The Warden gets fired ...
One of the prisoners who chose the right door and was released, reported the sadistic practices of the warden. The warden has received notice that he has been relieved of resposibilities at the prison .... today is his last day. He decides to have one more round of fun:
Prisoner 1:
(three doors are offered ... one hiding a lady and two containing tigers ... only one of the signs is true)
Sign 1: A TIGER IS IN THIS ROOM
Sign 2: A LADY IS IN THIS ROOM
Sign 3: A TIGER IS IN ROOM 2
Prisoner 2:
(3 doors ... the sign on the door containing the lady is true ... at least one of the other two signs are false)
Sign 1: A TIGER IS IN ROOM 2
Sign 2: A TIGER IS IN THIS ROOM
Sign 3: A TIGER IS IN ROOM 1
Prisoner 3:
(one room contains a lady ... another has a tiger ... and the third room is empty. The sign on the door containing the lady is true. The sign on the door of the room with the tiger is false. the sign on the empty room could be true or false. Find the room with the lady.)
Sign 1: ROOM 3 IS EMPTY
Sign 2: THE TIGER IS IN ROOM 1
Sign 3: THIS ROOM IS EMPTY
The warden decided to make his last game a bit more challenging.
Prisoner 4:
(one room has a lady ... the other rooms have a tiger or are empty. The sign on the door with the lady is true ... the signs on the tiger rooms are false ... emtpy room signs can be true or false)
Sign 1: THE LADY IS IN AN ODD-NUMBERED ROOM
Sign 2: THIS ROOM IS EMPTY
Sign 3: EITHER SIGN 5 IS RIGHT OR SIGN 7 IS WRONG
Sign 4: SIGN 1 IS WRONG
Sign 5: EITHER SIGN 2 OR SIGN 4 IS RIGHT
Sign 6: SIGN 3 IS WRONG
Sign 7: THE LADY IS NOT IN ROOM 1
sign 8: THIS ROOM CONTAINS A TIGER AND ROOM 9 IS EMPTY
Sign 9: THIS ROOM CONTAINS A TIGER AND 6 IS WRONG
The prisoner looked at the signs and said, "This problem is unsolvable!"
The warden: "I know!"
The prisoner: "At least tell me if room 8 is empty?
The warden: "ok ... " the warden proceeded to answer the question about room 8.
The prisoner: "Thank you ... now I can make my decision."
This is the last appearance of the evil warden ... but these prisoners still need help choosing doors! Which doors should they choose?
Prisoner 1:
(three doors are offered ... one hiding a lady and two containing tigers ... only one of the signs is true)
Sign 1: A TIGER IS IN THIS ROOM
Sign 2: A LADY IS IN THIS ROOM
Sign 3: A TIGER IS IN ROOM 2
Prisoner 2:
(3 doors ... the sign on the door containing the lady is true ... at least one of the other two signs are false)
Sign 1: A TIGER IS IN ROOM 2
Sign 2: A TIGER IS IN THIS ROOM
Sign 3: A TIGER IS IN ROOM 1
Prisoner 3:
(one room contains a lady ... another has a tiger ... and the third room is empty. The sign on the door containing the lady is true. The sign on the door of the room with the tiger is false. the sign on the empty room could be true or false. Find the room with the lady.)
Sign 1: ROOM 3 IS EMPTY
Sign 2: THE TIGER IS IN ROOM 1
Sign 3: THIS ROOM IS EMPTY
The warden decided to make his last game a bit more challenging.
Prisoner 4:
(one room has a lady ... the other rooms have a tiger or are empty. The sign on the door with the lady is true ... the signs on the tiger rooms are false ... emtpy room signs can be true or false)
Sign 1: THE LADY IS IN AN ODD-NUMBERED ROOM
Sign 2: THIS ROOM IS EMPTY
Sign 3: EITHER SIGN 5 IS RIGHT OR SIGN 7 IS WRONG
Sign 4: SIGN 1 IS WRONG
Sign 5: EITHER SIGN 2 OR SIGN 4 IS RIGHT
Sign 6: SIGN 3 IS WRONG
Sign 7: THE LADY IS NOT IN ROOM 1
sign 8: THIS ROOM CONTAINS A TIGER AND ROOM 9 IS EMPTY
Sign 9: THIS ROOM CONTAINS A TIGER AND 6 IS WRONG
The prisoner looked at the signs and said, "This problem is unsolvable!"
