**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?**Texas Howdy**At Texas A&M, 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?**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.