Riddles

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Phoneutria, my comment was addressed to you, not to A and B. You have to know that both have “12”'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 does’t matter that the other one doesn’t know that I know, so long as each of them knows that both are not 9[/tab]

So your riddle is, there’s 2 guys with 12 on their foreheads. What’s on their foreheads?

… 12, I know because… it’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, … ahem, … 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, … wait …, here comes the quote:

You should go on with that. (7), (8), (9), … 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 “if he saw 15, he would know his own number was 12 because…”, you implied that each person knew that the other had already disqualified “9”.

Why did you stop at 15 and 12 then?

Why did you not go on?

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

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Both of them know that both of them don’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? :slight_smile:

No, spider. We are alone here. Show your weapons! :sunglasses:

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

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

Next step:

A: “No” => b < 21.
B: “No” => 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]

No I don’t want to play with a recursive solution until you acknowledge that my inductive solution is sound.

It isn’t “sound” because

…that isn’t true.

The entire game is figuring out what the other person must know. That is why it is in the category of “Perfect Logicians”, else one couldn’t be certain of what the other might deduce.

If anything, that’ll add a couple of nos.

Then just count them.

Like at the first no I know I don’t have a 9, then at the second no you know you don’t have a 9 and I know that you know.

Exactly.