The booklet in the corner of the box is square, so it must take up the space of 1 or 4 or 9 or 16 -- and so on -- discs. The whole box, without the space for the booklet, would fit 100 discs, so the number of discs must be 100, less the square number taken up by the booklet.

If one twelfth (¹ /₁₂ ) are blue, then the total number of discs must be divisible by 12.