17.1. Discrete Mathematics

Try these first

1. 1.

   What is the midpoint of the points (2, 4) and (6, 8)?

   Hint

   Use the midpoint formula, averaging x and y coordinates.

2. 2.

   How many pairs of numbers from 1 to 8 can add to 9?

   Hint

   List down numbers and see which pairs sum to 9.

3. 3.

   What is the midpoint of (4, 6) and (8, 10)?

   • (6
   • 8)
   • (12
   • 16)
   • (3
   • 5)

   Hint

   Use the formula M = ((x1 + x2) / 2, (y1 + y2) / 2).

4. 4.

   True or False: The Pigeonhole Principle states that if n items are put into m containers, with n > m, at least one container must be empty.

   • True
   • False

   Hint

   Think about how items distribute into containers.

5. 5.

   Create a set of 10 numbers all distinct, find a pair among them that sums to a given number using pigeonhole principle.

   Hint

   What number pairs in your set could equal the desired sum?

6. 6.

   Demonstrate with an example how the pigeonhole principle guarantees an outcome involves at least one integer midpoint.

   Hint

   Sum the coordinates and look for evenness.