Truth in packaging

[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.]

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

[Guest]

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

[Guest]

1 screws

2 nails and screws

3 nails

[bonanova]

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]

[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]

[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.

[Guest]

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.

[Guest]

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.

Open the dang boxes, already!!

Fire the original lable guy!!! <_<

Edited February 12, 2008 by IceCreamTruck

[Guest]

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.

[bonanova]

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.

Pick something from the box labeled Nails and Screws.

What you find there tells you how to correct all the labels.

Did you think that through carefully?

[Guest]

pore them all into one box and lable it nails and screws.

Kiger

[bonanova]

pore them all into one box and lable it nails and screws.

Kiger

Nope. [1] It doesn't obey the rules, and [2] it doesn't solve the problem.

[1] You may remove only one item from one box.

[2] You have to label all three boxes correctly.

[Guest]

incorrect labels--

[box 1] nails

[box 2] screws

[box 3] nails and screws

My logic is---

As ALL THREE boxes are labelled incorrectly, so, the correct combination can be (remember cyclic order?)--

combination 1:

[box 1] nails and screws

[box 2] nails

[box 3] screws

OR

combination 2:

[box 1] screws

[box 2] nails and screws

[box 3] nails

Now, ONLY BOX 3 can contain either screw or nail, but not both. So, pick up a sample from box 3, if it is a screw, Then use combination1 to label the boxes, otherwise (if nails), then use combination 2 to label it. So, the puzzle have two answers. Am I wrong??

[Guest]

I agree with storm you must have two solutions given that the box your opening has 2 different outcomes.

[bonanova]

I agree with storm you must have two solutions given that the box your opening has 2 different outcomes.

[1] Remove one item from the "Nails and Screws" box. Call that the 1st box.

[2] Move the label for the removed item from its incorrect box, call that the 2nd box, to the 1st box.

[3] Move the label from the 3rd box to the 2nd box.

[4] Put the "Nails and Screws" label on the 3rd box.

[Guest]

[1] Remove one item from the "Nails and Screws" box. Call that the 1st box.

[2] Move the label for the removed item from its incorrect box, call that the 2nd box, to the 1st box.

[3] Move the label from the 3rd box to the 2nd box.

[4] Put the "Nails and Screws" label on the 3rd box.

I got your point....there is only one method...but the box combinations can be two.....

Edited March 3, 2008 by storm

[bonanova]

Exactly.

I might have been playing with semantics...

[Guest]

not able. for you may find the box to put the right label on- or it could be the wrong- say you pick up a screw ok so maybe there are nails and you felt one as you picked up the screw- so you get that one right, but the other two are unknowned

[Guest]

Assuming the boxes are all labeled incorrectly, why not just remove the box itself. that way it doesn't matter witch box you open, you will still know how they should all be labeled.

Ex. Remove box # 2 and what ever spills out, you put the appropriate label, and move the only label that hasn't moved to the blank spot and move the origional label on box # 2 to the remaining box.

[Guest]

I think I've seen something like this one before... ok ... here goes my logic...

first... ALL the labels are wrong. So I would grab an item from the box labeled both. Whatever you grab Nails or Screws... gets that label.

Because they are ALL wrong, then you move either nails or screws to the box you just removed. and then the label "nails and screws" goes to that one. Clear as mud, right?

N, S, NS pick something from NS, if its S put s on that box, put n on the 2nd box and NS on the first box.

if its N put N on that box, put 2 on first box and put NS on 2nd box.

[bonanova]

RR you have it.

[Guest]

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.]

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

The only way to be suare,that we'll label the boxes correct is to take an item from the box 3 with label"nails and screws".From the item.which we take will depend the name of the lable.

Example:If we take nail,the label on box 3 will be "nails".

We know,that all the boxes are labeld incorrect and we already know the correct label for box 3.Left only to remove leble "nails

from 1 to 3,lable"nails and screws" from 3 to 1 and lable "screws" from 2 to1.Now all boxes are correct labeled.

box 1-screws

box 2-nails and screws

box 3-nails

[Guest]

You start with

1- nails

2- screws

3- nails & screws

and are told ALL BOXES ARE LABELLED INCORRECTLY.

Therefore there are 2 possible correct answers as we have been told that the list above is INCORRECT. To solve the problem and determine which possibility is the right one do the following.

Pick from box 3 since you know it CANNOT be screws and nails because it is labelled as such INCORRECTLY, therefore it is either Screws or Nails, and whatever you pick out from that box will tell you the answer.

Therefore

If you get a Screw the solution is

1- Nails & Screws (can't be nails because it says its nail and that is incorrect, can't be screws because box 3 is screws)

2- Nails (only option left after 3 & 1 have been determined)

3- Screw (you picked a screw)

If you get a Nail the solution is

1- Screw (only option left after 3 & 2 have been determined)

2- Nails & Screws (can't be screws because it says it's screws and that is incorrect, can't be nails because box 3 is nails)

3- Nail (you picked a nail)

[Guest]

djkrys,

Thank you. I was about to make pretty much the same point.

It seems many people who responded to this puzzle were overlooking the original statement of the problem, namely that ALL OF THE BOXES ARE LABELED INCORRECTLY. That being the case, then picking an item from the box labeled "nails and screws" tells you what's in the box and the rest of the solution as stated above works fine.

[Guest]

NO, IT CANT BE DONE

IF U PULL ONE ITEM FROM ONLY ONE BOX AND ANY BOX. THEN ALL BOXES CAN HAVE BOTH ITEMS OR, IF THAT DIDNT MAKE SENSE...

PULL FROM A BOX IF IT IS A SCREW THEN THE ONLY THING U KNOW IS THAT, THAT BOX DID INDEED INCLUDE A SCREW, BUT THIS DOES NOT CONCLUDE THAT U DONT HAVE NAILS IN IT...THIS IS THE ONLY THING YOU CAN DEDUCE FROM PULLING ANY ONE OBJECT FROM ANY ONE BOX. SO U WILL ALWAYS GET AN ANSWER ON AN OBJECT THAT CAN INDEED BE INCLUDED IN THE BOX BUT THERE IS NO WAY TO BE SURE THAT THE BOX DOESNT INCLUDE THE OTHER TYPE OF ITEM OR NOT. SO YOU WILL NOT KNOW WHAT LABEL TO PUT ON THE BOX. IN THE DIAGRAM THE PART THAT SAYS [bOX 1], [bOX 2] AND SO ON IS JUST FOR LABELING PURPOSES TO BETTER DESCRIBE THE PUZZLE, IT DOESNT MEAN U KNOW BEFOREHAND WHICH BOX IS 1, 2, OR 3 NOR DO U KNOW WHICH BOX IS NAILS, SCREWS, OR NAILS AND SCREWS, ALL U KNOW IS THAT ALL THE LABELS ARE WRONG.