Let's solve Jerome's favorite puzzle from the Raymond Smullyan's book "The Lady and The Tiger."
This puzzle originates from a short story published in the 1882! In this story a king of an ancient land discovers that his daughter has taken a lover far beneath her status. He is deciding to punish this man and teach his daughter a lesson. So, the king places his daughter's lover in the arena with two draped doors. Behind one door is a simple woman whom the lover must marry if he opens this door, behind the second door is a tiger that will eat the man alive if this door is opened. The princess may use her powers to find out where is the tiger and where is the maiden but will she save her lover and give him to someone else? Can the lover trust the princess?
Our puzzle is less sentimental and cruel. You are standing in front of three rooms and must choose one. In one room is a Lady (whom you could and wish to marry), in the other two rooms are tigers (that if you choose either of these rooms, the tiger invites you to breakfast – the problem is that you are the main course). Your job is to choose the room with the Lady. The signs on the doors are
- A Tiger is in this room
- A Lady is in this room
- A Tiger is in room two
At most only 1 statement is true. Where’s the Lady?
Your answers are accepted any time until midnight Eastern Time on Sunday, on our Family Puzzle Marathon.
Top image by Lal Beral, distributed under CCL.
10 comments:
I don't think it is the one that says a lady is inside since chances are it is false. I do not think it is in the one that says a tiger is in room 2 I think the other tiger is in that room. That leaves the room that says a tiger is in this room and at most one statement is true ( but not necessarily) so chances are the lady is in the one that says a tiger is in the room.
Gurubandhu
Assume statement 1 is True; since at most, one is true, 2 & 3 must be false.
1 - Tiger in 1 - True
2 - Lady in 2 - False (tiger)
3 - Tiger in 2 - True, but must be false since at most one is true. Therefore, statement one CANNOT be true, and is false. Since statement one is false, there is NOT a tiger in the room, meaning there is a Lady in room 1.
The lady is in room 1.
For grins, you can check the other possibilities:
- Assuming #2 is true makes #1 have to be false, but since the lady is in #2, there's a tiger in #1, making #1 true, which is impossible.
- Assuming #3 is true puts a tiger in room 2, making #2 false. #1 must also be false, putting the lady in #1, which is possible, and matches the previous assumption.
- Assuming all three are false, since at most one is true means none can be true puts a lady in #1, a tiger in #2, and makes #3 true, which violates the "all false" assumption and is therefore impossible).
The condition of “at most one is true” means we should test the following four possible combinations: all false, only “1”is true, only “2” is true and only “3” is true.
* all false: is a contradiction because 1 and 3 place a Lady in rooms 1 and 2 and we only have one Lady
* only “1” is true: is a contradiction, since “2” being false means there is a Tiger in room 2, thus making “3” also true, along with “1”.
* only “2” is true: is a contradiction, since “1” and “2” place a Lady in both rooms 1 and 2
* only “3” is true: is the only valid combination, placing Lady in room 1.
Whew. Our hero would have been in real trouble if there turned out to be two valid possibilities with different location of a Lady in each. Because who said that a king has to be fair and logical when it comes to enforcing his will? :-)
If statement 1 is True, then 2 and 3 have to be False, but then 3 becomes true if 2 has to be False. Then there will be more than one statements True.
If statement 2 is True, then for 1 to be False the lady has to be in Room1 and Room2.
If statement 3 is True, then there are no contradictions. So statement 3 has to be True and the lady will be in Room1, considering both 1 and 2 to be false.
The lady is Room number 1.
The lady is in Room 1. Statement 3 is the only true statement. That leaves the lady in Room 1, a tiger in Room 2, and a tiger in Room 3. ( If the lady were in Room 2, that would make 2 statements correct, and if the lady were in Room 3, that would also make 2 statements correct.)
The lady is in room 1 and the tigers are in rooms 2 and 3.
So room 1 and 2 are false and room 3 is true.
The lady is in room 1.
so Tiger is in room 1 is false
Lady is in room 2 is false.
Tiger is in room 2 is true.
I ruled out lady in room 2 because
Tiger in room 1 would be true.
Lady in room 2 would be true.
Tiger in room 2 would be false
I also ruled out lady in room 3 because
Tiger is in room 1 would be true.
Lady in room 2 would be false
Tiger in room 2 would be true.
mathmover
Shall we open the door of room One?
Just a tiny bit so that the paws will not squeeze through. And reveal a ttttt...... Lady!
Great job everyone.
Many provided excellent explanations. It looks like there are few ways of solving this:
1)investigate all 4 situations: FFF, FFT, TFF, FTF.
2)consider that the Lady is in room 1, then 2, then 3.
3)Jerome, who offered this puzzle, points out that statements 2 and 3 contradict each other, so only one of them can be true.
Gurubandhu - I do not get your logic but your answer is correct.
I see that my dear daughter Nadia submitted her solution. She frequently tries to solve our puzzles but this is the first time she dared to post. Welcome!
Puzzle point for everyone who answered.
Mathmover - you earned your 10th puzzle point. We shall write a puzzle about you next Friday. Don't miss it!
Oops, solved it and then saw it was an old puzzle. Will add my solution (written before looking at the answers) anyway!
Lady is in room #1
Statement #3 must be correct: "A tiger is in room 2" … makes statement 2 incorrect (lady in this room), statement 1 incorrect would mean Lady was in room #1, and a tiger in room #3.
Statement #2 cannot be correct because that would mean that 1 would be wrong and if a lady was in room 2 then a tiger would have to be in room 1. This would make two statements that would be correct.
Statement #1 cannot be correct because if a tiger was in room #1 (making this correct), the statement that a lady was in room #2 would have to be incorrect, which would mean a tiger was in room 2 making #3 correct. That would mean 2 statements are correct (against rules).
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