Brain Teasers
Logic Problem Puzzle?
Mr. Puzzle has been coming home from the local watering hole a little bit the worse for wear. Mrs. Puzzle is becoming increasingly fed up with his behaviour.
When Mr. Puzzle arrived home one evening last week, his wife had left him in a bit of a dilemma. They have three bedrooms and they used them all from time to time. On each door Mrs. Puzzle had placed a sign and also another sign stating that only one of the three other statements was true and that was where Mrs. Puzzle was sleeping for that night. Of the other two rooms, one was empty and the other had the neighbours' highly strung Pit Bull Terrier - Bruty inside. Mr. Puzzle was very confused, having consumed a few too many that very evening and he stared blankly at each door.
Sign on Bedroom 1. Bedroom 3 is empty
Sign on Bedroom 2. Bruty is in here
Sign on Bedroom 3. Bedroom 2 is empty
Behind which door is his wife, where is the dog and which room is empty?
When Mr. Puzzle arrived home one evening last week, his wife had left him in a bit of a dilemma. They have three bedrooms and they used them all from time to time. On each door Mrs. Puzzle had placed a sign and also another sign stating that only one of the three other statements was true and that was where Mrs. Puzzle was sleeping for that night. Of the other two rooms, one was empty and the other had the neighbours' highly strung Pit Bull Terrier - Bruty inside. Mr. Puzzle was very confused, having consumed a few too many that very evening and he stared blankly at each door.
Sign on Bedroom 1. Bedroom 3 is empty
Sign on Bedroom 2. Bruty is in here
Sign on Bedroom 3. Bedroom 2 is empty
Behind which door is his wife, where is the dog and which room is empty?
Answer
Bedroom 1. DogBedroom 2. Empty
Bedroom 3. Wife
If the sign on Bedroom 1 were true this would mean the wife must be in Bedroom 1, but then Bedroom 3 would have to be empty and therefore Bruty would have to be in Bedroom 2. This would mean 2 true signs, so is incorrect.
The sign on Bedroom 2 must be incorrect, as if it were true Bruty would be in here, however, only the Bedroom sign where the wife is sleeping, is true. Therefore, this is incorrect too.
Therefore:
Bedroom 3 sign is true - So Mrs. Puzzle is in here.
Bedroom 2 sign is a lie - So Bruty, the dog, must be in Bedroom 1, and this room must be empty.
Bedroom 1 sign is a lie - Mrs Puzzle is in Bedroom 3
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Comments
Dec 08, 2004
I LOVE these kind of puzzles, please have more!! They remind me of Alice in Wonderland.
It seems to me that the solution to this problem is not correct.
Assume that Door 3 statement is true, Bedroom 2 is empty. Thus:
Bedroom 1: Bruty or Mrs.
Bedroom 2: Empty
Bedroom 3: Bruty or Mrs.
The false statements on the other doors do not determine where either Bruty or Mrs. are.
Again, by accepting that Door 3 statement is true, the opposites of the false statements must then be true, so Bedroom 3 is not empty (we know that because we accepted Bedroom 3 as truth) and Bedroom 2 does not have Bruty (which we know because it must be empty).
Since Bedroom 3 only gives Mr. Puzzle a 50/50 chance of finding Mrs., another answer must be viable.
Assume that the statement on Door 1 is true, Bedroom 3 is empty, thus:
Bedroom 1: Bruty or Mrs.
Bedroom 2: Bruty or Mrs.
Bedroom 3: Empty
By accepting that Door 1 is true, the opposite of Door 2 must be true. Door 2 statement, Bruty is in here, means that Bruty is NOT in here, so we can deduce that it must be Mrs.
Bedroom 1: Bruty or Mrs.
Bedroom 2: Mrs.
Bedroom 3: Empty
And, of course, since Mrs. can't be in two places at once, we now know:
Bedroom 1: Bruty
Bedroom 2: Mrs.
Bedroom 3: Empty
Score for Mr. Puzzles.
BUT WAIT! What if Mr. Puzzles accepts that the statement on Door 2 is true: Bruty is in here. Thus:
Bedroom 1: Empty or Mrs.
Bedroom 2: Bruty
Bedroom 3: Empty or Mrs.
Now the opposites of the false statements on Doors 1 and 3 are true, which is to say Bedroom 3 is NOT empty and Bedroom 2 is NOT empty. Well, we knew that Bedroom 2 was not empty because we accepted that Bruty was in there, but if Bedroom 3 is not empty it must be Mrs. Then:
Bedroom 1: Empty
Bedroom 2: Bruty
Bedroom 3: Mrs.
So, not only is the given solution incorrect, but Mr. Puzzles is just going to have to sleep on the couch.
Assume that Door 3 statement is true, Bedroom 2 is empty. Thus:
Bedroom 1: Bruty or Mrs.
Bedroom 2: Empty
Bedroom 3: Bruty or Mrs.
