Interview questions/riddlers

Ok guys. I have collected a few interview questions, in the form of riddlers, that I have encountered the past couple of years. So:

Question: Suppose we have 8 coins that look/smell/taste/roll exactly the same and a balance like the one in the picture. One of the coins is fake, it weights less than the rest. How can we find the fake coin with only two weightings.

Question: Suppose there is a rope of certain length and a lighter. How can someone find the exact midpoint of the rope?


Answers tomorrow as usual