Arminius
(Arminius)
March 31, 2016, 12:40pm
201
Phoneutria.

[tab]Both A and B have "12"s on their foreheads, and 12 + 12 = 24. So you should know from the premise (12 + 12) that the sum is 24, not 27. The sum must be 24. That is why your solution is false. The sum 27 is not possible because of the premise that both have "12"s on their foreheads.[/tab]
On their foreheads!

phoneutria
(phoneutria)
March 31, 2016, 3:34pm
202

Arminius:

Phoneutria.

[tab]Both A and B have "12"s on their foreheads, and 12 + 12 = 24. So you should know from the premise (12 + 12) that the sum is 24, not 27. The sum must be 24. That is why your solution is false. The sum 27 is not possible because of the premise that both have "12"s on their foreheads.[/tab]
On their foreheads!

[tab]I know that, but they donāt. All they know is the other dude has a 12 and that the total is either 24 or 27.

A 1a: If B had a 9, Iād have a 15.
1b: B has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15

A answers no

B 1a: If A had a 9, Iād have a 15.
1b: A has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15
1d: A answered no on the first round, so he doesnāt know whether the number on his forehead is 12 or 15 either.
1e: If the number he sees on my forehead was 15, he would know for sure that his is 12, since 15+15 is not a valid option.
1f: Since he does not know for sure he must see a 12 on my forehead.

B answers that his number is 12

I change my answer to ONE"[/tab]

[/tab]

Arminius
(Arminius)
March 31, 2016, 5:07pm
203

phoneutria:

Arminius:

Phoneutria.

[tab]Both A and B have "12"s on their foreheads, and 12 + 12 = 24. So you should know from the premise (12 + 12) that the sum is 24, not 27. The sum must be 24. That is why your solution is false. The sum 27 is not possible because of the premise that both have "12"s on their foreheads.[/tab]
On their foreheads!

[tab]I know that, but they donāt. All they know is the other dude has a 12 and that the total is either 24 or 27.

A 1a: If B had a 9, Iād have a 15.
1b: B has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15

A answers no

B 1a: If A had a 9, Iād have a 15.
1b: A has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15
1d: A answered no on the first round, so he doesnāt know whether the number on his forehead is 12 or 15 either.
1e: If the number he sees on my forehead was 15, he would know for sure that his is 12, since 15+15 is not a valid option.
1f: Since he does not know for sure he must see a 12 on my forehead.

B answers that his number is 12

I change my answer to ONE"[/tab]

No. That is false. I am sorry.

[tab]

So you are A. Okay.

Now you are B? Hey?

Yes, regardless whether you are A or B. Okay.

So you are B again. Okay.

Phoneutria:

1b: A has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15
1d: A answered no on the first round, so he doesnāt know whether the number on his forehead is 12 or 15 either.
1e: If the number he sees on my forehead was 15, he would know for sure that his is 12, since 15+15 is not a valid option.

But does he see a 15?

What?
It is clear, because of the premise of the riddle, that he sees a 12.

No, that is not allwoed because of the premise of the riddle.

Please read the task again:

Remember: Both are PERFECT logicians. So they knew, for example, mathematics too.

And read also the following posts again:

phoneutria
(phoneutria)
March 31, 2016, 6:33pm
205
James
[tab]if I know that I donāt have a 9 without even seeing my card, certainly the other logicians also knows that I donāt have a 9. Since we are both perfect logicians, we both know that both of us donāt have 9s.[/tab]

Arminius
(Arminius)
March 31, 2016, 6:59pm
206
Maybe it is easier to look for a formula.

Arminius
(Arminius)
March 31, 2016, 7:44pm
208

phoneutria:

Arminius:

Phoneutria.

[tab]Both A and B have "12"s on their foreheads, and 12 + 12 = 24. So you should know from the premise (12 + 12) that the sum is 24, not 27. The sum must be 24. That is why your solution is false. The sum 27 is not possible because of the premise that both have "12"s on their foreheads.[/tab]
On their foreheads!

[tab]I know that, but they donāt. All they know is the other dude has a 12 and that the total is either 24 or 27.

A 1a: If B had a 9, Iād have a 15.
1b: B has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15

A answers no

B 1a: If A had a 9, Iād have a 15.
1b: A has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15
1d: A answered no on the first round, so he doesnāt know whether the number on his forehead is 12 or 15 either.
1e: If the number he sees on my forehead was 15, he would know for sure that his is 12, since 15+15 is not a valid option.
1f: Since he does not know for sure he must see a 12 on my forehead.

