# Logic Teaser

by TD 45 Replies latest social humour

• ##### TD

My youngest is taking introduction to logic this year and the professors that teach these classes seem to enjoy stumping the class during the first couple of weeks. This was one of the puzzles assigned as homework and it was causing a certain amount of anguish.

I thought you all might find it amusing because the subject of formal logic frequently comes up here in connection with the wild, circular reasoning most JW's use.

Farkel explained it pretty well:

If #1 is a liar, he'll lie when asked if he's a liar and deny it. Conversely if #1 is a truthteller, he'll answer truthfully when asked if he's a liar and deny it. Either way he'll deny it.

#2 accurately reports this denial.

#3 claims that #1 is a liar. Therefore either #1 or #3 is lying, but they both can't be lying at once. (If #1 is lying, #3 is telling the truth. If #1 is telling the truth, #3 is lying.)

The answer to the question then is, "One of them is a liar"

(Note the question asked how many of the three were lying, not who they were.)

...

• ##### SixofNine

Yes, but if #3 is the liar, then he is a liar in everything he says, all the time, so (do your best Monty Python here) logically he wouldn't exclaim "But he is a liar!", he would would simply say "#1 is lying".

Unless of course, the fact that he cannot but lie has turned him into a very good actor/liar, in which case....

He's a Witch! Burn him!

• ##### Farkel

TD,

Here is another, similar logic puzzle that I've posted before:

A man is walking down the road and comes to a fork in the road. The two roads are not marked with any signs, except a sign that says, "if you take one of these roads, you will live. If you take the other road, you will die. There are two men across the street and both of them knows which road is the road to staying alive. One of them always tells the truth and the other always lies, but you won't know which one tells the truth and which one doesn't.

"You may ask only ONE question of either of these men, and if you ask the right question, you will know which road to take."

What question would solve this puzzle for the man?

Farkel

• ##### Open mind

I'll take a stab at Farkel's puzzle.

"Which road does the OTHER guy say is the road to life?"

om

• ##### TD

Six:

Yeah, I think the teacher was probably trying to make it harder for the students to google an answer. I guess that's a big problem anymore because stock textbook problems and answers get published on line about as fast as the books get written

Farkel:

Is that a variation of Martin Gardner's "Truthful and lying native?" I think the solution is phrasing the question as a conditional:

--Which direction would you have told me to go IF I had asked you which fork would lead in a safe direction?

--Which direction would you have told me to go if I asked you yesterday which fork would lead in a safe direction?

Since it's a question about a question instead of a direct question the lying man lies about the lie he would have told --which negates the lie

Since the truthful man would always have told the truth, even a question about a question produces a truthful answer.

• ##### Farkel

TD,

The only solution is to ask a binary question that would be given the same answer by both the truth teller and the liar.

Farkel

• ##### JeffT

Just kill all three of them and let God sort it out.

• ##### OnTheWayOut

Okay, I read none of the answers. I am on my own.

The first guy would say he is not a liar no matter whether he told the truth or lied.

Second guy must have told the truth when he said that the first guy said he denied it.

The third guy would be lying if the first guy told the truth, or would be telling the truth if the first guy lied.

There is one liar, the evidence is insufficient to determine if it is no. 1 or no. 3.

• ##### OnTheWayOut

Also, just ask anyone on the island:

If I were to ask a liar whether you told the truth or were a liar, what would the liar say?

"A liar would say I am...."
Whatever the man answers, he's the opposite.