# Logic puzzles

#### gbm46

Joined May 6, 2007
47
I quite like logic puzzles and hopefully you havent seen them, ill start off with the Wason selection task, simple yet hard-

[wikipedia]
Devised in 1966 by Peter Cathcart Wason,[1][2] the Wason selection task is a logical puzzle which is formally equivalent to the following question:

You are shown a set of four cards placed on a table each of which has a number on one side and a coloured patch on the other side. The visible faces of the cards show 3, 8, red and brown. Which cards should you turn over in order to test the truth of the proposition that if a card shows an even number, then its opposite face shows a primary colour?

A response which identifies a card which need not be inverted, or a response which fails to identify a card which needs to be inverted are both incorrect.

#### Dave

Joined Nov 17, 2003
6,969
Is there a limit on how many cards can you turn over at the first attempt?

Dave

#### gbm46

Joined May 6, 2007
47
no just select the cards that you need to answer the problem but dont select cards that are not needed, flipping unecessary cards is incorrect

#### bloguetronica

Joined Apr 27, 2007
1,541
This seems to be a trick question. You turn the card with the number 8. Then you must have a primary color on the other side. If you turn the red card, it also must show a even number. Only that way a equivalence between an even number and a primary color can be shown, since an equivalence is shown by two implications. Also, the card with a three or the brown card won't need to be turned (they are irrelevant).

P.S.: Is red a primary color or a primary light? It seems to me that it is a primary light!

#### recca02

Joined Apr 2, 2007
1,212
A response which identifies a card which need not be inverted, or a response which fails to identify a card which needs to be inverted are both incorrect.

i m really confused by these lines. can you explain which responses are not valid with an example if its not asking too much(in terms of giving a lead for solving the puzzle).

#### Eddy Kurent

Joined Apr 9, 2007
18
Red is a primary color. Turn over the red card, if the number is even, you have proven the supposition. redeven=1

Joined Aug 11, 2005
105
For the proposition to be true, the 8 must have a primary colour on the other side, and the brown must have an odd number on the other side. Don't turn the 3 or the red because they are irrelevant.

#### gbm46

Joined May 6, 2007
47
Next one - very hard. I think I may have also found this on wikipedia but it wasnt worded fantastically. Ill see if remember, here goes:

'The right way to heaven'

You are standing in front of Hitler, Goebbels and Ghandi but you dont know who is who (but they know who each other is). You know that Hitler always lies, Ghandi tells the truth and Goebbel's answers are purely random (can be truth or lies). There are two paths ahead of you, lets say path A and path B. One path is the right way to heaven.

The problem is, in two questions directed at any person (can be same person twice or different people), can you determine which path is the right way to heaven?

I didn't do this myself since the answer was right underneath it and it was too alluring, but the answers make perfect sense. This is very difficult, I'll try think of some hints.

Joined Aug 11, 2005
105
Experiments have shown that, presented with a Wason task as an uncontextualised logic puzzle, people perform very poorly. Furthermore, even of those who respond correctly, some obtain the correct result by conscious application of the contrapositive rule.
I'm amused to see that that's how I did it...

For the new problem, I've previously met the version with two people (one liar and one truth-teller) but this one seems to be harder

EDIT: If anyone wants to think about the one with two people, you only get one question there.

#### gbm46

Joined May 6, 2007
47
Knowing the two people case will help in this problem. hint1: From the answer from the first question you can determine a person who is not Goebbels. The second question is to be directed to this person.

#### recca02

Joined Apr 2, 2007
1,212
what wud be the response of a person to an answer which he is uncertain of?
let's say what wud be the response of Gandhi/hitler if he is asked abt a response from Goebbels ?
or waht wud be the response of Goebbels if he is asked abt which of the rest
of the two's answer he is unsure of?

#### gbm46

Joined May 6, 2007
47
hmm... I havent really thought about this. The answer I know doesnt require such a question but there are probably multiple ways to solve this. I guess Ghandi would say that he doesnt know and Hitler's head would explode or something. I think Goebbels would be sure of what they would say anyway so no problems there.

#### recca02

Joined Apr 2, 2007
1,212
useless post:
the person shout "i m a jew" and the one who shoots him with his pistol is hitler.
the person automatically goes to heaven after being shot.

ok so maybe i was thinking in wrong direction,
so, can the three respond in any way other than just pointing a finger towards someone or some direction and saying 'yes' or 'no' .

#### gbm46

Joined May 6, 2007
47
hmm the answer is finger pointing first then direction pointing but I guess you cant rule other methods out. I personally think Ghandi and Hitler would be fairly easy to tell apart but thats just me.

Joined Aug 11, 2005
105
Those are pretty big hints- a pointing question, to determine a person who is not Goebbels... The fourth guess I analysed worked. If you ask someone to point to the less truthful out of the other two, he'll point to someone who is not Goebbels. (Gandhi will tell the truth and point to Hitler as being less truthful than Goebbels, Hitler will lie and point to Gandhi as being less truthful than Goebbels, and it doesn't matter which one Goebbels points to because he can't point to himself.)

So, what to ask that person...

#### recca02

Joined Apr 2, 2007
1,212
building on san bladesabre's( hint will this question(to the person pointed) serve the purpose.
"according to hitler which road goes to heaven?"

Gandhi will point towards hell
so will hitler - this one is a bit controversial and i may be wrong but since only
his opinion abt the direction(and not on response by him) is asked he can not point to heaven.

edit:
another way of asking wud be:
to go to the pointed person and ask
"from those two other persons if i ask the person who is not Goebbels abt direction for heaven what direction wud he point to?"

Gandhi wud point to hell
so wud hitler. ----------since either the answer wud be a lie or the person's(who is supposed to answer the question) response wud
(i think this is a better guess)

Joined Aug 11, 2005
105
Hmm, I don't think that works. If the question is "which road does Hitler think goes to heaven?" then Gandhi will point to heaven and Hitler will point to hell, and if the question is "which road would Hitler say goes to heaven if I asked him?" then Hitler will point to heaven and Gandhi will point to hell...

(I'm not a "Mr" by the way )

#### recca02

Joined Apr 2, 2007
1,212
will this one also be correct,
go to the person pointed and ask

we have taken Goebbels out of picture (thanks to bladesabre san)
Gandhi wud point to heaven
so wud hitler --here is why
i asked which way wud he have pointed if asked , now he wud have originally
lied and pointed towards hell but if he points to hell now he wud say a truth
since he definitely wud have pionted towards hell if asked for a road to heaven so he wud lie again and point towards heaven as his original answer if asked.----think abt it (double negatives cancel out)

so have we won a free ticket to heaven? i m dying to get there