Riddles

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:

[/tab]

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.

They both know that they don’t have a 9 from the start. But neither knows that the other knows that because one might have a 15 and thus the other would have a 12 or a 9. Each can see a 12, but they can’t know they don’t have a 15 and thus the other person thinking that he might have a 9 or a 12.

If the person saying “no” suspects that he might have a 9, the reasoning that he said “no” because he realizes that he must have either 12 or 15, doesn’t hold. When the 15 is discounted, he would still wonder if he had 12 or 9.

Any of them would immediately say yes if they could see a 9. This is obvious to both.
If both of them say no on the 1st round, then none have 9.
This is evident.

?? How so?

If you see a 9, how do you know whether you have a 18 (for 27) or a 15 (for 24)?

Even after the first round, 9 is still an option.

[tab]

Next step:

A: “No” => b < 18.
B: “No” => a > 9.

And so on.[/tab]