Riddles

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Re: Riddles

Postby Ultimate Philosophy 1001 » Fri Jan 15, 2016 1:48 am

Arminius wrote:Six people in two groups.

There are six people A, B, C, D, E, F which are in each case either in group 1 or group 2. The following statements are given:

1. Both A and B are in 1.
2. F is in 2, and if E is in 2, then C is also in 2.
3. D is in 1 and if F is in 2, then A is also in 2.
4. A and E are both in 2.
5. D is in 2 and E is in 1, and if C is in 2, then B is in 1.
6. D and B are both in 2.
7. The statements 1-6 are wrong.

Who is in which group?


1. A and B cannot both be in 1. Either A is in 1, B is in 1, or Neither are in one
Either A or B, or both A and B is in group 2.
2. F is undefined. E is undefined. C is undefined.
3. D is undefined. F is undefined. A is undefined.
4. Either A or E, or both A and E are in group 1.
5. D is undefined. E is undefined. C is undefined. B is undefined.
6. Either D or B, or both D and B are in group 2.

No solution.

If a statement is wrong, only one component may be wrong. Therefore, F is undefined.
For instance, in 2. F may be in 2, because only the end of the statment may be wrong. Therefore F is undefined
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Re: Riddles

Postby Ultimate Philosophy 1001 » Fri Jan 15, 2016 2:52 am

Solution to ("Perfect Logicians")
A: Since he has 12, that means I do not have 9.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have nine. Because if he had nine, that would mean I have 15. But I am unsure if I have 15.
"No."
B: Him saying no means I do not have 9. Because if I had nine, he would know that his is 15. So he knows i do not have nine.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have have nine, and that I know he does not have nine. Because if he had nine that would mean I know I have 15. But I am unsure if I have 15.
"No."
A: Case 1. I have 15. Since I already made him know he doesn't have 9, this means he would think he has twelve. Since he doesn't know if he has twelve, this means Case 2 is true, that I have twelve.
"I have twelve."
Three turns
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Re: Riddles

Postby Arminius » Sun Feb 07, 2016 12:05 am

Ultimate Philosophy 1001 wrote:
Arminius wrote:Six people in two groups.

There are six people A, B, C, D, E, F which are in each case either in group 1 or group 2. The following statements are given:

1. Both A and B are in 1.
2. F is in 2, and if E is in 2, then C is also in 2.
3. D is in 1 and if F is in 2, then A is also in 2.
4. A and E are both in 2.
5. D is in 2 and E is in 1, and if C is in 2, then B is in 1.
6. D and B are both in 2.
7. The statements 1-6 are wrong.

Who is in which group?


1. A and B cannot both be in 1. Either A is in 1, B is in 1, or Neither are in one
Either A or B, or both A and B is in group 2.
2. F is undefined. E is undefined. C is undefined.
3. D is undefined. F is undefined. A is undefined.
4. Either A or E, or both A and E are in group 1.
5. D is undefined. E is undefined. C is undefined. B is undefined.
6. Either D or B, or both D and B are in group 2.

No solution.

Sorry, but there is a solution.
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Re: Riddles

Postby Arminius » Sun Feb 07, 2016 12:07 am

Ultimate Philosophy 1001 wrote:Solution to ("Perfect Logicians")
A: Since he has 12, that means I do not have 9.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have nine. Because if he had nine, that would mean I have 15. But I am unsure if I have 15.
"No."
B: Him saying no means I do not have 9. Because if I had nine, he would know that his is 15. So he knows i do not have nine.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have have nine, and that I know he does not have nine. Because if he had nine that would mean I know I have 15. But I am unsure if I have 15.
"No."
A: Case 1. I have 15. Since I already made him know he doesn't have 9, this means he would think he has twelve. Since he doesn't know if he has twelve, this means Case 2 is true, that I have twelve.
"I have twelve."
Three turns

Sorry, but that is false.
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Re: Riddles

Postby Lev Muishkin » Sun Feb 07, 2016 12:10 am

Arminius wrote:Perfect Logicians.

Players A and B both have got the number 12 written on her forehead. Everyone sees the number on the front of the other but does not know the own number. The game master tells them that the sum of their numbers is either 24 or 27 and that this numbers are positive integers (thus also no zero).

Then the game master asks repeatedly A and B alternately, if they can determine the number on her forehead.

A: "No".
B: "No".
A: "No".
B: "No".
A: "No".
....

After how many "no"s does the game end, if at all?


You need to learn to write. This makes no sense.

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Re: Riddles

Postby Lev Muishkin » Sun Feb 07, 2016 12:13 am

Arminius wrote:Greetings from ....

The following picture shows the island where I spend my holidays:

my_current_holiday_island.jpg

Which island is it?


Menorca.

