Huggl, he's also a Borfid and Borfids don't lie. #1 just told an un-truth.

We have #2 telling a truth and #1 telling an un-truth. #1 must be Mukl, so blast him!

[bonanova]

#2 says #1 is a Gosling and he's lying.

This gets us somewhere as we know that Goslings will lie because all Goslings are Foslings and all Foslings lie.

To make this statement untrue, you would have to separate the fact of being Gosling from the principal of lying.

The and in the sentence logically connectes the two concepts, so this must be a truth. #2 just told a truth.

I missed that conclusion in my solution.

I took all the statements as red herrings except for the last one.

I guess I concluded that both of them would accuse the other, and so nothing could be made of that.

It's an interesting puzzle, and It took me awhile to understand it.

[Guest]

none of that matters. stop mapping it out. it complicates it. 2 quick read throughs of the puzzle tell you...

1) your roll is to kill the liar

2)huggle dorfids are not liars

3)alien #1 said the other alien is a huggle dorfid, shoot him.

4) if you shoot the huggle dorfid you are killing a non liar which is the exact opposite of your mission....

[Guest]

You are right. That is basically all we said, except to expose the red herrings for what they were and to show that there was a reenforcer in the truth teller telling a truth, as well as the liar telling a non-truth.

[bonanova]

none of that matters. stop mapping it out. it complicates it. 2 quick read throughs of the puzzle tell you...

1) your roll is to kill the liar

2)huggle dorfids are not liars

3)alien #1 said the other alien is a huggle dorfid, shoot him.

4) if you shoot the huggle dorfid you are killing a non liar which is the exact opposite of your mission....

#1 said the other alien was both a Huggle and a liar. Impossible. That reveals #1 as the liar.

The guidance from #1 that the other alien is a huggle dorfid is not reliable.

As I noted in previous post:

If we take #1's last statements to be a logical argument [because A is true, you must therefore do B]

then we can analyze the argument if we want, and in this case find we'd find the argument is not valid.

Then we might conclude that a truth-teller cannot state an invalid argument.

Two problems with that:

[1] I don't think #1's last statements are an argument. He made 2 independent statements.

[2] Stating an invalid argument may not be the same as lying.

The speaker would have to have further said ...

It is valid to conclude that because A is true, you must therefore do B.

That statement would be a lie. But those words are not in the OP.

Liars and truth-tellers are more reliable revealed by [a] the truth values of their statements than by the validity of their arguments.