Riddles

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]

The whole solution (with the solution process):

[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.

A: “No” => b < 21.
B: “No” => a > 6.
A: “No” => b < 18.
B: “No” => a > 9.
A: “No” => b < 15.
B: “Yes”. Because together with the information of (2) there remains only one possibility.

Now add the „No“s!


The game ends after 7 „no“s.[/tab]

I remind you of the riddle I posted on 14 January 2016:

Who is depicted here?

Easy_Riddle.jpg

Incorrect (for several reasons).
Sorry, try again. :sunglasses:

My solution is absolutely correct.

Your “there-is-no-solution-solution” is incorrect.

That is incorrect. Sorry. Try again. :sunglasses:

“Famous last words.” :sunglasses:

You should know me well enough to at least accept a tiny bit of doubt if I am telling you that you are incorrect.
Would I say it without a reason? :sunglasses:

My actual words were:

First correction:
You must disqualify zero and all negative numbers when you word the riddle, else your count will be different.

Agreed?