The warden: "I know!"
The prisoner: "At least tell me if room 8 is empty?
The warden: "ok ... " the warden proceeded to answer the question about room 8.
The prisoner: "Thank you ... now I can make my decision."
This is the last appearance of the evil warden ... but these prisoners still need help choosing doors! Which doors should they choose?
posted by Zaux at
5:59 PM
9 Comments:
Prisoners 1,2,3 should pick Room1
Prisoner 4, I suspect that solution says it is Room 7.... however I would tend to say it is still unsolvable with the wording.
The issue I have with the wording is:
-Either A or B should = XOR(A,B) meaning one of A OR B, but not both A AND B.
-I suspect the solution treats the statement as A OR B. Meaning at least one of A OR B.
How the two evaluate:
A ,B
False, False= OR is False, XOR is False
True, False = OR is True, XOR is True
False, True= OR is True, XOR is True
True,True= OR is True, XOR is False
Detailed solutions to follow....
Cam
Cam ...
you are right
Cam, if you send an email to ToM asking to be added as an author, then you can log on to blogger.com and post your own puzzles ... at least, that's what I did
Warden gets fired (Prisoners 1-3)
For Rooms
R=Tiger , L=Lady
For Signs
T=True, F=False
Prisoner 1:
Room Sign
L,R,R =F,F,T
R,L,R=T,T,F
R,R,L=T,F,T
If only 1 True then must be L,R,R. Room 1 is choice.
Prisoner 2:
Room Sign
L,R,R =T,T,F
R,L,R=F,F,T
R,R,L=T,T,T
Only L,R,R amd R,R,L have Lady telling truth. Of those two only L,R,R has at least one false. Room 1 is the choice.
Prisoner 3:
Lady can not be in room 3 as sign can not be true with Lady in it.
If Lady is in 2 then Sign is true thus Tiger is in 1. Then Sign 1 is False and Room 3 is not empty. But one the Tiger and Lady have already been used so it must be empty... PARADOX
Thus Lady must be in Room 1. Check anyway:
-If Lady is in 1 then Room 3 is empty. Room 3 is empty and sign 3 is true is ok. Tiger in room 2 by elimination making sign false thus Tiger is not in room 1. Checks out ok.
Lady in Room 1.
Cam
Prisoner 4 (PART 1 of 2):
Sign 8 can not have a Lady. As it would mean the sign is true meaning it would require a Tiger in it. PARADOX.
Sign 8
-Sign must be False as if it contains a Tiger then the sign must be False per the rules.
-True Rooms: ,False Rooms:8
PATH 1)(Room 8 has Tiger)
-Assume room 8 has a Tiger then room 9 must be NOT empty for sign to be False.
Assume Room 9 is not empty.
-9 can not contain a Lady as for sign to be true it must have a Tiger.
-Sign must be False as if it contains a Tiger then the sign must be False per the rules.
-Room 9 is NOT empty thus it contains a Tiger thus sign 6 must be NOT wrong i.e. Sign 6 must be right
-True Rooms:6 ,False Rooms:8,9
Sign 6
-If sign 6 is right then sign 3 is wrong.
-True Rooms:6 ,False Rooms:3,8,9
Sign 3
-if sign 3 is wrong then to make XOR(A,B) False. Both statements must be True or both statement must be False. (Note: If just OR instead of XOR, then both statements must be False)
- (sign 5 is right AND sign 7 is wrong)OR (Sign 5 is wrong AND sign 7 is right)
-True Rooms:6 ,False Rooms:3,8,9
Sign 5+7
PATH 1A)(both statements True) (sign 5 is right AND sign 7 is wrong)
-Sign 5 is right and sign 7 is wrong
-Per sign 7 being False Lady is in Room 1. Must check to see if consistent.
-if sign 5 is right then XOR(A,B) . Only one statement is true. (Note: If just OR instead of XOR, then both statements may be True)
- (sign 2 is right AND sign 4 is wrong)OR (Sign 2 is wrong AND sign 4 is right)
- True Rooms:5,6 ,False Rooms:3,7,8,9
Sign 2+4
Path 1AA)(TF)( Sign 2 is right and Sign 4 is wrong)
-Sign 2 is right and Sign 4 is wrong
-Room 2 is empty
-Sign 4 is wrong thus sign 1 is right thus Lady must be in ODD rooms.
- True Rooms:1,2,5,6 ,False Rooms:3,4,7,8,9
-Rooms 1 and 5 are odd and true allowing Lady to be in Room 1.
Path 1AB)(FT)( Sign 2 is wrong and Sign 4 is right)
-Sign 2 is wrong and Sign 4 is right
-Room 2 is NOT empty
-Sign 4 is right thus sign 1 is wrong thus Lady must be in EVEN rooms.
- True Rooms:4,5,6 ,False Rooms:1,2,3,7,8,9
-Rooms 4 and 6 are even and true allowing Lady to be in Room 4 or 6. This is a PARADOX with room 7.
Path 1AC)(TT in case of OR instead of XOR)( Sign 2 is right and Sign 4 is right)
-Sign 2 is right and Sign 4 is right
-Room 2 is empty
-Sign 4 is right thus sign 1 is wrong thus Lady must be in EVEN rooms.
- True Rooms:2,4,5,6 ,False Rooms:1,2,3,7,8,9
-Rooms 4 and 6 are even and true allowing Lady to be in Room 4 or 6. This is a PARADOX with room 7.
BACK TO:
Sign 5+7
PATH 1B)(both statements False)( Sign 5 is wrong AND sign 7 is right)
- Sign 5 is wrong AND sign 7 is right
-Per sign 7 being right Lady is NOT in Room 1. Must check to see if consistent.
- if sign 5 is wrong then to make XOR(A,B) False. Both statements must be True or both statement must be False. (Note: If just OR instead of XOR, then both statements must be False)
- (sign 2 is right AND sign 4 is right)OR (Sign2 is wrong AND sign 4 is wrong)
- True Rooms:6,7 ,False Rooms:5,8,9
Sign 2+4
Path 1BA)(TT) (Sign 2 is right and Sign 4 is right)
-Sign 2 is right and Sign 4 is right
-Room 2 is empty
-Sign 4 is right thus sign 1 is wrong thus Lady must be in EVEN rooms.
- True Rooms:2,4,6,7 ,False Rooms:1,3,5,8,9
-Rooms 2,4,6 are even allowing Lady to be in Room 2,4,6, but room 2 is a paradox. So Lady can be in Room 4 or 6.
Sign 2+4
Path 1BB)(FF)( Sign 2 is wrong and Sign 4 is wrong)
-Sign 2 is wrong and Sign 4 is wrong
-Room 2 is NOT empty
-Sign 4 is wrong thus sign 1 is right thus Lady must be in ODD rooms.
- True Rooms:6,7 ,False Rooms:1,2,3,4,5,8,9
-Rooms 7 is odd allowing Lady to be in Room 7
-NOTE: For path 1 if all XORs are ORs then this is the only path.
2B Cont'd
Cam
Prisoner 4 (PART 2 of 2):
START BACK AT ROOM 8
-Assume room 8 is Empty then room 9 may or may not be Empty.
Assume Room 9 is not empty. Then it must have a Tiger and just follows down PATH 1.
-Assume Room 9 is empty and 6 is right, then it just follows down PATH 1.
-Assume Room 9 is empty and 6 is wrong, then we create a new PATH 2.
PATH 2) (Room 9 is empty and 6 is wrong)
Room 9 is empty and 6 is wrong
-True Rooms: ,False Rooms:6,8,9
Sign 6
-6 is wrong so sign 3 is right
-True Rooms: 3,False Rooms:6,8,9
Sign 3
-if sign 3 is right then XOR(A,B) . Only one statement is true. (Note: If just OR instead of XOR, then both statements may be True)
-XOR(5 is right,7 is wrong). (5 is right and 7 is right)OR(5 is wrong and 7 is wrong)
-True Rooms: 3,False Rooms:6,8,9
PATH 2A) (TF) (5 is right and 7 is right)
-Sign 5 is right
-Sign 7 is right, thus Lady NOT in Room 1. Need to check to see if consistent.
