Late in the game, Grigor will leave a "Personal Note" on his tablet titled, "Oh look, a problem you can't murder your way out of." Until you read that note, you can't touch the box.

How do I get into Grigor's tablet?

Once you read that note, come to the jewelry display and pick up the box. A puzzle that requires both math and sliders. Oh JOY. Read to the end of this hint for a step by step (which for once isn't too horribly difficult).

Before you start, click on the puzzle once to discover that it's actually two puzzles. The goal is to set the tiles so that when you close it up again, each set of two tiles that touch (one from each side) will add up to 7.

So, for example, if the tile in the upper right corner of the right panel is 3, the tile in the upper left corner of the left panel should be 4. Get it?

Here's the outlay you're looking for:

Gem Box Outlay

Personally I abominate slider puzzles, but this one isn't too hard; you can do it by moving just one tile on the left and concentrating on the tiles on the right. However, any way you do it that works is good.

Here's the step by step:

Gemstone Box Puzzle

What do I do with the thing in the box?