What am I supposed to do with the books?

What am I supposed to do in the area where theres 4 doors, Door Synchro Facility?

Just stopped playing the game because of this and cant find a guide.

A friend of mine found the solution to the Doors puzzle... something about doing them in a order depending how long it takes them to close.

This game's puzzles are so poorly designed it boggles my mind how they kept them in for so long. This one was pulled right out of some developer's ass. Never before have you had to do something similar to this, never after that.
It comes from nowhere, there is no explanation about it, and you are supposed to just figure it out.
Well, that or find the solution online.
I am yet to find a person who has not been stuck on this.