Logic & Deduction riddle: Everyone in a large group picks a number from 0 to 100. The winner is whoever is closest to two-thirds of the group average. What do you pick?

A server room has one bulb inside and three switches outside. Exactly one switch controls the bulb. The door is closed, and you may open it only once. How do you identify the right switch?

You have two lengths of fuse. Each burns for exactly one hour end to end, but neither burns evenly — half a fuse does not mean half an hour. With only a lighter, measure exactly forty-five minutes.

Eight identical servers sit in a rack. One has a faulty fan and runs measurably hotter; the rest are identical. You have a balance scale that compares the total heat of any two groups. Find the faulty one in two weighings.