## People Triangle: Like, Dislike

Six people who all know each other are in a room. Every two people either like each other or dislike each other. Show that there is a group of three people who either all like each other or all dislike each other.

## Defined Operations 2; Do Composition

If 3 h = 10, 7 h = 50, 5 h = 26; and 4 b = 1, 7 b = 2.5, 20 b = 9, then what is n
if n hb = 17.5?

## Salary = f(n students)

Many years ago a teacher’s salary was based on the number of students he had. Suppose a salary of \$60 per month was to be paid for 50 students and \$50 a month for 30 students. If the actual enrollment was 45 students, what should the teacher be paid?

## Defined Operation; Do Inverse

Suppose a linear operation �/� is defined so that:

5 / = 11;

8 / = 17;

12 / = 25.

What is n if n / = 35?

## Defined Operations 1; Do Composition

Suppose the operations “#” and “t” are defined so that:

6 # = 20; 2 # = 4; 10 # = 36; and 5 t = 4.5; 10 t = 7; 8 t = 6.

Then what is n if 3 # # t = n?

## Kite Strings

Buzz has three kite strings averaging 6600 feet in length. None is less than 6200 feet long. How long can the longest be?

## Pet Rocks

The town of Ware has exactly 5000 families. Every family has 0, 1, or 2 pet rocks. Every pet rock belongs to a family. Most families have 1 pet rock. Exactly half of the remaining families have 2 pet rocks. How many pet rocks are there in Ware?