The hardest logical puzzle according to George Boolos

**PhiloLearner** · Jul3-05, 06:15 PM

According to the late philosopher and logician George Boolos, who was a professor at MIT, the hardest logical puzzle is one that was invented by the logician and puzzle-master Raymond Smullyan, and modified slightly by the computer scientist John McCarthy. Here is the puzzle :

Three gods A , B , and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter.

Your task is to determine the identities of A , B , and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer in their own language, in which the words for yes and no are “da” and “ja”, in some order. You do not know which word means which.

Jul4-05, 12:14 AM

edit: misread

**mapper** · Jul4-05, 04:17 PM

In computer programming we use this all the time. IIF statements. Ask questions If god a = true when god b = condition etc..

**lueffy** · Jul5-05, 02:35 AM

Uhm, i believe i've seen this puzzle before in this brain teasers forum...........

**PhiloLearner** · Jul5-05, 05:07 AM

Originally Posted by lueffy

Uhm, i believe i've seen this puzzle before in this brain teasers forum...........

Similar subject titles but different contents

**Moo Of Doom** · Jul5-05, 12:22 PM

Originally Posted by PhiloLearner

Similar subject titles but different contents

No, I am certain I have read this exact problem. In fact, I remember it to have had a whole seperate thread for the answer. The only difference between it and this one is the yes and no words were changed slightly.

**wisredz** · Jul5-05, 03:46 PM

My first question would surely be are you a god? :) If I am lucky I learn two things :)

**Moo Of Doom** · Jul6-05, 03:24 AM

How can you learn anything if it depends on luck? If the god says "Da" what does that tell you? If A=True Then Da=yes. If A=False Then Da=no. If A=Random Then Da=yes or no. Not much information there...

Jul6-05, 11:30 AM

We definately had this question posted before. The answer has to do with some technicality of "iff".

**PhiloLearner** · Jul9-05, 01:25 PM

The answer is ......

http://hcs.harvard.edu/~hrp/issues/1996/Boolos.pdf

**Mr. dude** · Jul13-05, 02:12 PM

well da means yes in Russian and Ja means yes in German so we have a couple funked up gods here.

**delton** · Aug1-05, 10:11 PM

WOW this is tough... but since I know it's solvable mayby I'll try to take a crack at it when I'm bored....

Aug2-05, 05:28 PM

(From your Link;)

Your first move is to find a god who you can be certain is not Random, and
hence is either True or False. (so he claims he finds the god (which is not random) with one question..LoL!)

To do so, turn to A and ask Question 1: Does da mean yes iff,you are True iff,B is Random?

(Assume that Da means no,A is true god and b is random. A's answer would be Da..

Now Assume that Da means no, A is False God and B is random.
Da means no but While A is false god he will think of the first statement;

- Da means yes? as True
- You are True God? as True
- B is random? as False

He will end up with a False, therefore will answer with a True which is "Ja" )

If A is True or False and you get the answer da(According to what i showed you this is megabull****), then as we have seen,
B is Random(Really? Why is that?), and therefore C is either True or False; but if A is True or False and you get the answer ja, then B is not Random, therefore B is either True or False.But what if A is Random?

(How the **** do you make logical conclusions? you have no idea if "da" is yes or no; Let alone if A is random)

If A is Random, then neither B nor C is Random! (Really? No ****!... Now tell me how did that help you?)

So if A is Random and you get the answer da, C is not Random neither is B,
but that's irrelevant(You said that before and i said "Really? No ****!...), and therefore C is either True or False; and if A is Random and you get the answer ja, B is not random neither is C, irrelevantly, and therefore B is either True or False.

Thus, no matter whether A is True, False, or Random, if you get the answer da to Question 1, C is either True or False, and if you get the answer ja, B is either True or False!

(sorry but this answer is total bull****, only confusing people it is no answer..

Add: Above you can see A gave the answer "Ja" while B was Random..As i said this answer is just to confuse people it is bull****))

**whozum** · Aug3-05, 07:59 AM

Thus, no matter whether A is True, False, or Random, if you get the answer da to Question 1, C is either True or False, and if you get the answer ja, B is either True or False!

Shocking conclusion, theyre either true.... or false.

**gravenewworld** · Aug10-05, 09:10 PM

The answer is already in the forums. I posted the Q and A a while ago...and yes the solution is very difficult.

**gurkhawarhorse** · Aug13-05, 06:50 AM

it goes like this.
ask A="hey, A if i ask B a question ="do u speak truth ?" what will B say.

ask B again="hey , B if i ask C a question ="do u speak truth ?" what will C say.

ask C again="hey , C if i ask C a question ="do u speak truth ?" what will C say.

now u will get the god answer. whoever says no either is random or false speaker but not truthful.
the truthful god will say yes to the question.
false one says no.random one either says yes or no.

but u do not know what do those gods mean do u; language problem? so we have a trick. i can assure u that two gods answer same words and one is the odd one. so u get a pair.one thing is that the god who speaks lie and the one who is truthful do not have the same answer. ie they dont couple up.

see, whoever is the odd one out in the answer ie. whose answer does not match with others either says truth or lies.

got it? so u get the god who is random. now again compare their answers but exclude the random god. now u have either false god caught or truthful then catch the next one.

gurkha-war-horse