"Science is entirely Faith Based.... Obama is Muslim....Evil is the opposition to life (e-v-i-l <=> l-i-v-e ... and not by accident). Without evil there could be no life.", James S. Saint.
"The Holocaust was the fault of the Jews; The Holocaust was not genocide", Kriswest
"A Tortoise is a Turtle", Wizard
" Hitler didn't create the Nazis. In reality, the Judists did ... for a purpose of their own. Hitler was merely one they chose to head it up after they discovered the Judist betrayal in WW1, their "Judas Iscariot";James S Saint.
These just keep getting funnier.
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Re: Riddles

Postby Arminius » Sun Feb 07, 2016 1:05 am

Lev Muishkin wrote:
Arminius wrote:Perfect Logicians.

Players A and B both have got the number 12 written on her forehead. Everyone sees the number on the front of the other but does not know the own number. The game master tells them that the sum of their numbers is either 24 or 27 and that this numbers are positive integers (thus also no zero).

Then the game master asks repeatedly A and B alternately, if they can determine the number on her forehead.

A: "No".
B: "No".
A: "No".
B: "No".
A: "No".
....

After how many "no"s does the game end, if at all?


You need to learn to write. This makes no sense.

Obviously you are the only one here who is not capable of reading.

Lev Muishkin wrote:
Arminius wrote:Greetings from ....

The following picture shows the island where I spend my holidays:

my_current_holiday_island.jpg

Which island is it?


Menorca.

This riddle was alraedy solved by James S. Saint (viewtopic.php?f=4&t=188593&start=150#p2567357).

Again: Obviously you are the only one here who is not capable of reading.

Q.E.D.
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Re: Riddles

Postby phoneutria » Tue Mar 29, 2016 7:32 am

PERFECT LOGICIANS

A: HIS IS 12 SO MINE MUST BE EITHER 12 OR 15. IF HE THINKS I SEE A 12 HE WILL THINK HIS IS EITHER 12 OR 15. IF HE THINKS I SEE A 15, HE WILL THINK HIS IS EITHER 9 OR 12.

"NO"

B: HE SAID NO, SO THAT MEANS I DON'T HAVE A 9. IF I HAD A 9 HE WOULD KNOW FOR SURE THAT HIS WOULD BE 15.
HOWEVER I STILL DON'T KNOW IF MY NUMBER IS 12 OR 15.

"NO"

A: WE BOTH KNOW THAT WE'RE NOT 9 AND THEREFORE THE OTHER EITHER 12 OR 15, BUT DON'T KNOW WHICH. WE CAN'T BOTH BE 15, SO IF I HAD 15 HE WOULD KNOW FOR SURE HIS IS 12. SINCE HE ANSWERED NO, I MUST HAVE A 12.

"BOOYAH, BITCHES"
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Re: Riddles

Postby Arminius » Tue Mar 29, 2016 7:31 pm

phoneutria wrote:PERFECT LOGICIANS

A: HIS IS 12 SO MINE MUST BE EITHER 12 OR 15. IF HE THINKS I SEE A 12 HE WILL THINK HIS IS EITHER 12 OR 15. IF HE THINKS I SEE A 15, HE WILL THINK HIS IS EITHER 9 OR 12.

"NO"

B: HE SAID NO, SO THAT MEANS I DON'T HAVE A 9. IF I HAD A 9 HE WOULD KNOW FOR SURE THAT HIS WOULD BE 15.
HOWEVER I STILL DON'T KNOW IF MY NUMBER IS 12 OR 15.

"NO"

A: WE BOTH KNOW THAT WE'RE NOT 9 AND THEREFORE THE OTHER EITHER 12 OR 15, BUT DON'T KNOW WHICH. WE CAN'T BOTH BE 15, SO IF I HAD 15 HE WOULD KNOW FOR SURE HIS IS 12. SINCE HE ANSWERED NO, I MUST HAVE A 12.

"BOOYAH, BITCHES"

Hello again, Phoneutria. :)

The question of that riddle again: "After how many "no"s does the game end, if at all?"
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Re: Riddles

Postby phoneutria » Tue Mar 29, 2016 8:03 pm

Two, robot.
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Re: Riddles

Postby Arminius » Tue Mar 29, 2016 9:46 pm

No, spider. That is false. Please try again.

I am a real human, my spider. :P
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Re: Riddles

Postby phoneutria » Tue Mar 29, 2016 10:02 pm

My logic checks, robot. You may require calibration.
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Re: Riddles

Postby Arminius » Tue Mar 29, 2016 10:12 pm

Okay, spider.

Good luck!
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Re: Riddles

Postby phoneutria » Tue Mar 29, 2016 10:33 pm

Can you please check my logic?
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Re: Riddles

Postby Arminius » Wed Mar 30, 2016 12:00 am

You are on the right track.

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Re: Riddles

Postby phoneutria » Wed Mar 30, 2016 12:48 am

Well, if you don't tell me what is wrong with my answer, I cannot continue, since my solution works as far as I can tell.
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Re: Riddles

Postby Arminius » Wed Mar 30, 2016 1:12 am

You are on the right track - that means: You can go on, because there is no logical error; only the answer is false, but the logical track is right so far.

And if so, then you merely have to follow this track for a longer time, with more patience, and especially with more consequence!

Cue: Recursive conclusion.

