14.1. Discrete Mathematics

Try these first

1. 1.

   What is the arithmetic mean of 2 and 8?

   Hint

   Add the two numbers and divide by 2.

2. 2.

   Convert the number 5 to binary.

   Hint

   Think of it as sums of powers of 2.

3. 3.

   What does the arithmetic mean represent?

   • Average of numbers
   • Product of numbers
   • Difference of numbers

   Hint

   Think about how we calculate the average.

4. 4.

   The geometric mean of numbers is always ____ the arithmetic mean.

   • True
   • False

   Hint

   Remember the relationship between the two means.

5. 5.

   Show that there are 10 distinct powers of two that sum to the number 1023.

   Hint

   Start from the largest power of 2 that fits into 1023.

6. 6.

   In the context of the celebrity problem, explain how you would test for a celebrity among 5 guests with minimum queries.

   Hint

   Keep a tally of known relationships to eliminate non-celebrities.