If you open the cupboard above the foot locker, you'll find a whole wall full of crystals, blue, yellow, and grey. This is the crystal display Magnus referred to in the letter you found in Elisabet's purse.
If you took a picture of that letter as I suggested, it tells you that the goal here is to have four blue and four yellow crystals in each row and column, with no more than two of a color touching. Read to the end of this hint for the solution.
You don't have to move the crystals around; just click on them to cycle through the three possible colors (grey to yellow to blue and back to grey).
The colored crystals have a little outline around the box if they're in an acceptable array. If you add a piece that makes three in a row of one color, that outline disappears.
The numbers to the left and under the puzzle tell you how many of each color you have, first yellow and then blue. If it says "1/2," it means you've placed one yellow and two blue crystals, and the rest are grey.
The ideal number is 4/4, meaning 4 of each color. If it says 5/3, you've got a yellow where a blue should be.
On the first pass, go through and look for two in a row of one color (Grey -- Blue -- Blue -- Grey). This means you can place the other color on both ends.
Now look for a color, a grey, and the same color (Blue -- Grey -- Blue). The grey has to be the other color because if it were the same, you'd have three in a row of the same color.
Don't forget to check the columns as well. I find it easiest to do all the rows, then all the columns, then go back to the rows.
At this point, you can start checking the numbers. If you see one that's 4/3 or 3/4, or 4/2 or 2/4, you can fill in the empty spots instantly.
If you can't get the hang of this or just don't like it, here's the solution: