Alex Y
You have a flashlight that requires two batteries. You have eight batteries, but know that only four of them are good. The only way of finding two good batteries is to try them two at a time until the light comes on.

What is the smallest number of battery pairs you can try in order to guarantee that you end up with a good pair in the flashlight?

P.S., if you could borrow a known-good battery, you could be assured of getting the light on with two of your batteries with at most 6 pairs tried. But we don't have that known-good battery; all you have to work with are the eight unknown batteries.