The prison doors ...
The prisoner sat and listened to the evil scenario the warden was revealing. The warden stood and said, "Follow me."
The warden lead the prisoner down a corridor which had two doors, faily close together.
On the left door was a sign: IN THIS ROOM THERE IS A LADY AND IN THE OTHER ROOM IS A TIGER
On the right door was another sign: IN ONE OF THESE ROOMS THERE IS A LADY, AND IN ONE OF THESE ROOMS THERE IS A TIGER
The prisoner smiled: "Warden, I guess you are about to tell me that one of the signs states the truth and the other is false."
The warden: "This wouldn't be much fun if they were both true, now would it? However, just to show my fair nature ... if you select the correct door, you will earn your freedom. Yet, select the wrong door ... and I will have a vacancy ... and room for another pawn in one of my fun games."
The prisoner: "Is it also possible that there could be a lady behind each door ... or a tiger behind each door?"
The warden: "Ah ... you are too smart to be incarcerated ... those are possibilities. Choose wisely."
Which door should the prisoner choose?
The warden lead the prisoner down a corridor which had two doors, faily close together.
On the left door was a sign: IN THIS ROOM THERE IS A LADY AND IN THE OTHER ROOM IS A TIGER
On the right door was another sign: IN ONE OF THESE ROOMS THERE IS A LADY, AND IN ONE OF THESE ROOMS THERE IS A TIGER
The prisoner smiled: "Warden, I guess you are about to tell me that one of the signs states the truth and the other is false."
The warden: "This wouldn't be much fun if they were both true, now would it? However, just to show my fair nature ... if you select the correct door, you will earn your freedom. Yet, select the wrong door ... and I will have a vacancy ... and room for another pawn in one of my fun games."
The prisoner: "Is it also possible that there could be a lady behind each door ... or a tiger behind each door?"
The warden: "Ah ... you are too smart to be incarcerated ... those are possibilities. Choose wisely."
Which door should the prisoner choose?
posted by Zaux at
8:35 PM
16 Comments:
If the sign on door 2 is true, that means there is a lady behind one door and a tiger behind the other. This also means that the sign on door one is false, therefore the lady has to be behind door 2
I've seen this one somewhere before
forgot to add that the warden says there's a right door and a wrong door, so there can't be a tiger in both or a lady in both.
Sorry for posting here, but posting at 'post your puzzle' payed no heed. Can anyone help me to send a puzzle - I tried the mail but it’s not working.
Thanx
Borris,
Click my name and it will send you to
my blog, where can click my "Email" and send email to me.
The prisoner should pick the correct door !
Assume Doors must contain either a lady or a tiger.
Given: Both doors can't be true
Left Door, Right Door
Lady, Lady= False, False
Lady, Tiger= True, True
Tiger, Lady= False, True
Tiger, Tiger= False, False
Lady,Tiger must be eliminated since both signs are true leaving us with:
Left, Right
Lady, Lady
Tiger, Lady
Tiger, Tiger
Left=1 Lady+ 2 Tigers
Right=2 Ladies + 1 Tiger
If he picks the left door 1/3 times will be the lady, and if he picks the right door 2/3 times is the lady. Best to pick right door.
One could assume that Tiger, Tiger is invalid as both doors would be "wrong" doors, but the answer would not change as the left door would be 1/2 times will be a lady, and the right door would be 2/2 times a lady.
Similiarly excluding Lady, Lady or Lady, Lady and Tiger, Tiger as options has no impact on the decision. The right door is optimal.
Answer:
Picking the right door is optimal.
Cam
If you do not assume Doors must contain either a lady or a tiger, then:
Left Door lies:
left=Tiger
right= Lady
or
left=Tiger and Lady
(in _One of the rooms_ does not mean they cannot be both in one, but since left lies, then Lady cannot be in room 1...)
right= empty (or smth)
--------------------------
Right Door lies:
left=Lady
right=Tiger
-----------------------------
so it it still only one "good" room in every case. But the "bad"
rooms...one has certainly a tiger in it, but in the other case (left Door lies), it could be that a Lady and a Tiger share the room.
If The Tiger is hungry, then he eats the Lady and the prisoner is kind of safe for a while...
So I would suggest to pick the left room and hope to find either a
Lady or a sleepy Tiger.
erm....
and if one room lies and the other does not, the the right room cannot lie, because in this case, left must be correct saying to have a Lady inside and Tiger to be in the right room which makes the right's statement also true. So, Left lies and it has a Tiger inside. Unless
both lie, which is another possibility, and there could be anything but Tigers and Ladies in the rooms.
If it was up to a statistical chance, I would answer "Can I go back to my cell...?"
If the statement on the left was true, then the one on the right would be true -- the statement on the right ("In one of these rooms") entails the statement on the left ("In this room"). Since we're told that only one statement is true, we know that the statement on the left is false.
If the statement on the left is false, then either there is no lady in the left room, or there is no tiger in the right room.
Consistent possibilities are:
(no lady in left)
T/T (tiger on left, tiger on right)
T/L
T/LT
T/0
0/T
0/L
0/LT
0/0
(no tiger on right)
L/L
T/L
LT/L
0/L
L/0
T/0
LT/0
0/0
Four possibilities are "safe", with no tigers on either side.
Four possibilities have tigers on the right.
Eight possibilities have tigers on the left.
There is no guaranteed safe door, and no guaranteed dangerous door. If all possibilities are equally likely, then he should flip a coin, and choose the left door if heads, right door if tails.
Clearly this isn't going to be the published scenario, but I'd like to hear why I'm wrong.
Now if you leave only the possibilities where there is at least one lady and at least one tiger somewhere,
you will have
T/L
T/LT
0/LT
and
T/L
LT/L
LT/0
so...
go right :)
Ragknot ...
you are right ... the prisoner should pick the right door. This was also verified by Cam and Kapakoi.
This warden has some evil games ... we may see him again.
The logic:
Assume the left sign is true. If that's the case, then the right sign is also true ... this violates the condition that there is one true and one false sign. Therefore, the sign on the right door, must be true. Now, we know two things:
1. There is, in fact, a lady behind one door and a tiger behind the other.
2. Since, the left sign is false, the lady must be behind the right side door.
The prisoner should pick the right side door ... unless, of course, he enjoys tiger wrestling :).
I Think the prosoner should choose the right door.
I came across a superficially similar problem a while back. For that the doors had the hinges next to each other. So the prisoner opens both doors, and hides between them. Everyone, except the prisoner gets eaten. Wait for the tiger to have a kip, then sneak off.
Ok, four possibilities-TT,TF,FT, FF.
True True
Door A has a Lady
Door B has a tiger
TF
Not an option. If it says there is a lady in this room and a tiger in the other, but the second is false saying there is a lady and tiger, they cancel each other out-its just not possible!
FT
Door A has a tiger
Door B has a lady
FF
Door A contents unknown, just not a lady in this room.
Door B contents unknown. just not a tiger!
His best bet is probably door B. If it is TT, he loses. if it is FT or FF, he survives and possibly has a lady in there.
If he chooses door A, he wins 1/3 times, as opposed to 2/3 for choosing door B.
-Soli
Post a Comment
Links to this post:
Create a Link
<< Home