Jump to content


Welcome to BrainDen.com - Brain Teasers Forum

Welcome to BrainDen.com - Brain Teasers Forum. Like most online communities you must register to post in our community, but don't worry this is a simple free process. To be a part of BrainDen Forums you may create a new account or sign in if you already have an account.
As a member you could start new topics, reply to others, subscribe to topics/forums to get automatic updates, get your own profile and make new friends.

Of course, you can also enjoy our collection of amazing optical illusions and cool math games.

If you like our site, you may support us by simply clicking Google "+1" or Facebook "Like" buttons at the top.
If you have a website, we would appreciate a little link to BrainDen.

Thanks and enjoy the Den :-)
Guest Message by DevFuse
 

Photo
- - - - -

Aliens Exist!


  • Please log in to reply
12 replies to this topic

#1 Writersblock

Writersblock

    Senior Member

  • Members
  • PipPipPipPip
  • 597 posts

Posted 15 November 2007 - 09:43 AM

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?
  • 0

#2 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5705 posts
  • Gender:Male
  • Location:New York

Posted 15 November 2007 - 02:15 PM

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
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#3 Writersblock

Writersblock

    Senior Member

  • Members
  • PipPipPipPip
  • 597 posts

Posted 15 November 2007 - 08:17 PM

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.
  • 0

#4 Linzd21

Linzd21

    Junior Member

  • Members
  • PipPip
  • 37 posts

Posted 16 November 2007 - 12:03 AM

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.
  • 0

#5 Writersblock

Writersblock

    Senior Member

  • Members
  • PipPipPipPip
  • 597 posts

Posted 16 November 2007 - 01:06 AM

Well, one of you is in deep trouble. Who is it?
  • 0

#6 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5705 posts
  • Gender:Male
  • Location:New York

Posted 16 November 2007 - 02:18 AM

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: [B] 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.
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#7 Writersblock

Writersblock

    Senior Member

  • Members
  • PipPipPipPip
  • 597 posts

Posted 16 November 2007 - 04:53 AM

... and Bona saves the world!
  • 0

#8 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5705 posts
  • Gender:Male
  • Location:New York

Posted 16 November 2007 - 05:31 AM

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;) -->
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#9 Writersblock

Writersblock

    Senior Member

  • Members
  • PipPipPipPip
  • 597 posts

Posted 18 November 2007 - 08:08 PM

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!
  • 0

#10 bonanova

bonanova

    bonanova

  • Moderator
  • PipPipPipPip
  • 5705 posts
  • Gender:Male
  • Location:New York

Posted 19 November 2007 - 04:49 PM

#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.
  • 0
The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




0 user(s) are reading this topic

0 members, 0 guests, 0 anonymous users