The Warden's Game
As in "The prison doors (2)", The prison doors (2) , the warden has set up several fiendish situations for several prisoners. Here are are the door and sign situations:
Prisoner 1:
(one sign is true, and the other is false)
Sign 1: EITHER A TIGER IS IN THIS ROOM OR A LADY IS IN THE OTHER ROOM
Sign 2: A LADY IS IN THE OTHER ROOM
Prisoner 2:
(If a lady is in room 1, then the sign on the door is true ... if it contains a tiger, then the sign is false. In room 2, a lady in the room means the sign is false, and a tiger means the sign is true. It is still possible that both rooms have a lady, or both rooms have a tiger, or that one room has a lady and the other one a tiger.)
Sign 1: BOTH ROOMS CONTAIN LADIES
Sign 2: BOTH ROOMS CONTAIN TIGERS
Prisoner 3:
(same rules apply as for prisoner 2)
Sign 1: AT LEAST ONE ROOM CONTAINS A LADY
Sign 2: THE OTHER ROOM CONTAINS A LADY
Prisoner 4:
(same rules apply as for prisoner 2)
Sign 1: IT MAKES NO DIFFERENCE WHICH ROOM YOU PICK
Sign 2: THERE IS A LADY IN THE OTHER ROOM
Prisoner 5:
(same rules apply as for prisoner 2)
Sign 1: IT DOES MAKE A DIFFERENCE WHICH ROOM YOU PICK
Sign 2: YOU ARE BETTER OFF CHOOSING THE OTHER ROOM
Prisoner 6:
(same rules apply as for prisoner 2 ... the signs have not yet been posted on the doors. The prisoner asked how he was suppose to choose a room when the signs aren't mounted. The warden informed him that a solution was possible without knowing which sign should be on which door.)
Sign (not posted): THIS ROOM CONTAINS A TIGER
Sign (not posted): BOTH ROOMS CONTAIN TIGERS
Will you help these prisoners choose the correct doors, and escape this madman warden?
Prisoner 1:
(one sign is true, and the other is false)
Sign 1: EITHER A TIGER IS IN THIS ROOM OR A LADY IS IN THE OTHER ROOM
Sign 2: A LADY IS IN THE OTHER ROOM
Prisoner 2:
(If a lady is in room 1, then the sign on the door is true ... if it contains a tiger, then the sign is false. In room 2, a lady in the room means the sign is false, and a tiger means the sign is true. It is still possible that both rooms have a lady, or both rooms have a tiger, or that one room has a lady and the other one a tiger.)
Sign 1: BOTH ROOMS CONTAIN LADIES
Sign 2: BOTH ROOMS CONTAIN TIGERS
Prisoner 3:
(same rules apply as for prisoner 2)
Sign 1: AT LEAST ONE ROOM CONTAINS A LADY
Sign 2: THE OTHER ROOM CONTAINS A LADY
Prisoner 4:
(same rules apply as for prisoner 2)
Sign 1: IT MAKES NO DIFFERENCE WHICH ROOM YOU PICK
Sign 2: THERE IS A LADY IN THE OTHER ROOM
Prisoner 5:
(same rules apply as for prisoner 2)
Sign 1: IT DOES MAKE A DIFFERENCE WHICH ROOM YOU PICK
Sign 2: YOU ARE BETTER OFF CHOOSING THE OTHER ROOM
Prisoner 6:
(same rules apply as for prisoner 2 ... the signs have not yet been posted on the doors. The prisoner asked how he was suppose to choose a room when the signs aren't mounted. The warden informed him that a solution was possible without knowing which sign should be on which door.)
Sign (not posted): THIS ROOM CONTAINS A TIGER
Sign (not posted): BOTH ROOMS CONTAIN TIGERS
Will you help these prisoners choose the correct doors, and escape this madman warden?





6 Comments:
Prisoner 1 - Door with sign 1.
Sign 1 is false (can't be either/or as they are the same) so Sign 2 is True.
Warden's Game
Optimal doors are given. Assume Warden is twisted and both doors having Tigers is allowed. If they are not allowed the choice will remain the same.
Prisoner 1
Assume door must contain either Tiger or Lady
Given: One True one False sign
Interpret (Either A OR B) as exclusive or (XOR) where XOR evaluates as:
XOR(False,False)=False
XOR(False,True)= True
XOR(True,False)=False
XOR(True,True)=False
Door 1, Door2, Sign1,Sign2
Tiger,Tiger, True, False
Tiger,Lady, False(XOR),False
Lady, Tiger, False, True
Lady, Lady, True,True
Eliminate False,False and True, True. Door 1 has P=1/2 Lady, Door 2 has P=0/2 Lady.
