# Logic Teaser

by TD 45 Replies latest social humour

• ##### glenster

It reminds me of something you might see in one of Raymond Smullyan's logic
puzzle books like "What is the Name of This Book? The riddle of Dracula and
other logical puzzles."
http://en.wikipedia.org/wiki/Raymond_Smullyan

One of the easier ones I remember:

While two men look at a portrait, one says to the other: "Brothers and sisters
have I none, but that man's father is my father's son." Whose portait is it?

#### 1 Corinthians 12:3 (New International Version)

3 Therefore I tell you that no one who is speaking by the Spirit of God says, "Jesus be cursed," and no one can say, "Jesus is Lord," except by the Holy Spirit.

All the best, Stephen

• ##### HintOfLime
In a remote village, half the population lies all the time; the other half tells the truth all the time

... boring details ...

How many of these three natives are liars?

1.5 out of the 3 natives are liars.

- Lime

• ##### glenster

Ruling out the possibility of being mistaken:

A. If 1 said he's not a liar and he's not a liar, he'd be an honest villager
who told the truth about himself, 2 told the truth, and 3 is lying about 1
(falsely accusing 1 of being a liar, not 2 of translating 1 falsely) or 3 is
lying about 2 (falsely accusing 2 of falsely translating 1--that 1 actually
identified himself as a liar, although that can't happen: see C and D below).

B. If 1 said he's not a liar and he is a liar, he'd be a liar who lied about
himself, 2 told the truth, and 3 either told the truth about 1 being a liar (not
2 of translating 1 falsely) or lied about 2 (falsely accusing 2 of falsely
translating 1--that 1 actually identified himself as a liar, even though that
can't happen: see C and D below).

C. If 1 said he's a liar and he is a liar, he'd be a liar who told the truth
about himself, but that can't happen because the villagers either tell the truth
all the time or lie all the time.

D. If 1 said he's a liar and he isn't a liar, he'd be an honest villager who
lied about it, which can't happen because the villagers either tell the truth
all the time or lie all the time.

• ##### Twitch

While two men look at a portrait, one says to the other: "Brothers and sisters
have I none, but that man's father is my father's son." Whose portait is it?

His son's

• ##### Twitch

"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."

I agree with OpenMind's answer - "Which road does the OTHER guy say is the road to life?"

• ##### TD

Here is one that is so counterintuitive it will give anybody a headache. It's based on a 60's era American televsion show called, "Let's Make a Deal."

The contestant is shown three closed doors. Behind one of these three doors is a fabulous prize. Behind the other two doors are worthless 'gag' prizes.

The contestant is allowed to chose one of these three doors.

At this point, the host would reveal one of the gag prizes by opening one or the other of the two remaining doors.

He would then ask the contestant, "There are only two doors now, one of which is the grand prize. Do you want to change your mind and pick the other door?"

What should the contestant do?

Marilyn Vos Savant answered this question correctly years ago in her column and took a lot of heat for it. One particularly nasty letter she got was from a college level mathematics professor. The correct answer appears to defy logic. (It actually doesn't though --- just shows how our perceptions can get in the way...)

• ##### Farkel

TD,

I read Marilyn's piece on that puzzle, so I won't cheat by pretending I figured it out and post the answer. And yes, the answer DOES defy an answer that seems to be logical!

But now I know why Monty Boy did what he did on those shows!

Farkel

• ##### TD

Yes.

When the contestant is asked if they want to switch, the first reaction out of most people is, "There are only two doors now, and the contestant has already picked one of them. Logically, the odds are 50/50 and switching doors won't change that."

The reality is the contestant's odds of winning the prize will double if they do switch.

Even Marilyn seemed to struggle to put this into words so here's my best stab at explaining it.

The contestant's odds of picking the correct door are 1 in 3. When the game show host reveals one of the gag prizes by opening one of the doors those odds don't change.

This seems counterintuitive, but the reason they don't change is because the game show host already knows what is behind each of the doors, so his choice is not random. He must pick a door that is: A, Not the winning door and B, Not the contestant's choice.

So instead of the odds splitting evenly at 50/50 when the host knowingly eliminates a bad door, the contestant continues with his/her initial chance of 1 in 3. The remaining door now has a 2 out of 3 chance of being the winning door. Therefore the contestant's odds of winning will double from 33.3% to 66.7% if they switch doors when given the chance.