The false statements on the other doors do not determine where either Bruty or Mrs. are.
Again, by accepting that Door 3 statement is true, the opposites of the false statements must then be true, so Bedroom 3 is not empty (we know that because we accepted Bedroom 3 as truth) and Bedroom 2 does not have Bruty (which we know because it must be empty).
Since Bedroom 3 only gives Mr. Puzzle a 50/50 chance of finding Mrs., another answer must be viable.
Assume that the statement on Door 1 is true, Bedroom 3 is empty, thus:
Bedroom 1: Bruty or Mrs.
Bedroom 2: Bruty or Mrs.
Bedroom 3: Empty
By accepting that Door 1 is true, the opposite of Door 2 must be true. Door 2 statement, Bruty is in here, means that Bruty is NOT in here, so we can deduce that it must be Mrs.
Bedroom 1: Bruty or Mrs.
Bedroom 2: Mrs.
Bedroom 3: Empty
And, of course, since Mrs. can't be in two places at once, we now know:
Bedroom 1: Bruty
Bedroom 2: Mrs.
Bedroom 3: Empty
Score for Mr. Puzzles.
BUT WAIT! What if Mr. Puzzles accepts that the statement on Door 2 is true: Bruty is in here. Thus:
Bedroom 1: Empty or Mrs.
Bedroom 2: Bruty
Bedroom 3: Empty or Mrs.
Now the opposites of the false statements on Doors 1 and 3 are true, which is to say Bedroom 3 is NOT empty and Bedroom 2 is NOT empty. Well, we knew that Bedroom 2 was not empty because we accepted that Bruty was in there, but if Bedroom 3 is not empty it must be Mrs. Then:
Bedroom 1: Empty
Bedroom 2: Bruty
Bedroom 3: Mrs.
So, not only is the given solution incorrect, but Mr. Puzzles is just going to have to sleep on the couch.
On each door Mrs. Puzzle had placed a sign and also another sign stating that only one of the three other statements was true and that was where Mrs. Puzzle was sleeping for that night.
The number and placement of the signs is not in question. Only the logic is faulty.
There is more information here that you do not appear to be using.
Please explain then..
One of these is true; two are false:
Sign on Bedroom 1. Bedroom 3 is empty
Sign on Bedroom 2. Bruty is in here
Sign on Bedroom 3. Bedroom 2 is empty
Here is your explanation for why Bedroom 1 cannot be true:
"If the sign on Bedroom 1 were true this would mean the wife must be in Bedroom 1...." Why? Why must the wife be in Bedroom 1 if Bedroom 3 is empty? If bedroom 3 is empty, she can be in Bedroom 1 or 2 and that still leaves Bedroom 3 empty. Please explain your rationale for spontaneously concluding she must be in Bedroom 3.
One of these is true; two are false:
Sign on Bedroom 1. Bedroom 3 is empty
Sign on Bedroom 2. Bruty is in here
Sign on Bedroom 3. Bedroom 2 is empty
Here is your explanation for why Bedroom 1 cannot be true:
"If the sign on Bedroom 1 were true this would mean the wife must be in Bedroom 1...." Why? Why must the wife be in Bedroom 1 if Bedroom 3 is empty? If bedroom 3 is empty, she can be in Bedroom 1 or 2 and that still leaves Bedroom 3 empty. Please explain your rationale for spontaneously concluding she must be in Bedroom 3.
Look for more information in the puzzle about where Mrs. Puzzle is sleeping for the night.
NORTHHEAD -- I thought the same thing when I first saw the puzzle, until I realized Mrs. Puzzle was behind the door with the true sign on it. This does indeed leave only one solution. Excellent teaser!
Thanks tsimkin - Wasn't sure how much information to give away.
That is a very nice teaser..needs some thinking,but is comepletly logical
- Nice to see it's one of your favourites Tiffi!
great one!
Hey great job, and we need to escuse people who blow up with anger if they get a problem wrong.
Therez another solution....
Conisder the sign on bedroomm-1 is true...then we get the following answer...It satisfies all the other conditions too....
==>
Bedroom 1. Dog
Bedroom 2. Wife
Bedroom 3. Empty
Conisder the sign on bedroomm-1 is true...then we get the following answer...It satisfies all the other conditions too....
==>
Bedroom 1. Dog
Bedroom 2. Wife
Bedroom 3. Empty
Mr. Solution -- I think you missed a point -- "only one of the three other statements was true and that was where Mrs. Puzzle was sleeping for that night." Therefore, if the sign on door one was true, she would be behind that door, but if it were true, the dog would be. So there is only the posted solution.
Well I sure missed the part where the Mrs was sleeping behind the door with the TRUE sign!
I was sure there was a problem with this teaser... turns out the problem was me!
Great teaser... once I understood what I was looking for !
I was sure there was a problem with this teaser... turns out the problem was me!
Great teaser... once I understood what I was looking for !
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