How many Valentines are exchanged

1
How many Valentines are exchanged?

• On Valentines Day, there is a tradition of
  exchanging a Valentines Greeting with someone.
  Suppose you wanted to exchange Valentines with
  each person in the room. If all the students in
  the class exchanged Valentines with each other
  only once, how many total Valentines would be
  exchanged?

2
Texas Howdy

• At Texas AM, people are greeted with a warm
  smile, a friendly handshake, and a Howdy! If
  all the students in class shook hands with each
  other only once, how many handshakes would there
  be?

3
Which ball is heavier?

• Eight balls all look alike. One of them is
  heavier than the other seven, all of which weigh
  the same. Determine how you find the heavier
  ball if you can only use a balance scale two
  times.