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]

OOOOOOOOOOOOOOOOOOO, TO DJKRYS MY LAST POST WAS A WASTE THNX FOR THE ANSWER, I DIDNT REALIZE THAT

[Guest]

reach into the nails and screws and if you pull out screws then its the screws if you pull out nails its nails

[Guest]

This should be easy since ALL boxes are labeled incorrectly.

Start from box 3. This can only be labeled as nails or as screws since it is incorrectly labeled. Whatever you picked up from here is the correct label.

SITUATION 1:

If you picked up a screw on the 3rd box, label this as “SCREWS”.

With box 3 confirmed as screw, you can move to box 1. Since we have eliminated screws on the option, box 1 can only be nails or nails and screw. However, it is incorrectly labeled so you cannot label it as nails, you can then conclude that box 1 should be labeled as “NAILS AND SCREWS”. The remaining label is “NAILS” so you can then conclude that this belongs to box 2.

SITUATION 2:

If you picked up a nail on the 3rd box, label this as “NAILS”.

With box 3 confirmed as nails, you can move to box 2. Since we have eliminated nails on the option, box 2 can only be screws or nails and screws. However, it is incorrectly labeled so you cannot lable it as screws, you can then conclude that box 2 should be labeled as “NAILS and SCREWS”. The remaining label is “SCREWS” so you can then conclude that this belongs to box 1.

[Guest]

This should be easy since ALL boxes are labeled incorrectly.

Start from box 3. This can only be labeled as nails or as screws since it is incorrectly labeled. Whatever you picked up from here is the correct label.

SITUATION 1:

If you picked up a screw on the 3rd box, label this as “SCREWS”.

With box 3 confirmed as screw, you can move to box 1. Since we have eliminated screws on the option, box 1 can only be nails or nails and screw. However, it is incorrectly labeled so you cannot label it as nails, you can then conclude that box 1 should be labeled as “NAILS AND SCREWS”. The remaining label is “NAILS” so you can then conclude that this belongs to box 2.

SITUATION 2:

If you picked up a nail on the 3rd box, label this as “NAILS”.

With box 3 confirmed as nails, you can move to box 2. Since we have eliminated nails on the option, box 2 can only be screws or nails and screws. However, it is incorrectly labeled so you cannot lable it as screws, you can then conclude that box 2 should be labeled as “NAILS and SCREWS”. The remaining label is “SCREWS” so you can then conclude that this belongs to box 1.

[Guest]

Sunkissed.

Congratulations. Very clearly explained.

[Guest]

This one's fairly easy.

If the labels are surely incorrect, just pick an item from the nails and screws. If its screws, then interchange it with the screw label. Then, put the nail label where it was previously screws. The previous nail box is the nail and screw.

Interchange it if you picked nails.

[Guest]

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

We know all the boxes are incorrectly labelled.

We know we can't shake the boxes, look into them or take out more than one item.

There is no rule, however, stating that we cannot feel around inside the chosen box when we reach inside it.

Reach into the box labelled "Screws". Since we know it's mislabelled, it would have to contain either Nails or Nails & Screws. Since the nails would be thinner, they would drift to the bottom of the box, & the screws would be on top. Ergo, if you reached in & were able to feel a number of nails, you would know it should be labelled "Nails". If you felt screws & knew the box was mislabelled, you would know to label it "Nails & Screws".

Taking the first case as an example, remove the Screws label from Box 2. Then take the Nails label from Box 1 and place it on Box 2. Since Box 3 is also incorrectly marked, and Box 2 is now OK, you just switch the label on Box 3 to Box 1 & put the Screws label on Box 3.

Ireally did this off the top of my head - hope I'm not missing something.

[Moses]

As all three boxes were labelled incorrectly there will only be 2 ways of doing this.

Say this is correct order 

1. Nails 2. Nails and screws 3.screws

No dearrangments will be

1.S   2.N   3.N&S

And 

1.N&S  2.S  3.N

So we will get the actual arrangememt by doing either doing two swaps  ( 1&2, 2&3) for dearrangement 1 or four swaps (1&2,2&3) again (1&2,2&3) for dearrangement 2.

So after doing two swaps we can take an item from a box and check. If it turn outs to be the wrong one. Then make two swaps. And we will get the actual arrangememt.