Which Box?

When she takes a donut from box 3, she has to be taking the only donuts box, because it is labeled, "both". This means the "Bagel" labeled box must be the bagel and donut box, and the "Donut" labeled box must be the only bagel box. BOX 2...

Box 3 is labeled "Both", but that's the wrong label (since "none of the labels is on the correct box"), so box 3 only contains one item. Since Lil' John took out a donut from box 3, that one item must be donut. Therefore, box 1 must have the label "Both" and box 2 have the label "Bagels".

The answer is box 2 .

None of the labels are correct

Therefore there are donuts, in some way or another, in Box 1

We also know that there are donuts in box 3

Thus, the lone bagels are in box 2

When Lil' John takes out a donut from box three, the correct label must be donuts because it certainly not bagels and the incorrect label was donuts and bagels. So box 1 and 2 must contain donuts and bagel and the other one should contain just bagels but box one was INCORRECTEDLY labeled bagels so box 1 must contain donuts and bagels. Therefore, box 2 must be containing bagels because that is the only label that is left.

Box 1 is labeled "Donuts" but we know the labels are incorrect, thus box 1 has either Bagels or Both. Similarly, box 3, by the fact that it contained a donut, must ALSO be either Bagels or Both. So only 2 is left for Donuts alone.

Let's start by looking at the three boxes:

Box 1 : $B$

Box 2 : $D$

Box 3 : $BD$

Since John picks out a Doughnut from Box 3 and all labels are wrong, Box 3 must contain only Doughnuts.

Now suppose we were to take the label from Box 2 and swap it with that of Box 3 . Box 1 cannot only contain Bagels and therefore must contain both Doughnuts and Bagels. This means that Box 2 contains only Doughnuts.

Since Lil' John takes a dount out of the 3rd box, than that means that the third box only has bagles, since it can't be bagles and dounts knowing that the box is misslabeled.

So the box with bagles is either 1 or 2, and since we know all the boxes are mislabeled,it can't be 1 either.

So, we are left with box 2.

There is enough explanation in this problem to solve and no need to report this problem. Pay attention people!

Box 3 contains donuts. This means it can’t have only bagels.

Box 3 is also labelled as having both bagels and donuts. We know it’s incorrectly labelled, so we eliminate this option as well.

Therefore, 3 has only donuts.

Box 1 is incorrectly labelled as having bagels, so it can’t have bagels. It also can’t have only donuts, since that’s 3.

That means that Box 1 has both bagels and donuts.

1 has both, 3 has only donuts, which leaves 2 with only bagels.