the answer
[tab]A. His number is 12? It adds up to either 24 or 27. Mine is either 15 or 12.
I do not know what my number is.
B. A does not know what his number is. His number is 12 though. He must be thinking
his number is 15 or 12. But if his number is possibly 15, that means my number is not 15.
So my number is 12.
So it should only be after 1 no will the game end.[/tab]
You are wandering through the wilderness in the middle of the night and come up to a fork in the path.
There you meet two old men sitting on a large wood stump.
Legends tell that one of these old men speaks only the truth and that the other one always lies.
One of these paths leads to certain death while the other grants safe passage home. Both of those old men know about those two paths and which leads to which destiny.
You get to ask one of these two men one question.
Try to figure out, with this one question, asking one of the two men, which path is safe.
[tab]If you not gonna try doing it on your own, at least google it…[/tab]
[tab]I ask one of the men which path the other one would show me as being the safe one. The liar would lie and tell me the wrong path, because this is not what the other man would say. The truth teller would tell the truth and also show me the wrong path, because this is the lie which the other one would tell me. So both would tell me the wrong path and I would take the other one.[/tab]
[tab]I didn’t google it! But I knew the riddle :-" .[/tab]
I tried to reconstruct this riddle with a friend a few years ago and even knowing roughly the key idea behind the solution* it still took quite some time to do so.
[tab]that the question has to involve the other man in some way or form[/tab]
You know I haven’t studied logic and I have no good way to annotate, but I will make a start…
Start Moment:
A knows that B has 12, that A has 12 or 15, that B sees either 12 or 15 and no other number.
A says No.
B knows that A has 12 and that A has seen either 12 or fifteen on B. He knows he must have 12 or fifteen. If A has seen 15, then he is thinking either I have 9 or 12. If A has seen 12, then A is thinking I have either 12 or 15. B knows this is what A is thinking.
B says no.
A knows now that if B has seen 12 he is thinking that he either has 12 or 15. While at the same
I can imagine where one takes into account the limited possibilities and what the other must be thinking that at some point an elimination happens. But I cannot hold it in my head.
Though I suspected such to be the intent of the puzzle, I also suspect the proposed solution to be fallacious. I currently don’t think that it can be solved that way, although misleading into the illusion of a solution. We’ll see.
A and B cannot both be in 1. Either A is in 1, B is in 1, or Neither are in one
Either A or B, or both A and B is in group 2.
F is undefined. E is undefined. C is undefined.
D is undefined. F is undefined. A is undefined.
Either A or E, or both A and E are in group 1.
D is undefined. E is undefined. C is undefined. B is undefined.
Either D or B, or both D and B are in group 2.
No solution.
If a statement is wrong, only one component may be wrong. Therefore, F is undefined.
For instance, in 2. F may be in 2, because only the end of the statment may be wrong. Therefore F is undefined
Solution to (“Perfect Logicians”)
[tab]A: Since he has 12, that means I do not have 9.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have nine. Because if he had nine, that would mean I have 15. But I am unsure if I have 15.
“No.”
B: Him saying no means I do not have 9. Because if I had nine, he would know that his is 15. So he knows i do not have nine.
Case 1. I have 15. This means he thinks he has 12 or 9.
Case 2. I have 12. This means he thinks he has 12 or 15.
If I say no, that will tell him that he does not have nine, and that I know he does not have have nine, and that I know he does not have nine. Because if he had nine that would mean I know I have 15. But I am unsure if I have 15.
“No.”
A: Case 1. I have 15. Since I already made him know he doesn’t have 9, this means he would think he has twelve. Since he doesn’t know if he has twelve, this means Case 2 is true, that I have twelve.
“I have twelve.” Three turns[/tab]