Some puzzles

Originally posted by bobbob1056th
Good job.

This next one is more of a fun maze thingy. You have to work your way through the "doors" to get to the next door and sadly, the inevitable end. The signs on the doors are what I will be posting, they are not nessisarily true or false. Which door should be opened and why? In order for the answer to be correct you must explain why the ...[text shortened]... are six more choices! After this is finished, I will post progressively more difficult puzzles.

If the signs are not necessarily true or false, then there's no reason for me to bother reading them and I might as well pick randomly.

Originally posted by bobbob1056th
You have to work your way through the "doors" to get to the next door and sadly, the inevitable end. The signs on the doors are what I will be posting, they are not nessisarily true correct you must explain why the correct door is the correct one.

If the signs are not necessarily true or false, then they are meaningless. That means that you can hang a sign on the door that says anything, and what the sign says on it has no impact on whether or not its the right door to take.

You need to word the question a little more carefully....

Edit: Just saw Thousdandyoung's post....didn't mean to be repetitive

Originally posted by AThousandYoung
If the signs are not necessarily true or false, then there's no reason for me to bother reading them and I might as well pick randomly.

Actually, you are wrong, because the signs contain information about which of the signs are true or false. This can be enough to provide you with enough information not to pick randomly.

And this is the case, I believe.

Originally posted by Palynka
Actually, you are wrong, because the signs contain information about which of the signs are true or false. This can be enough to provide you with enough information not to pick randomly.

And this is the case, I believe.

Not so. If you don't know whether the signs are true or false, the writing might as well be gibberish.

To help picture this, assume you stand before two doors one of which you must choose, one leads to death the other to life. There is a sign hanging on each door, but you have been told that the signs are not necessarily true or false. Write whatever you want on the two signs. Select your door. Now switch the doors that the signs are hanging on and select your door again. Did switching which door the signs are hanging on change which door leads to life?

For a problem like this to make sense, you have to provide some guiding principal like: "at least one of the signs on the doors is true," or "one is true, one is false," or "either all or true, or all are false," etc. When you say the signs are not necessarily true or false, they immediately become useless.

Originally posted by The Plumber
Not so. If you don't know whether the signs are true or false, the writing might as well be gibberish.

To help picture this, assume you stand before two doors one of which you must choose, one leads to death the other to life. There is a sign hanging on each door, but you have been told that the signs are not necessarily true or false. Write wha ...[text shortened]... etc. When you say the signs are not necessarily true or false, they immediately become useless.

Come on, guys. Puzzles like these are based on the assumption that the signs make together a consistent set of true/false statements, which should allow to make with certainty the right decision, even if there remains uncertainty about individual signs..

Wether or not my decisions were the right ones, and wether or not some of my remarks on the precision of some of the statements are valid, the puzzles above seem meaningful to me.

Originally posted by AThousandYoung
If the signs are not necessarily true or false, then there's no reason for me to bother reading them and I might as well pick randomly.

This has to do with ruling out impossiblities. Here's a simple example: "This statement is false". How can that statement be true or false? It can't, it simply doesn't make sense. In this puzzle maze thingy you have to determine such impossibilities to find the only possiblity. So maybe a better way to explain the puzzle is to say any given sign is either true or false, but not neither. I hope this helps you to understand the concept. See the first choice to understand how the above example fits in.

Originally posted by Mephisto2
Come on, guys. Puzzles like these are based on the assumption that the signs make together a consistent set of true/false statements, which should allow to make with certainty the right decision, even if there remains uncertainty about individual signs..

Wether or not my decisions were the right ones, and wether or not some of my remarks on the precision of some of the statements are valid, the puzzles above seem meaningful to me.

You got all of them right so far.

6th choice
A Exactly two of these signs are false
B This is the door to go through
C Enter the next room through this door

7th choice
A These signs are all false
B The sign on door A is true
C This is the correct door to open

8th choice
A Exactly two of these signs are true
B Go this way
C This is not the door to go through
D Door B is not the way to go

Originally posted by bobbob1056th
This has to do with ruling out impossiblities. Here's a simple example: "This statement is false". How can that statement be true or false? It can't, it simply doesn't make sense. In this puzzle maze thingy you have to determine such impossibilities to find the only possiblity. So maybe a better way to explain the puzzle is to say any ...[text shortened]... ou to understand the concept. See the first choice to understand how the above example fits in.

I'm sorry, it is you who doesn't understand. The problem as you have stated it is indeterminate. You have an unstated assumption which is this: "The correct door can be logically identified based on the signs on the doors." If you had stated that, then the problem would be OK. Take, for example as you have suggested, the first problem:

The first choice:
door A. "Only one of these signs is false"
door B. "This is the door you should go through"

As Mephisto so carefully explained, the correct answer is "A". Now, suppose a certain mischievious imp sneaks into your maze and changes nothing except the two signs on doors A and B, how does your logic then hold up? See? It's important to understand and state all of the necessary assumptions....

I found this at http://www.wordsmith.demon.co.uk/paradoxes/:

The unexpected hanging
1st paragraph
[A man condemned to be hanged] was sentenced on Saturday. "The hanging will take place at noon," said the judge to the prisoner, "on one of the seven days of next week. But you will not know which day it is until you are so informed on the morning of the day of the hanging."