-if sign 5 is right then XOR(A,B) . Only one statement is true. (Note: If just OR instead of XOR, then both statements may be True)
-XOR(2 is right,4 is right). (2 is right and 4 is wrong)OR(2 is wrong and 4 is right)
-True Rooms: 3,5,7 False Rooms:6,8,9
PATH 2AA)(TF) (2 is right and 4 is wrong)
-Sign 2 is right and room 2 is empty
-Sign 4 is wrong thus sign 1 must be right thus Lady in ODD room
- True Rooms: 1,2,3,5,7, False Rooms:4,6,8,9
-Lady may be in Room 1,3,5,7 but if 7 is True 1 is invalid. so she may reside in Rooms 3,5,7.
PATH 2AB)(FT) (2 is wrong and 4 is right)
-Sign 2 is wrong and room 2 is NOT empty
-Sign 4 is right thus sign 1 must be wrong thus Lady in EVEN room
- True Rooms: 3,4,5,7, False Rooms:1,2,4,6,8,9
-Lady may be in Room 4.
PATH 2AC)(TT) (2 is right and 4 is right)
-Sign 2 is right and room 2 is empty
-Sign 4 is right thus sign 1 must be wrong thus Lady in EVEN room
- True Rooms: 2,3,4,5,7, False Rooms:1,4,6,8,9
-Lady may be in Room 2,4. Being in Room 2 would be a Paradox, thus she must be in Room 4.
PATH 2B) (FT) (5 is wrong and 7 is wrong)
-Sign 5 is wrong
-Sign 7 is wrong, thus Lady in Room 1. Need to check to see if consistent.
- if sign 5 is wrong then to make XOR(A,B) False. Both statements must be True or both statement must be False. (Note: If just OR instead of XOR, then both statements must be False)
- (sign 2 is right AND sign 4 is right)OR (Sign2 is wrong AND sign 4 is wrong)
-True Rooms: 3 False Rooms:5,6,7,8,9
PATH 2BA)(TT) (2 is right and 4 is right)
-Sign 2 is right and room 2 is empty
-Sign 4 is right thus sign 1 must be wrong thus Lady in EVEN room
- True Rooms: 2,3,4 False Rooms:1,5,6,7,8,9
-Lady may be in Room 2,4. Being in Room 2 would be a Paradox, thus she must be in Room 4.
PATH 2BB)(FF) (2 is wrong and 4 is wrong)
-Sign 2 is wrong and room 2 is NOT empty
-Sign 4 is wrong thus sign 1 must be right thus Lady in ODD room
- True Rooms: 1,3 False Rooms:2,4,5,6,7,8,9
-Lady may be in Room 1,3. Since sign 7 is false she must be in Room 1. consistent.
Path 2 results in many possible answers.
-2AA=Room 3,5,7,
-2AB=Room 4
-2AC=Room 4
-2BA=Room 4 (XOR path)
-2BB= Room 1
Multiple answers for path 2 thus no unique answer.
But problem must have unique as prisoner indicates decision can be made, thus answer must be Warden said Room 8 is not empty i.e. it has a Tiger.
Path 1 Summary:
-1AA- Room 1 (XOR path)
-1AB- Paradox (XOR path)
-1AC-Paradox (XOR path)
-1BA-Room 4 or 6 (XOR path)
-1BB-Room 7
-No unique answer unless we remove all the XOR paths i.e. interpret all XORs as ORs.
-Then the lady must be in Room 7.
Cam
The truth comes out: the "Warden" was actually a pimp (all those ladies) and wild animal smuggler.
Zaux,
Thanks for the advice re: posting puzzles and thanks again for your continued amazing work on posting puzzles.
Cam
Cam ...
if you ever want me to post puzzles for you, I will be glad to ... if you want to offer email address or goever you want to do it.
Thanks for the outstanding analyses you do ... I have learned lots from you and Chris ...my math skills have suffered from lack of usage, but I still enjoy the process.
mmmmmm ..."goever" -> "however"
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