# Riddles

Menorca.

Obviously you are the only one here who is not capable of reading.

This riddle was alraedy solved by James S. Saint (viewtopic.php?f=4&t=188593&start=150#p2567357).

Again: Obviously you are the only one here who is not capable of reading.

Q.E.D.

PERFECT LOGICIANS

[tab]A: HIS IS 12 SO MINE MUST BE EITHER 12 OR 15. IF HE THINKS I SEE A 12 HE WILL THINK HIS IS EITHER 12 OR 15. IF HE THINKS I SEE A 15, HE WILL THINK HIS IS EITHER 9 OR 12.

“NO”

B: HE SAID NO, SO THAT MEANS I DON’T HAVE A 9. IF I HAD A 9 HE WOULD KNOW FOR SURE THAT HIS WOULD BE 15.
HOWEVER I STILL DON’T KNOW IF MY NUMBER IS 12 OR 15.

“NO”

A: WE BOTH KNOW THAT WE’RE NOT 9 AND THEREFORE THE OTHER EITHER 12 OR 15, BUT DON’T KNOW WHICH. WE CAN’T BOTH BE 15, SO IF I HAD 15 HE WOULD KNOW FOR SURE HIS IS 12. SINCE HE ANSWERED NO, I MUST HAVE A 12.

“BOOYAH, BITCHES”[/tab]

Hello again, Phoneutria.

The question of that riddle again: "After how many “no"s does the game end, if at all?”

Two, robot.

No, spider. That is false. Please try again.

I am a real human, my spider.

My logic checks, robot. You may require calibration.

Okay, spider.

Good luck!

Can you please check my logic?

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]

[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:

No I didn’t, and no it isn’t.