The Magic Café
Username:
Password:
[ Lost Password ]
  [ Forgot Username ]
The Magic Cafe Forum Index » » Puzzle me this... » » True or False? (0 Likes) Printer Friendly Version

panlives
View Profile
Inner circle
2087 Posts

Profile of panlives
From Roberto Casati:

"All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false.
All the statements below this one are false."

This array manages to be paradoxical without being circular.

The statements can’t all be false, because that would make the first one true, a contradiction.

But neither can any one of them be true, as a true statement would have to be followed by an infinity of false statements, and the falsity of any one of them implies the truth of some that follow.

“A paradox — but a rectilinear one.”
"Is there any point to which you would wish to draw my attention?"
"To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
"That was the curious incident," remarked Sherlock Holmes.
Scott Cram
View Profile
Inner circle
2579 Posts

Profile of Scott Cram
I see you've discovered Futility Closet.
;)

There are a lot of good puzzles and math facts there!
panlives
View Profile
Inner circle
2087 Posts

Profile of panlives
Quote:
On 2011-12-01 02:02, Scott Cram wrote:
I see you've discovered Futility Closet.
;)

There are a lot of good puzzles and math facts there!


Yes, indeed!

Hundreds of pages, in fact...amazing resource.

Here is another from that great site:

"You and I are having an argument. Our wives have given us new neckties, and we’re arguing over which is more expensive.

Finally we agree to a wager. We’ll ask our wives for the prices, and whoever is wearing the more expensive tie has to give it to the other.

You think, “The odds are in my favor. If I lose the wager, I lose only the value of my tie. If I win the wager, I gain more than the value of my tie. On balance I come out ahead.”

The trouble is, I’m thinking the same thing. Are we both right?"
"Is there any point to which you would wish to draw my attention?"
"To the curious incident of the dog in the night-time."
"The dog did nothing in the night-time."
"That was the curious incident," remarked Sherlock Holmes.
TomasB
View Profile
Inner circle
Sweden
1127 Posts

Profile of TomasB
I'm not sure how to interpret the lowest "All the statements below this one are false." Is that one always false since there are no statements below it?

As for the tie thing, it's quite hard to pinpoint the error in the way the expected gain is calculated, which is what makes that such a great puzzle. If you calculate the expected value of your tie if the game is played you of course get 0.5 * [value of my tie] + 0.5 * [value of his tie] which tells you nothing since you do not know the value of his tie.

Anyone have a good way of explaining why it's wrong to calculate with the expected gain?

/Tomas
TomasB
View Profile
Inner circle
Sweden
1127 Posts

Profile of TomasB
Let's see if I understand this:

The fifth statement is false since there are no statements below it.
The fourth statement says that it is false, which is true.
The third statement says that all below are false, which is false.
The second statement says that all below are false, which is false.
The top statement says that all below are false, which is false.

Where's the paradox?

If I've misunderstood the fifth statement, let's say that it's true instead.
The fifth statement is true, since there are no statements below it.
The fourth statement will be false.
The third statement will be false.
The second statement will be false.
The first statement will be false.

Again no paradox, no matter how the fifth statement is interpreted.

/Tomas
Mr. Mystoffelees
View Profile
Inner circle
I haven't changed anyone's opinion in
3507 Posts

Profile of Mr. Mystoffelees
Quote:
On 2011-12-01 02:02, Scott Cram wrote:
I see you've discovered Futility Closet.
;)

There are a lot of good puzzles and math facts there!


Oh, no! Scott, what have you done to me? Now I AM HOOKED! O, whoa is me...

Jim
Also known, when doing rope magic, as "Cordini"
scalito
View Profile
New user
95 Posts

Profile of scalito
Here's a parody on a classic: If I make a statement. And my mother in law isn't there to here it. Am I still Wrong?!!!!
The Magic Cafe Forum Index » » Puzzle me this... » » True or False? (0 Likes)
<<< Previous Topic Next Topic >>>
[ Top of Page ]
All content & postings Copyright © 2001- 2014 Steve Brooks. All Rights Reserved.
This page was created in 0.062131 seconds, requiring 30 database queries.
The views and comments expressed on The Magic Café
are not necessarily those of The Magic Café, Steve Brooks, or Steve Brooks Magic.
> Privacy Statement <

[1] [0] [4] [8] [2] [7] [7] [2] [7] [4]