Door 1 is optimal.
Prisoner 2
Door 1, Door2, Sign1,Sign2
Tiger,Tiger,False,True
Tiger,Lady,False,False
Lady,Tiger,False,False
Lady,Lady,True, False
By rules:
- Lady,Tiger must be removed since lady in room 1 and sign is false.
2 Tigers possible, 2 Ladies possible, Tiger in room 1 and Lady in Room 2 possible. If forced to pick door pick Door 2. Door 1 is P=1/3 Lady, Door2 is P=2/3 Lady.
Door 2 is optimal.
Prisoner 3:
Door 1, Door2, Sign1,Sign2
Tiger,Tiger,False,False
Tiger,Lady,True,False
Lady,Tiger,True,True
Lady,Lady,True, True
By rules:
- Tiger, Lady must be removed since Tiger in room 1 and sign is True.
-Tiger,Tiger must be removed since Tiger in room 2 and sign is False.
-Lady, Lady must be removed since Lady is in room 2 and sign is True
2 Tigers not possible, 2 Ladies not possible, Lady in room 1 and Tiger in Room 2 possible. If forced to pick door pick Door 1. Door 1 is P=1/1 Lady, Door2 is P=0/1 Lady.
Door 1 is optimal.
Prisoner 4:
Door 1, Door2, Sign1,Sign2
Tiger,Tiger,True,False
Tiger,Lady,False,False
Lady,Tiger,False,True
Lady,Lady,True, True
By rules:
- Tiger, Tiger must be removed since Tiger in room 1 and sign is True.
-Lady,Tiger must be removed since Lady in room 1 and sign is False.
-Lady, Lady must be removed since Lady is in room 2 and sign is True
2 Tigers not possible, 2 Ladies not possible, Tiger in room 1 and Lady in Room 2 possible. If forced to pick door pick Door 2. Door 1 is P=0/1 Lady, Door2 is P=1/1 Lady.
Door 2 is optimal.
Prisoner 5:
Door 1, Door2, Sign1,Sign2
Tiger,Tiger,False,False
Tiger,Lady,True,False
Lady,Tiger,True,True
Lady,Lady,False,False
By rules:
- Tiger, Tiger must be removed since Tiger in room 1 and sign is True.
-Tiger,Lady must be removed since Tiger in room 1 and sign is True.
-Lady, Lady must be removed since Lady is in room 1 and sign is False
2 Tigers not possible, 2 Ladies not possible, Lady in room 1 and Tiger in room 2 possible. If forced to pick door, pick Door 1. Door 1 is P=1/1 Lady, Door2 P= 0/1 Lady.
Door 1 is optimal.
Prisoner 6:
Door 1, Door2, Sign1,Sign2
Tiger,Tiger,True,True
Tiger,Lady, True,False OR False, False
Lady,Tiger, False,False OR False, True
Lady,Lady,False,False
By rules:
- Tiger, Tiger must be removed since Tiger in room 1 and sign is True.
-Lady, Lady must be removed since Lady is in room 1 and sign is False
-Lady,Tiger must be removed since LAdy in Room 1 and sign is False
Tiger,Lady by rules must be False,False thus signs are arrange as:
Both room contains Tigers on Door 1.
This room contains a Tiger on Door 2.
2 Tigers not possible, 2 Ladies not possible, Tiger in room 1 and Lady in Room 2 possible. If forced to pick door pick Door 2. Door 1 is P=0/1 Lady, Door2 is P=1/1 Lady.
Door 2 is optimal.
Cam
Prisoner 2
Door 2 is best...
If a lady behind door 1 sign is tru so sign 1 on door 1, 2 on 2.
So must be a tiger in room 1 to make both signs false, and if both are false then there must be a lady in room 2.
Cam ....
2,3,4,5,and 6 all correct
#1 - the published solution varies from yours ... can you take another look?
Zaux
for #1 I suspect it's an issue with the interpretation of Either A OR B. statement. If the solution assumes it is a simple OR rather than an XOR then:
Door 1, Door2, Sign1,Sign2
Tiger,Tiger, True, False
Tiger,Lady, True,False
Lady, Tiger, False, True
Lady, Lady, True,True
Then the choice is 50/50. 1/2 times a Lady for Door 1 and 1/2 Times a Lady for Door 2. No choice is optimal.
Cam
Cam ...
exactly right ... there is lady behind doors 1 and 2
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