How does Ollivander distinguish wands by sight?

Throughout the series, Ollivander displays a particular skill at enumerating a wand's properties by only looking at it, even down to the wand core. Is there any mention of how he does this?

Some of the instances where Ollivander shows this skill is quite explainable but others are just...well...magical!

• Not exactly the skill I'm interested in but multiple times (Diagon Alley in PS, Weighing of Wands in GoF) Ollivander can easily recall the properties of the wand he sold to a particular witch or wizard. While unusual---it would seem that Ollivander has eidetic memory---it is not unheard of; some of our kind, fellow Muggles, can perform a similar feat.


• But in Weighing of Wands, he easily enumerates the properties of Fleur's wand by mere visual inspection. Like Krum, I would expect Fleur's wand is not one of Ollivander's. He even states that he wouldn't use Veela hair as core as they make for temperemental wands.

(FWIW, I'd understand that he easily recognized Krum's wand down to its maker; it makes business sense to study the product of your competitors.)

To complicate matters, there are way too many wand combinations. And remember that Ollivander enumerates wand properties down to wand core (something not automatically obvious by sight alone)!