Another tricky math problem!?

It can be done:

1)Take out a single item from [box 3] labelled "nails and screws". if the item popped out is nail then we have:

a) [box 3] is labelled "nails and screws" which cannot be true according to problem

b) [box 3] must be either nails or screws

c) but we popped out nail

which would mean this box should be correctly labelled as "Nail"

2) Then the labels of the remaing two boxes need to be swapped. We get the correct labels.

#Repeat the same step if the 1 if the item taken out was "screw" and label that box with "screw"

Take something out of box 3. If it is a nail, then box 3 is actually the 'Nails' box; if it's a screw, then box 3 is the 'Screws' box (it can't be 'Nails and screws', as we know that box 3, like the others, is labeled incorrectly).

Let's suppose that box 3 is the Nails box. Then, box 3 is not the Screws box. Box 2 can't be the Screws box either, as it's labeled 'Screws', and we know it's labeled incorrectly. This means that box 1 has to be the Screws box, and so box 2 must be the Nails and Screws box (as this is the only one left).

If, instead, box 3 is the Screws box, then it's not the Nails box. Box 1 isn't the Nails box either, as we know it's labeled incorrectly. Therefore, box 2 must be the Nails box, and box 1 must be the Nails and Screws box (as this is the only one left).

Hope that helps!

This one is tricky!

I am purely guessing that you can not tell.

Picking a nail successfully from a box means either that you've picked from the nail box or the mixed box. Also, picking a screw means the same thing for the screws. Without any prior knowledge of the number or proportion of screws to nails in the mixed box, I believe you're totally in the dark.

You would need this mix information to apply Bayes' rule in the case of the mixed box. And you would still, think, have to apply Bayes' rule to all three boxes because you still don't have a definite fix on the contents of any box.

You would need, I think, to be able to make successive samplings from each box, with or without replacement, and know the number of items in each box to be able to solve this. For instance, if there were 200 nails and 100 screws in the mixed box and you drew 6 nails without replacement, (erroneous) probability of it's being the mixed box would be low but computable. But even if you drew them from the nails box you'd still never be able to know that with certainty.

Sorry I don't have a definitive answer for you.

From box 3.Since labels are wrong,if the item is nail,then box 3 is nails.Then box 2 is screws and nails and box 1 is screws.Otherwise if it is screws,then box 3 screws,box2 nails,box 1 nails and screws.

EDIT:FUUUUU JUST 21 SECONDS!SH*T!