Interesting Problem: Self-correcting Random Walks

Section 3 was added on October 11. Section 4 was added on October 19. A $2,000 award is offered to solve any of the open questions, click here for details. This is another off-the-beaten-path problem, one that you won't find in textbooks. You can solve it using data science methods (my approach) but the mathematician with some spare time could find an elegant solution.