In a line of people you are looking for a subsequence of 4 (not necessarily consecutive = neighboring) people with increasing height. How many people should be in the line so that you can be sure to find this subsequence?
The answer is 8
We consider such a question: you want to make sure to find a subsequence of k people with increasing height, then at least n people should be on the line.
This shows how to find a subsequence with given characteristics.