B answers that his number is 12

I change my answer to ONE"[/tab]

[tab]

Phoneutria, my comment was addressed to you , not to A and B. You have to know that both have ā12ā's on their foreheads (so that the sum must be 24 in your calculaltion). That was meant. This premise is given in the riddle.[/tab]
Good luck!

phoneutria
(phoneutria)
March 31, 2016, 8:33pm
209

phoneutria:

James
[tab]if I know that I donāt have a 9 without even seeing my card, certainly the other logicians also knows that I donāt have a 9. Since we are both perfect logicians, we both know that both of us donāt have 9s.

The other doesnāt know that you know.[/tab]

[tab][Tab]it doesāt matter that the other one doesnāt know that I know, so long as each of them knows that both are not 9[/tab]

phoneutria
(phoneutria)
March 31, 2016, 8:39pm
210

Arminius:

phoneutria:

Arminius:

Phoneutria.

[tab]Both A and B have "12"s on their foreheads, and 12 + 12 = 24. So you should know from the premise (12 + 12) that the sum is 24, not 27. The sum must be 24. That is why your solution is false. The sum 27 is not possible because of the premise that both have "12"s on their foreheads.[/tab]
On their foreheads!

[tab]I know that, but they donāt. All they know is the other dude has a 12 and that the total is either 24 or 27.

A 1a: If B had a 9, Iād have a 15.
1b: B has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15

A answers no

B 1a: If A had a 9, Iād have a 15.
1b: A has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15
1d: A answered no on the first round, so he doesnāt know whether the number on his forehead is 12 or 15 either.
1e: If the number he sees on my forehead was 15, he would know for sure that his is 12, since 15+15 is not a valid option.
1f: Since he does not know for sure he must see a 12 on my forehead.

B answers that his number is 12

I change my answer to ONE"[/tab]

[tab]

Phoneutria, my comment was addressed to you , not to A and B. You have to know that both have ā12ā's on their foreheads (so that the sum must be 24 in your calculaltion). That was meant. This premise is given in the riddle.[/tab]
Good luck!

So your riddle is, thereās 2 guys with 12 on their foreheads. Whatās on their foreheads?

ā¦ 12, I know becauseā¦ itās in the premise.

Are we having a natural language issue, robot?

Not so. Each depends upon what the other is thinking when they answer.

phoneutria
(phoneutria)
March 31, 2016, 9:07pm
212
Can you show me how not knowing that prevents them from arriving at the answer after 1 no?

Arminius
(Arminius)
March 31, 2016, 9:59pm
213

phoneutria:

So your riddle is, thereās 2 guys with 12 on their foreheads. Whatās on their foreheads?

ā¦ 12, I know becauseā¦ itās in the premise.

Are we having a natural language issue, robot?

Spi hider, ā¦ ahem, ā¦ hi spider.

No. The sum you gave as a solution was false. And you would have known this, if you had considered the premise. Therefore I reminded you of the peremise.

[tab]Your solution was the sum 27 (read your posts again), but the sum 27 is not possible as a solution, because the sum has to be 24. Do not think too much about what you would think if you were A and B, although it is not absolutely irrelevant. Remember what I said to you in this post . Or, ā¦ wait ā¦, here comes the quote:

Arminius:

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 ānoā 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 ānoā of B and from (3) and (5) follows (6) a > 3.

And so on.

You should go on with that. (7), (8), (9), ā¦ and so on. Do you understand? If yes: Can you do that?[/tab]

phoneutria
(phoneutria)
April 1, 2016, 12:35am
214
I did not give a sum as answer. I said that both of them know that they have 12 on their forehead after one no.

I started to include that, but it got complicated.

As soon as you said āif he saw 15, he would know his own number was 12 becauseā¦ā, you implied that each person knew that the other had already disqualified ā9ā.

Arminius
(Arminius)
April 1, 2016, 2:12pm
216
Why did you stop at 15 and 12 then?

phoneutria:

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

They canāt 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.[/tab]

Why did you not go on?

[tab]Remember that five "no"s are already given:

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?

[/tab]

I started to include that, but it got complicated.

As soon as you said āif he saw 15, he would know his own number was 12 becauseā¦ā, you implied that each person knew that the other had already disqualified ā9ā.

Both of them know that both of them donāt have 9. So it is not necessary for one to know that the other knows.

I stopped because I provided what the problem asked.

Can we get carleas in here?

Arminius
(Arminius)
April 1, 2016, 4:23pm
219
No, spider. We are alone here. Show your weapons!

Carleas is observing the precesses in this thread from outside anyway, but currently he has no chance to get in.

Arminius
(Arminius)
April 1, 2016, 4:37pm
220
[tab]Okay, I will give you the next step.

Arminius:

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 ānoā 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 ānoā of B and from (3) and (5) follows (6) a > 3.

And so on.

Next step:

A: āNoā => b < 21.
B: āNoā => a > 6.

And so on.

By this I have given you almost the whole solution. [size=85](Now, hurry up, because the others are coming soon.)[/size]

Good luck![/tab]