18.4.1. Restrictions on Solution Counts

Try these first

1. 1.

   Define a strictly increasing sequence.

   Hint

   Think of a series of numbers written in ascending order.

2. 2.

   What is a subsequence?

   Hint

   You can pick numbers from a list without following their order.

3. 3.

   What is a strictly increasing sequence?

   • A sequence where terms decrease
   • A sequence where terms increase
   • A random sequence

   Hint

   Focus on the direction of the numbers.

4. 4.

   True or False: A subsequence must consist of consecutive elements of the original sequence.

   • True
   • False

   Hint

   Subsequences maintain original order, but elements can be non-consecutive.

5. 5.

   Given a set of 15 distinct integers, demonstrate a subsequence of at least length 5 that is increasing or decreasing. Provide a strategic approach and reasoning.

   Hint

   Formulate pairs of subsequences and check overlaps.

6. 6.

   Analyze a sequence of floating-point numbers and determine a subsequence length of at least 6 that is strictly increasing. What is your reasoning?

   Hint

   Consider each pair and track where the values trend up.