How is the damage you receive computed when you have armor and the opponent has armor penetration (flat and %)?

A fictional example:
I have 1000 hp and 100 armor.
My opponent has 80 attack damage, 20 armor penetration, and 10% armor penetration.

1. How much hp do I have left after one hit?
2. How is this exactly computed?
3. Are the computations for magic resist and magic penetration the same?
4. What happens when the armor is negative (When using the Black Cleaver with Corki the armor of the opponent can get a negative value)?

I'll brake the formula for you =)

A fictional example:
I have 1000 hp and 100 armor.
My opponent has 80 attack damage, 20 armor penetration, and 10% armor penetration.

1. Flat pen is applied first. Your armor goes down by 20. You have 100-20=80 armor left.
2. % pen is applied second. Your armor goes down by 10%80=8. You have 80-8 = 72 armor left.

72 armor increases your effective hp by 72%. This means that your oponent would need to do 1720 damage to kill you. You can find the % from here. 1720* X% = 1000

72 armor provides 42% damage reduction.

He hits you for 80, you take 80*58% = 46,5 damage.


Works exactly the same way for magic resistence/penetration.

If the armor is negative, it is calculated by the same formula, but instead it amplifies the damage (in place of reducing it).

There is slightly more to this, as there is also armor/magicresist reduction. Things like Ryze's spell flux for example provide a debuff that reduces magic resist of the champion.

This happens first, and can push armor/MR into the negatives.
penetration will never push armor/MR below zero.

This is why when you play a champ like amumu, who's physical attacks reduce MR by something like 20/30/40 (based upon champion level) for a short period of time (maybe 3-5 seconds), magic penetration isn't useful if your enemy champion has no MR items.
This is because his MR will already be at or below zero.
the same thing applies to armor

order:
Armor reduction
flat penetration
% penetration

Thanks for the explanation, now I can make a good decision in what runes, masteries and items to get before and during a game.