Solution to (“Perfect Logicians”)

[tab]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[/tab]

Sorry, but there is a solution.

Solution to (“Perfect Logicians”)

[tab]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[/tab]

Sorry, but that is false.

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.

Greetings from …

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

[attachment=0]my_current_holiday_island.jpg[/attachment]

Which island is it?

Menorca.

Arminius: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.

Arminius:Greetings from …

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

[attachment=0]my_current_holiday_island.jpg[/attachment]

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.

PERFECT LOGICIANS

[tab]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”[/tab]

PERFECT LOGICIANS

[tab]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”[/tab]

Hello again, Phoneutria.

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

Two, robot.

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

I am a real human, my spider.

My logic checks, robot. You may require calibration.

Okay, spider.

Good luck!

Can you please check my logic?

You are on the right track.

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.

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.

[tab]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.[/tab]

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

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?

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.

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

Shall I give you examples?[/tab]

Yes please.

[tab]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.[/tab]