The judge was known to be a man who always kept his word. The prisoner, accompanied by his lawyer, went back to his cell. As soon as the two men were alone, the lawyer broke into a grin. "Don't you see?" he exclaimed. 1"The judge's sentence cannot possibly be carried out."

"I don't see," said the prisoner.

4th paragraph
"Let me explain They obviously can't hang you next Saturday. Saturday is the last day of the week. On Friday afternoon you would still be alive and you would know with absolute certainty that the hanging would be on Saturday. You would know this before you were told so on Saturday morning. That would violate the judge's decree."

"True," said the prisoner.

"Saturday, then is positively ruled out," continued the lawyer. "This leaves Friday as the last day they can hang you. 2But they can't hang you on Friday because by Thursday only two days would remain: Friday and Saturday. Since Saturday is not a possible day, the hanging would have to be on Friday. Your knowledge of that fact would violate the judge's decree again. So Friday is out. This leaves Thursday as the last possible day. 3But Thursday is out because if you're alive Wednesday afternoon, you'll know that Thursday is to be the day."

"I get it," said the prisoner, who was beginning to feel much better. 4"In exactly the same way I can rule out Wednesday, Tuesday and Monday. That leaves only tomorrow. But they can't hang me tomorrow because I know it today!"

... He is convinced, by what appears to be unimpeachable logic, that 5he cannot be hanged without contradicting the conditions specified in his sentence. Then on Thursday morning, to his great surprise, the hangman arrives. Clearly he did not expect him. What is more surprising, 6the judge's decree is now seen to be perfectly correctly. 6The sentence can be carried out exactly as stated.

Evaluate the statements as true/false:
1. 1st paragraph
2. sentence preceeded by a "1"
3. 4th paragraph
4. sentence preceeded by a "2"
5. sentence preceeded by a "3"
6. sentence preceeded by a "4"
7. the phrase preceeded by a "5"
8. the phrases preceede by a "6"

Is this really a paradox?
What is wrong with the logic used?
etc.
This is merely an exercise to see if you can completely understand the above story/paradox thingy.

Originally posted by The Plumber
I'm sorry, it is you who doesn't understand. The problem as you have stated it is indeterminate. You have an unstated assumption which is this: "The correct door can be logically identified based on the signs on the doors." If you had stated that, then the problem would be OK. Take, for example as you have suggested, the first problem:

The fi ...[text shortened]... hen hold up? See? It's important to understand and state all of the necessary assumptions....

You have an unstated assumption which is this: "The correct door can be logically identified based on the signs on the doors."

Based on the fact that each sign's statement has merit (is true or false), it would a redundancy to include the "unstated assumption"

Originally posted by bobbob1056th
[b]6th choice
A Exactly two of these signs are false
B This is the door to go through
C Enter the next room through this door

7th choice
A These signs are all false
B The sign on door A is true
C This is the correct door to open ...[text shortened]... C This is not the door to go through
D Door B is not the way to go to

6th choice: door A
If A is true, then B and C are false hence door A
If A is false then there are two possibilities left (none false is impossible):
- three false, in which case from B it is not door B and from C not door C, hence door A
- one false (A), but then B and C contradict, hence this is impossible

7th choice: door C
A is false because if not it would be false
B is false because of A false
from A false follows that at least one is true, must be C , hence door C

8th choice: door C
B and D cannot be both wrong or both true, limiting the options.
If A is true then C is false (B or D must be true), leading to door C, which is possible if B is false and D is true
If A is false, then we have still following options:
- all false is impossible because of B and D opposite
- one true; if it is B, then C contradicts, so it has to be D leading to door C.

I posted this one a few months ago:
http://www.redhotpawn.com/board/showthread.php?threadid=10543&page=3

Originally posted by bobbob1056th
[b]You have an unstated assumption which is this: "The correct door can be logically identified based on the signs on the doors."

Based on the fact that each sign's statement has merit (is true or false), it would a redundancy to include the "unstated assumption"[/b]

No, the signs are not necessarily true or false. You said the signs have "merit" because they are either true or false, but this is not the case.

Here. Let's examine the possibilities for the first pair of doors.

The first choice:
door A. "Only one of these signs is false"
door B. "This is the door you should go through"

Let's suppose that door A is the door we must go through. Then sign B is false, and sign A is correct.

Suppose door B is the door we must go through. Sign B is correct, sign A is neither true nor false, because either situation results in a paradox. This does not mean that B cannot be the correct door. i mean, I could set up the signs such that B is the correct door. This is not physically impossible.

Originally posted by The Plumber
Not so. If you don't know whether the signs are true or false, the writing might as well be gibberish.

To help picture this, assume you stand before two doors one of which you must choose, one leads to death the other to life. There is a sign hanging on each door, but you have been told that the signs are not necessarily true or false. Write wha ...[text shortened]... etc. When you say the signs are not necessarily true or false, they immediately become useless.

You are right, of course. Interesting, nevertheless, the number of assumptions we make everyday without even thinking about them...