This is not my own, unfortunately. The late, great Raymond Smullyan may have created it.
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Boy -- Proposes Marriage to Girl.
Girl (with a titter, having already prepared): "Of these three boxes, one contains a dagger, while the other two are empty. I'll gladly marry you if pick and open an empty box."
Written on box one: "The dagger is in here."
Written on box two: "This box is empty."
Written on box three: "At most one of these three statements is true."
The boy thinks very carefully, then opens one of the boxes. He freaks out. "Ahhhh!"
Which box did the boy open, what did he find, and where did he go wrong?
Comments
Here's My Analysis...
Unfortunately, I don't know how to turn my answer into the same color as the box. So if you don't want to see it, try not to read the white type.
{Highlight to read} ...I'm guessing he picked box one, assuming that box three was the only true statement.
If box three is true, he'd be right, and he could pick either box one or box three.
If box three is false, he'd need to pick either box two or box three.
So either way, he can safely choose box three.
Eric
Since this is BigCloset
I'm guessing that step 1 in her preparation was to cut a hole in a box.
He opened Box 2
Which held the dagger. He should have opened box 3, as it had the only true statement.
Gumby - I'm flexible
"Imagination is more important, than knowledge" - Albert Einstein
“The most exciting phrase to hear in science, the one that heralds
new discoveries, is not ‘Eureka!’, but ‘that’s funny…’” - Isaac Asimov
What He Did
His analysis: if statement three is true, then it's the only true statement. Therefore the other two are false, and the dagger is in the second one.
If statement three is false, then the other two must be true, because there must be at least two true statements. The dagger is in the first one.
Therefore, he should open the third one, as it's impossible for the dagger to be there.
His act: he opens the third one, and finds the dagger. The girl opens the other two, and verifies that they are empty.
What went wrong?
-- Daphne Xu (a page of contents)
What went wrong?
The boy should have chosen "go to hell" option. You don't use such tests for the ones you love or care about.
Otherwise, I hate that kind of puzzles. "Go to hell" is still my number 1 choice. ;-)
Playing with Him
According to Smullyan, she was just having fun with him, messing with his mind. What went wrong here was not realizing that nothing prevented her from putting the dagger in the third box.
The movie "Labyrinth" had such a problem, with another huge fallacy. After some talk between a pair of doors and Sarah, one of the doors tells Sarah, "One of us always lies, and one of us always tells the truth." If that's true, one knows who the truth teller is. If it's false, then it's false, period.
-- Daphne Xu (a page of contents)
honestly, she trapped herself.
by saying "Pick and OPEN an empty box"... she is, by her phrasing, allowing him to test the boxes.
"This box feels heavy, and something rattles when I shake it. I'm not going to pick it."
"This box feels light, and nothing moves around in it or makes noise. I pick this box, and I will open it."
doesn't matter which box is opened
they could all contain daggers or all be empty.
Its not a logic puzzle but more of leap of faith.
But more importantly...did the boy WANT to marry the girl?
In my guess he found an empty box and went ahh because he didnt want to marry her.
Not English
I'm not English, so please correct me if I'm wrong. The statement "At most one of these three statements is true" says no more than one statement can be true.
1. Dagger in the first box - two statements true (1 and 2)
2. Dagger in the second box - one statement true (3, because it says nothing about the dagger)
3. Dagger in the third box - one statement true (2)
50/50 for the dagger to be in 2 or 3, so I would choose the first box.
Third Box
1. Dagger in the 1st box: two statements true, and the third statement false.
2. Dagger in the 2nd box: two statements false, and the third statement true.
3. Dagger in the 3rd box: the first statement is false, the second is true, the third is true if and only if it is false.
If the third statement is false, count the number of true statements and reconsider. If it's true, count the number of true statements and reconsider.
The girlfriend told the boy that one had the dagger and the other two were empty, and she was honest there. She told the truth.
-- Daphne Xu (a page of contents)
Thinking "Outside the Boxes" ...
a) Boy screams, opens no boxes, and leaves. He's not going to spend spend his life with a child who likes to play high-stakes silly-buggers games.
b) Same as (a), except girl also receives, via express delivery, a DVD of the opera "Turandot".
c) Girls screams, while learning the the last thing she will ever learn: "Do not provide a suitor with a weapon, and then jilt him".
d) Boy follows the logic chains others have suggested, makes his choice, but puts his hand on 'his' box, and says "Open the other two."
If the other two are empty, he then decides:
d-1) He wants to marry this ditz anyway, and closes and re-opens an empty box.
d-2) He's better off without her, (optional: opens 'his' box) and walks anyway
One more excursion ...
... thinking about poker.
If the boy is a decent, worthwhile and mature person - he wants his Love to be happy.
He puts his hand on a box - while watching her face and body language. "And perhaps I choose this one... and (moves hand to third box) there is this one."
Very carefully "reading" her "tells", she will look happier when it seems he is about to choose the box she wants him to choose. So that is the box he opens.
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Of course, boy can also play games, and never tell her how he knew the right box.