Pile of cards: 35 identical cards with a picture of
Koala throwing a boomerang on one side of each card.

13 of the cards are upside down.

While blindfolded (after being told the above), Lex
divides the cards into 2 piles, each pile having the
same number of upside down cards.

How d'heck did Lex accomplish that amazing feat?

Note:
-any 35 playing cards (from a deck of 52) could be used
-upside down means face up

Lex rips them all in half with the skill of a strongman!

Nay Sir Cue; Sir Lex is a liar, whoops, lawyer,
and performs the task legally...

1. Without damaging the cards in any way, Lex divides the
pile into two piles having 13 and 22 cards respectively.

2. Then with a grin on his face, Lex flips the pile with 13 cards
and declares, "Both piles now have the same number of upside
down cards."

Keerect CC!

I first saw this using 52 cards of which 10 were upside down.
Have a look:
http://mindyourdecisions.com/blog/2010/09/22/a-fun-card-puzzle/#.VCy2b-ktB9A

I had a look, but will have to try it to be convinced!

Meanwhile I liked this comment: “The existentialist’s solution: throw all the cards in the trash and make two piles of zero.”

Try a simpler one, like 15 cards, of which 4 are upside down...
See what happens due to turning over the pile of 4.