## September 20, 2012

### Box Packing Puzzle

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

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?

Anonymous said...

Yes. Remove an item from box 3. If it's a nail, move the "nails" label to box 3, the "screws" label to box 1, and the "nails and screws" label to box 2. It it's a screw, move the "screws" label to box 3 and the "nails" label to box 2 and the "nails and screws" label to box 1.

Anonymous said...

I do not agree. If you get a nail from box 3 does not mean that it can't have screw in it and if you get a screw from the box 3 doesnt mean that it cant have nails in it. Cant be arranged according to me.

Matt B. said...

The key bit of information here is that "Three boxes are all labeled incorrectly". With this, you can assume that box 3 either has nails or has screws. So if you take an item from that box, you can be sure that that box contains only those items. If the box contained a nail, then box 1 would be screws, and box 2 would be nails and screws. If the box contained a screw, then box 1 would be nails and screws, and box 2 would be nails.
If it is a possibility that any of the boxes could be already correct, then it is impossible to solve this problem. This is because if you pick an item from any box, you would have at least 2 choices for what could actually be in that box.

Anonymous said...

correct

Anonymous said...

That one stumped me. Thanks Matt B.

tiger said...

This leads us to the conclusion that the unit cubes must be placed in the long diagonal of the box. riddles

Anonymous said...

It says all 3 were labeled incorrectly in the beginning... thus the label with screw+nail (box 3) will only contain either one of them (since the label is wrong)... take one item out lets say u get a screw then (Box 3 = screw)and now Box 2 is unlabelled... but since we know Box 1 is not nails and Box 3 is screw then (Box 1 = screw+nail)... and of course Box 2 in the beginning labelled screws (wrong) then (Box 2 = nails)

Anonymous said...

It says all 3 were labeled incorrectly in the beginning... thus the label with screw+nail (box 3) will only contain either one of them (since the label is wrong)... take one item out lets say u get a screw then (Box 3 = screw)and now Box 2 is unlabelled... but since we know Box 1 is not nails and Box 3 is screw then (Box 1 = screw+nail)... and of course Box 2 in the beginning labelled screws (wrong) then (Box 2 = nails)

Anonymous said...

Since Box 1 is not nails. It is either screws and nails or just screws.

Since Box 2 is not screws. It is either nails or screws and nails

Since Box 3 says screws and nails and it not that. If a screw comes out it is a screws box. If a nail comes out is a nails box. Since there are two possible choices for the first two boxes box 1 or box 2 would be nails or nails and screws so the problem is not able to be solved with this limited information. IMO

AA said...

No. It can't be done unless you get to pick one thing from two of the boxes.

Maharaja Subramanian said...

Here the clue is : Three boxes are all labelled incorrectly.

So, just Pick an item from Box 1,

Scenario 1: If that item is Nail, then label that Box 1 as "Nails and Screws", Box 2 as "Nails" and Box 3 as "Screws"