Nails and screws

[Butch]

You have 3 boxes. 1 box contains nails, 1 contains screws and 1 contains both.

All three boxes have the wrong labels.

You can open boxes and remove items from them but you cannot look in the boxes.

How many boxes would you need to open and how many items would you need to remove to figure out how to label them correctly?

The boxes are labeled "nails", "screws", "nails and screws".

Edited November 19, 2016 by Butch

[CharonY]

 

If I take out one item from the box labeled screws and nails I know whether it has only screws or nails.
Thus, if it has nails, the box with screws would be automatically screws+nails and the nail box has screws (as all labels are wrong).
And vice versa if it is a screw.

 

[Butch]

Correct.

[AbstractDreamer]

I wouldn't need to open any boxes.

Just replace all the labels with "Nails AND/OR Screws".

Then they would all be labelled correctly.

[imatfaal]

I wouldn't need to open any boxes.

Just replace all the labels with "Nails AND/OR Screws".

Then they would all be labelled correctly.

My thought was similar - put everything in the box marked nails and screws; but charon has the correct answer quicker than anyone else

[John Cuthber]

The question refers to nails and screws but they are essentially equivalent.

If you went through the whole puzzle and replaced the word "nails" with "screws" and vice versa, the meaning of the puzzle would be the same.

Since this symmetry exists for the puzzle, it must also exist for the answer (assuming there is a unique answer).

The only answer that can have that symmetry is "nails and screws" and so that must be the correct response.

[AbstractDreamer]

There are actually two solutions to that symmetry, but for there to be only one unique answer, both need to coexist.

 

"nails and screws"

"screws and nails"

[Butch]

My thought was similar - put everything in the box marked nails and screws; but charon has the correct answer quicker than anyone else

You would have to open all three boxes and remove all items from two.

[John Cuthber]

There are actually two solutions to that symmetry, but for there to be only one unique answer, both need to coexist.

 

"nails and screws"

"screws and nails"

That's two ways f writing one answer.

[AbstractDreamer]

That's two ways f writing one answer.

 

I prefer to see it as as one of way writing both answers.

If you just threw away the 3 boxes, we can deduce that "There would be no more boxes incorrectly labelled"

 

Although that would not be quite the same as saying that the remaining boxes are correctly labelled, as there is no specification about any desire to keep the contents of the boxes, the nature of the problem in having incorrectly labelled boxes is solved.

 

Therefore, throwing away the boxes is a valid solution.

 

The nature of the riddle DOES suggest a desire to find an optimal solution. Whether it is easier to throw away the boxes, or to re-label them is a probably something that can never be answered.