The Hardest Logic Problem In the World

This is a game invented by philosophers -- and although it may seem silly and trivial, it actually provides rules and research for how human brains handle ambiguities... and a clue to how we might understand an alien language when we meet aliens.

But first... the problem:

"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 all questions 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."

Welcome to the "Hardest Logic Puzzle Ever". If you should happen upon three questions that will unmask the gods, don't stop there. Your next task: make the puzzle even harder.
Source: en.wikipedia.org...

Yes, it's actually solveable (I figured out the first level... that's a classic variation of "Knights and Knaves".) Where I ran into trouble was assuming that you could only ask a simple question such as "Which way will the other guy tell me to go?" The answer lies in a type of logic called "If and only if" (and relies on your Mysterious Gods having an attention span longer than a fruit fly's and able to follow multiple "if" truth clauses.)

In pure logic, you can answer whether a statement such as "If the Kremlin is in Ireland, then the Pope is a penguin" -- that happens to be a true statement (if the first part is true (it isn't) and the second part isn't true (it isn't), then the statement is true.

Confused?

Good. Let me confuse you further with Boolos' solution to the Three Gods problem: In this one, the gods don't speak English, either, and you don't speak their language. However, they do understand English. Isn't that convenient?

Anyway, a fun little brain exercise for you guys to chew on.

Why must you do this to me?

reply to post by Byrd


This is NOT a Logic Problem, to attempt while drinking, that's for sure !!!





Thanks Byrd.

I forgot how fun these things are......

reply to post by sonnny1


Yes, in fact, I can. Took about 10 seconds for the first, a minute for the second, and two minutes for the third. Fun!

reply to post by Byrd



Q1 for A
are you the first of three I am asking this question
Q1 for B
are you the second of the three I am asking this question
Q1 for C
are you the 3rd of three I am asking this question

reply to post by iSHRED


Because it's FUN (she says gleefully). Exercises your brain. Makes you live longer.

Once you see the pattern, it's not that difficult. The really HARD part is making it harder in a rational way (I could make it harder by writing it out in ancient Egyptian hieroglyphs, but that's just obfuscation and not really making it harder.)

Originally posted by Byrd...
In pure logic, you can answer whether a statement such as "If the Kremlin is in Ireland, then the Pope is a penguin" -- that happens to be a true statement (if the first part is true (it isn't) and the second part isn't true (it isn't), then the statement is true.
...

The statement is neither true nor false since the statement assigns meaning to the Pope based on the location of the Kremlin. If the Kremlin is in Ireland, the Pope is a penguin. If the Kremlin is not in Ireland, the Pope is undefined (assuming the Pope has not otherwise been defined earlier, beyond the scope of this query).

Logically speaking

reply to post by Byrd




It will take my children longer.....or maybe not. My son is already looking over my shoulder asking me, what is that?
I will throw them the Hardest Logic problem also. Heck, maybe I will throw them Molyneux's problem.....

93 does not equal 6 is the first I come up with. Equal sign with line through it. If changing the match sticks from a 90 degree angle to a 45 degree angle isn't against the rules

Originally posted by Ophiuchus 13
reply to post by Byrd

 

Q1 for A
are you the first of three I am asking this question
Q1 for B
are you the second of the three I am asking this question
Q1 for C
are you the 3rd of three I am asking this question

edit on 12/30/12 by Ophiuchus 13 because: (no reason given)

Clever. Quite clever! It would work if you knew which word was "yes" and which was "no."

Originally posted by Byrd

Originally posted by Ophiuchus 13
reply to post by Byrd

 

Q1 for A
are you the first of three I am asking this question
Q1 for B
are you the second of the three I am asking this question
Q1 for C
are you the 3rd of three I am asking this question

edit on 12/30/12 by Ophiuchus 13 because: (no reason given)

Clever. Quite clever! It would work if you knew which word was "yes" and which was "no."

But 1 already knows the answer before 1 asked in order...

after the first responded
I would know the next 1z answer

Question number one. Why in the hell would anyone want to take this test?

Nevermind...I completely misread the post...

Originally posted by GoOfYFoOt

Originally posted by cconn487
93 does not equal 6 is the first I come up with. Equal sign with line through it. If changing the match sticks from a 90 degree angle to a 45 degree angle isn't against the rules

Actually, its 9 minus 3 equals 6. And if you take the "matchstick" from the 6 that would make it into a 5 and place it back into the same position on the 8, you would solve the puzzle...

edit on 12/30/2012 by GoOfYFoOt because: I did...

I took the stick from the 9 to make a 3...added it to the minus to make a plus. 3 + 3 = 6

Took me a minute!

ETA Still working on the op problem. I'm terrible at these.

Can you move one matchstick and still have an equation that is correct? I think there are at least three answers – can you find all three?

LINK

3-9=6
3+3=6
not sure of the last one


That's a good one.

Here is a math logic question

3 men decide to rent a room for the night, The room is $30

They each pay $10 and go up to the room.

The manager made a mistake and realizes that the room only cost $25 for the night, so he gives the bellboy $5 to give back to the 3 men.

As the bellboy was in the elevator, he knew that he couldn't split $5 between 3 people so he pocket $2 and gave each man $1 back.

How much did each man pay for the room?

Where did the missing dollar go?

sirric

Just off the top of my head....I would ask A if they were a lier. Then ask B if A were a lier. Then ask C if B were a lier. That should about rap it up.

Am I on the right track?

Posed to each God:
If yes means ja then no means da.

I think it would need to go something like that but I can't work it out yet.

There questionable scenarios can play out

- God 1 (Random) Are you random God Da or Ja answer
- God 2 (true) Did God 1 answer truthfully Da or Ja answer
-God 3 (false) Did God 1 answer truthfully Ja or Da answer

Therefore sequences for scenrios 1
Da, Da, Ja or
Ja Ja Da

Therefore in scenario 1 if your first two questions yield a common sequence you know that the first God is the random God and the second the truth God. This is the only reliable scenario. the other scenarios below give duplicating sequences under scenarions 2 and 3. Therefore you can get the answer in three questions, with one to each God, as along as you are lucky enough to ask the questions in the sequnce order of scenario 1


Or Scenarios 2 >>>>>>>
- God 1 (True) Are you random God Ja or Da answer
- God 2 (Random) Did God 1 answer truthfully Da or Ja answer
God 3 (false) Did God 1 answer truthfully Da or Ja answer
Sequences
Ja Da Da or
Ja Da Ja or
Da Ja Ja or
Da Ja Da or



Or Scenario 3 >>>

- God 1 false (False) Are you random God Da or Ja answer
- God 2 (Truth) Did God 1 answer truthfully Ja or Da answer
- God 3 (Random) Did God 1 answer truthfully Ja or Da answer
Sequences etc
Da Ja Ja or
Da Ja Da or
Ja Da Da or
Ja Da Ja or

reply to post by sirric


There isn't a dollar missing. Hotel has $25, bellboy has $2, men have $3 back = $30. Never could figure why this was considered a brain teaser. Want to play poker some time?