Is it okay for you now, or shall I give you more information?
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Re: Riddles

Postby phoneutria » Wed Mar 30, 2016 5:56 pm

Arminius, I arrived at certainty that they both know they are 12 after 2 "no"s.
If you think that my last sentence does not provide certainty, can you please point out the flaw?
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Re: Riddles

Postby Arminius » Wed Mar 30, 2016 8:24 pm

phoneutria wrote:Arminius, I arrived at certainty that they both know they are 12 after 2 "no"s.
If you think that my last sentence does not provide certainty, can you please point out the flaw?

Yes, I can.

There are still more than one number possible after both have said 2 "no"s.

Shall I give you examples?
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Re: Riddles

Postby phoneutria » Wed Mar 30, 2016 9:17 pm

Yes please.
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Re: Riddles

Postby Arminius » Wed Mar 30, 2016 10:16 pm

In the beginning A knows that (1) a = 12 or a = 15, and (2) B knows that b = 12 or b = 15.

Okay. But A does not know that B (2) knows, and B does not know that A (1) knows. So the statement above is not suited for the recursive conclusion.

But both A and B know all of the following statements and that each of them knows that the other one knows them:

(3) a = 24 - b or a = 27 - b and (4) b = 24 - a or b = 27 - a.

Now, from the first "no" of A and from (4) follows (5) b < 24, because if b >= 24, then A would be able to conclude a. This is the motor for the recursive conclusion.

Now, from the first "no" of B and from (3) and (5) follows (6) a > 3.

And so on.
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Re: Riddles

Postby phoneutria » Wed Mar 30, 2016 11:15 pm

Arminius wrote:
In the beginning A knows that (1) a = 12 or a = 15, and (2) B knows that b = 12 or b = 15.

Okay. But A does not know that B (2) knows, and B does not know that A (1) knows. So the statement above is not suited for the recursive conclusion.

But both A and B know all of the following statements and that each of them knows that the other one knows them:

(3) a = 24 - b or a = 27 - b and (4) b = 24 - a or b = 27 - a.

Now, from the first "no" of A and from (4) follows (5) b < 24, because if b >= 24, then A would be able to conclude a. This is the motor for the recursive conclusion.

Now, from the first "no" of B and from (3) and (5) follows (6) a > 3.

And so on.


After 9 was eliminated, they know that 12 and 15 are the only valid options.

They can't both be 15.

If I see a 15 I would know that my number is 12, however I see a 12, so I have to answer no.

The other one must realize that the situation above ensued and therefore be must see a 12 on my forehead.
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Re: Riddles

Postby Arminius » Thu Mar 31, 2016 12:43 am

phoneutria wrote:
Arminius wrote:
In the beginning A knows that (1) a = 12 or a = 15, and (2) B knows that b = 12 or b = 15.

Okay. But A does not know that B (2) knows, and B does not know that A (1) knows. So the statement above is not suited for the recursive conclusion.

But both A and B know all of the following statements and that each of them knows that the other one knows them:

(3) a = 24 - b or a = 27 - b and (4) b = 24 - a or b = 27 - a.

Now, from the first "no" of A and from (4) follows (5) b < 24, because if b >= 24, then A would be able to conclude a. This is the motor for the recursive conclusion.

Now, from the first "no" of B and from (3) and (5) follows (6) a > 3.

And so on.


After 9 was eliminated, they know that 12 and 15 are the only valid options.

They can't both be 15.

If I see a 15 I would know that my number is 12, however I see a 12, so I have to answer no.

The other one must realize that the situation above ensued and therefore be must see a 12 on my forehead.

That is false.

And you have - again (!) - forgotten one of the premises:

I wrote:Perfect Logicians.

Players A and B have got the number 12 written on their foreheads. ....

:P
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Re: Riddles

Postby phoneutria » Thu Mar 31, 2016 10:17 am

No I didn't, and no it isn't.
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Re: Riddles

Postby James S Saint » Thu Mar 31, 2016 12:49 pm

phoneutria wrote:PERFECT LOGICIANS

A: HIS IS 12 SO MINE MUST BE EITHER 12 OR 15. IF HE THINKS I SEE A 12 HE WILL THINK HIS IS EITHER 12 OR 15. IF HE THINKS I SEE A 15, HE WILL THINK HIS IS EITHER 9 OR 12.

"NO"

B: HE SAID NO, SO THAT MEANS I DON'T HAVE A 9. IF I HAD A 9 HE WOULD KNOW FOR SURE THAT HIS WOULD BE 15.
HOWEVER I STILL DON'T KNOW IF MY NUMBER IS 12 OR 15.

The sums being either 24 or 27, If you had a 9, his number could be either 15 or 18.

"NO"

A: WE BOTH KNOW THAT WE'RE NOT 9 AND THEREFORE THE OTHER EITHER 12 OR 15, BUT DON'T KNOW WHICH. WE CAN'T BOTH BE 15, SO IF I HAD 15 HE WOULD KNOW FOR SURE HIS IS 12. SINCE HE ANSWERED NO, I MUST HAVE A 12.

The only thing that you both know at this point is that neither has a number greater than 24.

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