# The Naked Scientists Forum

### Author Topic: Riddle/ logic puzzle  (Read 3811 times)

#### harryneild

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• Posts: 88
##### Riddle/ logic puzzle
« on: 12/03/2006 23:53:45 »
Ok lets see if the brain boxes of this forum know the answer to this puzzle!

You have died and before heaven there are two identical doors. In front of each door there is a guard. Both guards are identically looking. The one guarding the door to heaven will always tell the truth. The one guarding the door to hell will always lie. If you can ask them 1 question which they both answer, in order to find out which door is which, what do you ask them?

"Knowledge has to be improved, challenged, and increased constantly, or it vanishes." Peter F. Drucker
« Last Edit: 05/04/2007 22:17:12 by harryneild »

#### neilep

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##### Re: Riddle/ logic puzzle
« Reply #1 on: 13/03/2006 00:26:00 »
This is an oldie but a goodie and has many variations and for the life of me I can't remember the answer but it's something along the lines of asking each one something like  "If I ask the other guard will he tell me the truth(or tell me a lie)...something like that....

...am i close ?

#### another_someone

• Guest
##### Re: Riddle/ logic puzzle
« Reply #2 on: 13/03/2006 05:06:08 »
It is an old question, with a number of variations.

The solution is fairly straight forward.

Regard the two guards as logic circuits, one will invert the answer, and the other will give a positive result.  If you feed a response through both circuits, you will get a single negation (this is true no matter which order the response passes through).

Thus you ask one guard what the other guard would have said (thus, either the first guard will invert the answer, and the second will just pass the answer through; or the first guard will pass the answer through, and the second will invert the answer; in either case you know the answer will have been inverted only once).

This if you ask one guard to tell you what answer the other guard would have told you, you know that the answer you will get is the exact inverse of the truth.

George

#### harryneild

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• Posts: 88
##### Re: Riddle/ logic puzzle
« Reply #3 on: 13/03/2006 07:56:19 »
yep lol. You've got it. I thought it was quite interesting. Heres another i put to you lot :) -

Argentine, Brazil, Colombia, Dominican Republic and Equator competed at the Olympic Games, placing first through fifth in an event. They said:

Argentine: "I was not last."
Dominican Republic: "Equator got silver."
Equator: "Dominican Republic didn't get gold."

The gold and silver winners lied, but the other three told the truth. How did the event end?

"Knowledge has to be improved, challenged, and increased constantly, or it vanishes." Peter F. Drucker
« Last Edit: 05/04/2007 22:16:50 by harryneild »

#### another_someone

• Guest
##### Re: Riddle/ logic puzzle
« Reply #4 on: 14/03/2006 01:28:04 »
quote:
Originally posted by harryneild

Argentine, Brazil, Colombia, Dominican Republic and Equator competed at the Olympic Games, placing first through fifth in an event. They said:

Argentine: "I was not last."
Dominican Republic: "Equator got silver."
Equator: "Dominican Republic didn't get gold."

The gold and silver winners lied, but the other three told the truth. How did the event end?

Harry Eakins

"Knowledge has to be improved, challenged, and increased constantly, or it vanishes." Peter F. Drucker

I assume you are referring to Ecuador, not equator.

That apart, Argentine cannot be lying, because for it to have told a lie it must have come last, and you have said that only the top two lied.  Thus the Argentine must have been in position 3 or 4.

Clearly, Brazil could not have git the Bronze, since it claimed Canada got the Bronze.  If Brazil is telling the truth, then the Bronze has already been taken, and it could not take it; if it was lying, then Brazil must have got Gold or Silver, and so it did not get Bronze.

If we assume that the Dominican Republic is telling the truth, then it means that Ecuador has silver, and thus Ecuador is lying.  This means that when Ecuador is saying that the Dominican Republic did not get gold, it is lying.  This would imply that the Dominican Republic did get gold, which means that the Dominican Republic is lying.  This clearly is an untenable paradox, thus the assumption that the Dominican Republic is telling the truth is a false assumption, thus requiring that the Dominican Republic got gold or silver, and also requiring that Ecuador did not get silver.

The fact that we now know Ecuador is in one of the first two positions tells us that Canada is telling the truth, and thus Canada is not in one of the first two positions.

If we assume that Ecuador is lying, then it implies DR did get gold, which implies that Ecuador got silver.  But we know that Ecuador did not get silver, so Ecuador must be telling the truth, and DR got silver, and Ecuador was not in the top two positions.

So we now know that Canada, Ecuador and the Argentine are all telling the truth, thus only Brazil can still be lying.  Thus Brazil must have got gold.

If Brazil is lying, it means that Canada did not get Bronze, and so must have taken position 4 or 5.

We know that Ecuador was not in the top two positions, but was above the Argentine, thus Ecuador must be position 3, and the Argentine position 4, leaving Canada in position 5.

Thus:

A: position 4 (truthful : A < 5)
B: position 1 (false: C = 3)
C: position 5 (truthful: A > E)
D: Position 2 (false: E = 2)
E: Position 3 (truthful: D != 1)

George
« Last Edit: 14/03/2006 01:35:16 by another_someone »

#### The Naked Scientists Forum

##### Re: Riddle/ logic puzzle
« Reply #4 on: 14/03/2006 01:28:04 »