Here's the systematic strategy we'll apply for solving problems:

1. State the problem clearly. Identify the input and ouput formats.
2. Come up with some example inputs and outputs. Try to cover all edge cases.
3. Come up with a correct solution for the problem. State it in plain English.
4. Implement the solution and test it using example inputs. Fix bugs, if any.
5. Analyze the algorithm's complexity and identify inefficiencies, if any.
6. Apply the right technique to overcome the inefficiency. Repeat steps 3 to 6.