Here's an assignment I had to do when I was 14 or 15, quite easy really:
Imagine a square with a width of L.
If you cut corners of the square you could fold the paper into a box without a lid. The corners you cut out must be square in shape and all be the same size. Their length is X.
How does X relate to L in order to get the maximum volume of the box?

I'l give an example to clarify, lets say the square paper is 5x5 cm. Lets cut out 1x1 cm squares out of each corner. The paper can now be folded into a box with a base of the dimensions 3x3 cm and a highe of 1 cm. This gives a volume of 3*3*1 = 9cm^3. Cutting out a different size could result in a bigger volume.

Now, in order to get the maximum volume, how does X relate to L?