Daniel Erman did a guest video with the youtube series Numberphile about the Josephus problem. This was one of the first problems he encountered in high school where he didn't know how to approach a complex problem with a wide variability of inputs and solutions. He talks about an early mentor who encouraged him to spend time experimenting with the inputs and solutions to see if he could find a pattern. He explains the process to web viewers in a simple and accessible way, much like his early mentor did.
Check out his video here: https://youtu.be/uCsD3ZGzMgE
Daniel Erman is also the faculty advisor for the UW Math Circle (https://www.math.wisc.edu/wiki/index.php/Madison_Math_Circle), which is an outreach group dedicated to helping younger students interested in math learn more about the many exciting things you can discover by experimenting with numbers.