Diamond Among a Hundred Boxes

Suppose that the box that contains the diamond is between two boxes. Both boxes will have a truthful statement. It can't happens because there are only one truthful statement. So, the diamond must be in the leftmost box or in the rightmost box. You only need to open one of these two boxes. If the diamond is in the box you chose to open, then it is done. If the diamond isn't in the box you chose to open, then you can be sure that the diamond is in the other box in the end of the row of boxes.

Note that if the diamond is not on the edge of the line of boxes, then the boxes on the left and right of it would be telling the truth. However, this is impossible, as then two boxes would be telling the truth. So, the diamond must be on the edges. Check the leftmost edge. If it is there, then we have found the diamond. If it is not there, we know that the diamond must be in the other box. So, it takes $\boxed{1}$ check.

If the box containing the diamond has 2 neighbours, both those boxes tell the truth, which we were told cannot be. Open one of the endpoint boxes. If it is not in there, it must be in the other endpoint box.

As I was viewing this on my mobile, I didn't see the label, and assumed I could wiegh the boxes. Well it is pre-coffee time

Shake each box to find the one containing the diamond, open that one.

The wording of the question isn't very good, because regardless of what the boxes say or what the puzzle is or how the boxes are arranged, the MINIMUM number of boxes required to check is always 1. No matter how arbitrarily complex the puzzle is, if you happen to open the box with the diamond on your first attempt, then the answer is 1. I know this seems like a nitpick, but for this riddle in particular it's an interesting coincidence.

However, if the wording is changed to say "what is the MAXIMUM number of boxes REQUIRED to check," the answer for this particular riddle happens to be 1, but now we have to engage with the puzzle rather than taking the trivial solution.

There are 2 possible scenarious for the box with the diamond: it is either in one of the first/last boxes or somewhere in the middle.

If it was in a middle box, there would be two correct statements - the one on the right of the correct box and the one on the left. But there is only one correct statement.

Therefore the box with the diamond is either the first or the last one. In order to find out where is it exactly, we need to check only one of the two - if there is a diamond, this is the correct box, if it is empty, the diamond is in the box in the other end of the row.

That gives the correct answer 1.

I answered correctly BUT I have a problem with this problem since we are told that only one box tells the truth. Why then does the box with the diamond lie?

Open any box.

If it contains the diamond, the problem is solved.

It it does not contain the diamond, weigh the box. Then weigh the other boxes until you find one that weighs more than the open box. The heavier box contains the diamond.

In either case, the minimum number of boxes to open is one.

The box with diamonds must only be next to one other box as that one other box is the only one telling the truth. So the diamonds must be in one of the boxes at the ends. There are only 2 of these, so once you check one you will know which box has diamonds either by elimination or finding the diamonds directly.

Think when you found diamond at the first opportunity. It is the reason why the answer is "1"

There are 100 boxes of 0.01 chance of being selected. The probability of picking the one containing the diamond is also 0.01, since there is a chance of being selected 0 is out of it.
Let's assume now that a selection is made, then either it contains the diamond or it doesn't, if it does, then no need for a second selection, because now, the probability of picking a box containing a diamond would be 0.
All you need is to pick once

Labels may be D for having the diamond and N for not having the diamond. Two cases: the box with diamond is truthful or box with diamond is not truthful. In truthful case, all boxes have D label. It may require as many as 99 open boxes to find the diamond. In the case where the box with diamond is not truthful, there will be two boxes with N label, the box with the diamond and one of the other 99 boxes because there can be only one untruthful box(whoops I meant to say truthful here). All others will be labeled D. Open 1 of the N boxes to reveal where the diamond is. This represents the minimum case.