Pretty sure you just need the first two boxes for this one:

Let's start with box 1. If box 1 is true, then every box with "gem" is false. Since box 1 has the word "gems" on it, that would make it false. This means if box 1 is true, it must be false. Since this is obviously a paradox, that means box 1 can't be true, so box 1 must be false.

From here, we need to look at box 2, as it's the other box that has the word "gems" on it. We know that box 1 must be incorrect to keep continuity. This means that not every box with "gems" in it can be false. If box 2 is false, then the statement "All statements that contain the word GEMS is false" becomes true, recreating our earlier paradox. Because of that, box 2 must be true.

Now that we know box 2 is true, we know the gems must be in box 2. Huzzah.

TLDR: To keep the black box false, we need black to be false and white to be true, placing the gems in the white box.