Riddles

You are on the right track.

Well, if you don’t tell me what is wrong with my answer, I cannot continue, since my solution works as far as I can tell.

You are on the right track - that means: You can go on, because there is no logical error; only the answer is false, but the logical track is right so far.

[tab]And if so, then you merely have to follow this track for a longer time, with more patience, and especially with more consequence!

Cue: Recursive conclusion.[/tab]
Is it okay for you now, or shall I give you more information?

Arminius, I arrived at certainty that they both know they are 12 after 2 "no"s.
If you think that my last sentence does not provide certainty, can you please point out the flaw?

Yes, I can.

[tab]There are still more than one number possible after both have said 2 "no"s.

Shall I give you examples?[/tab]

Yes please.

[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.[/tab]

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

They can’t 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]

That is false.

And you have - again (!) - forgotten one of the premises:

:stuck_out_tongue:

No I didn’t, and no it isn’t.

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! :stuck_out_tongue:

[tab]I know that, but they don’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, I’d have a 15.
1b: B has a 12, therefore I don’t 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, I’d have a 15.
1b: A has a 12, therefore I don’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 doesn’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? :laughing:
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. :laughing:

:laughing:

Please read the task again:

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 don’t have a 9 without even seeing my card, certainly the other logicians also knows that I don’t have a 9. Since we are both perfect logicians, we both know that both of us don’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 “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]