[bonanova]

Three boxes are all labeled incorrectly, and you must get the labels right.
The labels on the boxes read as follows:

[box 1] nails
[box 2] screws
[box 3] nails and screws

To gain the information you need to move the labels to the correct boxes,
you may remove a single item from one of the boxes. You may not look
into the boxes, nor pick them up and shake them, etc.

Can this be done? If so, how? If not, why not?

[Edit to add solution.]
[Edit again to explain.]

Spoiler for Solution:

Remove an item from box 3.
The item tells you what label to put on box 3.
Move the nails and screws label to the box labeled with the other item, and its label to the remaining box.

Example: you remove a nail from box 3.
Move the label nails from box 1 to box 3.
You can't move the nails and screws label to box 1: that would be a swap, and all three labels must be corrected.
Move it instead to box 2, and the screws label to box 1.

[box 1] screws
[box 2] nails and screws
[box 3] nails

[Aaron Burr]

Perhaps?
The only way this works is to assume all the boxes are in fact wrong. First draw from the [box 3] nails and screws. You will get either a nail or a screw. You will label it as which ever you draw out. Let's say it's a nail. The [box 1] nails can not contain nails so it must contain the screws. The [box 2] screws must there for be the mixture. In short:
[box 1] screws
[box 2] nails and screws
[box 3] nails

'No excuses!' We cannot shift that burden onto God, or nature, or the ways of the world

[comperr]

1 screws
2 nails and screws
3 nails

[bonanova]

Quote

Perhaps?

Correct.

@comperr, that might be correct, but we cant know until we inspect
an object from one of the boxes. which box should be drawn from,
and how do we reason from what we find to find the correct labeling?

[unreality]

Quote

[box 1] N
[box 2] S
[box 3] BOTH

all three are incorrect

thus:

box 1 - S or BOTH
box 2 - N or BOTH
box 3 - N or S

now lets pick S for box 1 (this color means that is not possible to have 1 of each):
box 1 - S
box 2 - N or BOTH
box 3 - N or S

thus it must be S, BOTH and N if box 1 is S

but say box 1 is BOTH:

box 1 - BOTH
box 2 - N or BOTH
box 3 - N or S

thus is must be BOTH-N-S

there are two possibilities. So somone please correct me if i am wrong, but it could be either of these two...

another way to come at that conclusion is that the only way to stay differnet is to keep the same order, just shift it by 1 or 2 to get different variations

BOTH = B

current variation: NSB
shift one: BNS (matches my second solution in the above proof)
shift two: SBN (matches my first solution in the above proof)

[bonanova]

Quote

Quote

[box 1] N
[box 2] S
[box 3] BOTH

all three are incorrect....

So somone please correct me if i am wrong, but it could be either of these two....

it could be any of four cases, depending on what object is drawn from one of the boxes.

The solution is to decide which box to draw from and how to reason to the correct labeling based on what is found.

[normdeplume]

Yes.

Remove an object from box three. If it is a screw, then you can safely place the screw label on box 3. Since all boxes are wrong, we know that there isn't nails in box 1 so this must be nails and screws, which leaves box 2 as nails. If you pick out a nail from box 3 then simple transpose the above to suit.
Edit to correct typo.

[bonanova]

Aaron Burr and normdeplume both have it.

I'm putting the answer into the first post.

[IceCreamTruck]

of course you cannot look into the boxes, as that would be too easy!!

This puzzle is absolutely dependant on all three of the boxes being labled incorrectly to begin with otherwise you'd have a real mess of screws and nails on your hands and no idea where to place lables.

Spoiler for your mother:

Open the dang boxes, already!!

Fire the original lable guy!!! <_<

This post has been edited by IceCreamTruck: 12 February 2008 - 02:46 PM

[void28]

This will not work, as long as all the labels are indeed false. If they are, then if you pick up a nail from one of the boxes, it could be nails or nails and screws. same difference with the screws.