# Riddles

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]

[tab]I know that, but they donāt. 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, Iād have a 15.
1b: B has a 12, therefore I donāt have a 9.
1c: 12+12=24 and 12+15=27, therefore the number on my forehead is either 12 or 15

B 1a: If A had a 9, Iād have a 15.
1b: A has a 12, therefore I donāt 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 doesnāt 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]

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.

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.

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

And read also the following posts again:

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

Maybe it is easier to look for a formula.

[tab]

Phoneutria, my comment was addressed to you, not to A and B. You have to know that both have ā12ā'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!

[tab][Tab]it doesāt matter that the other one doesnāt know that I know, so long as each of them knows that both are not 9[/tab]

ā¦ 12, I know becauseā¦ itās in the premise.

Are we having a natural language issue, robot?

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

Can you show me how not knowing that prevents them from arriving at the answer after 1 no?

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:

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

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 āif 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 ā9ā.

Why did you stop at 15 and 12 then?

Why did you not go on?

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

[/tab]

Both of them know that both of them donāt 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?

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.

[tab]Okay, I will give you the next step.

Next step:

A: āNoā => b < 21.
B: āNoā => 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]